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diff --git a/elm-stuff/0.19.1/lock b/elm-stuff/0.19.1/lock
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diff --git a/elm-stuff/0.19.1/o.dat b/elm-stuff/0.19.1/o.dat
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diff --git a/elm.json b/elm.json
new file mode 100644
index 0000000..70e6ec9
--- /dev/null
+++ b/elm.json
@@ -0,0 +1,25 @@
+{
+    "type": "application",
+    "source-directories": [
+        "src"
+    ],
+    "elm-version": "0.19.1",
+    "dependencies": {
+        "direct": {
+            "elm/browser": "1.0.2",
+            "elm/core": "1.0.5",
+            "elm/html": "1.0.0",
+            "elm/parser": "1.1.0"
+        },
+        "indirect": {
+            "elm/json": "1.1.3",
+            "elm/time": "1.0.0",
+            "elm/url": "1.0.0",
+            "elm/virtual-dom": "1.0.2"
+        }
+    },
+    "test-dependencies": {
+        "direct": {},
+        "indirect": {}
+    }
+}
diff --git a/index.html b/index.html
new file mode 100644
index 0000000..ba8a4dc
--- /dev/null
+++ b/index.html
@@ -0,0 +1,5265 @@
+<!DOCTYPE HTML>
+<html>
+<head>
+  <meta charset="UTF-8">
+  <title>Main</title>
+  <style>body { padding: 0; margin: 0; }</style>
+</head>
+
+<body>
+
+<pre id="elm"></pre>
+
+<script>
+try {
+(function(scope){
+'use strict';
+
+function F(arity, fun, wrapper) {
+  wrapper.a = arity;
+  wrapper.f = fun;
+  return wrapper;
+}
+
+function F2(fun) {
+  return F(2, fun, function(a) { return function(b) { return fun(a,b); }; })
+}
+function F3(fun) {
+  return F(3, fun, function(a) {
+    return function(b) { return function(c) { return fun(a, b, c); }; };
+  });
+}
+function F4(fun) {
+  return F(4, fun, function(a) { return function(b) { return function(c) {
+    return function(d) { return fun(a, b, c, d); }; }; };
+  });
+}
+function F5(fun) {
+  return F(5, fun, function(a) { return function(b) { return function(c) {
+    return function(d) { return function(e) { return fun(a, b, c, d, e); }; }; }; };
+  });
+}
+function F6(fun) {
+  return F(6, fun, function(a) { return function(b) { return function(c) {
+    return function(d) { return function(e) { return function(f) {
+    return fun(a, b, c, d, e, f); }; }; }; }; };
+  });
+}
+function F7(fun) {
+  return F(7, fun, function(a) { return function(b) { return function(c) {
+    return function(d) { return function(e) { return function(f) {
+    return function(g) { return fun(a, b, c, d, e, f, g); }; }; }; }; }; };
+  });
+}
+function F8(fun) {
+  return F(8, fun, function(a) { return function(b) { return function(c) {
+    return function(d) { return function(e) { return function(f) {
+    return function(g) { return function(h) {
+    return fun(a, b, c, d, e, f, g, h); }; }; }; }; }; }; };
+  });
+}
+function F9(fun) {
+  return F(9, fun, function(a) { return function(b) { return function(c) {
+    return function(d) { return function(e) { return function(f) {
+    return function(g) { return function(h) { return function(i) {
+    return fun(a, b, c, d, e, f, g, h, i); }; }; }; }; }; }; }; };
+  });
+}
+
+function A2(fun, a, b) {
+  return fun.a === 2 ? fun.f(a, b) : fun(a)(b);
+}
+function A3(fun, a, b, c) {
+  return fun.a === 3 ? fun.f(a, b, c) : fun(a)(b)(c);
+}
+function A4(fun, a, b, c, d) {
+  return fun.a === 4 ? fun.f(a, b, c, d) : fun(a)(b)(c)(d);
+}
+function A5(fun, a, b, c, d, e) {
+  return fun.a === 5 ? fun.f(a, b, c, d, e) : fun(a)(b)(c)(d)(e);
+}
+function A6(fun, a, b, c, d, e, f) {
+  return fun.a === 6 ? fun.f(a, b, c, d, e, f) : fun(a)(b)(c)(d)(e)(f);
+}
+function A7(fun, a, b, c, d, e, f, g) {
+  return fun.a === 7 ? fun.f(a, b, c, d, e, f, g) : fun(a)(b)(c)(d)(e)(f)(g);
+}
+function A8(fun, a, b, c, d, e, f, g, h) {
+  return fun.a === 8 ? fun.f(a, b, c, d, e, f, g, h) : fun(a)(b)(c)(d)(e)(f)(g)(h);
+}
+function A9(fun, a, b, c, d, e, f, g, h, i) {
+  return fun.a === 9 ? fun.f(a, b, c, d, e, f, g, h, i) : fun(a)(b)(c)(d)(e)(f)(g)(h)(i);
+}
+
+
+
+
+// EQUALITY
+
+function _Utils_eq(x, y)
+{
+	for (
+		var pair, stack = [], isEqual = _Utils_eqHelp(x, y, 0, stack);
+		isEqual && (pair = stack.pop());
+		isEqual = _Utils_eqHelp(pair.a, pair.b, 0, stack)
+		)
+	{}
+
+	return isEqual;
+}
+
+function _Utils_eqHelp(x, y, depth, stack)
+{
+	if (x === y)
+	{
+		return true;
+	}
+
+	if (typeof x !== 'object' || x === null || y === null)
+	{
+		typeof x === 'function' && _Debug_crash(5);
+		return false;
+	}
+
+	if (depth > 100)
+	{
+		stack.push(_Utils_Tuple2(x,y));
+		return true;
+	}
+
+	/**_UNUSED/
+	if (x.$ === 'Set_elm_builtin')
+	{
+		x = $elm$core$Set$toList(x);
+		y = $elm$core$Set$toList(y);
+	}
+	if (x.$ === 'RBNode_elm_builtin' || x.$ === 'RBEmpty_elm_builtin')
+	{
+		x = $elm$core$Dict$toList(x);
+		y = $elm$core$Dict$toList(y);
+	}
+	//*/
+
+	/**/
+	if (x.$ < 0)
+	{
+		x = $elm$core$Dict$toList(x);
+		y = $elm$core$Dict$toList(y);
+	}
+	//*/
+
+	for (var key in x)
+	{
+		if (!_Utils_eqHelp(x[key], y[key], depth + 1, stack))
+		{
+			return false;
+		}
+	}
+	return true;
+}
+
+var _Utils_equal = F2(_Utils_eq);
+var _Utils_notEqual = F2(function(a, b) { return !_Utils_eq(a,b); });
+
+
+
+// COMPARISONS
+
+// Code in Generate/JavaScript.hs, Basics.js, and List.js depends on
+// the particular integer values assigned to LT, EQ, and GT.
+
+function _Utils_cmp(x, y, ord)
+{
+	if (typeof x !== 'object')
+	{
+		return x === y ? /*EQ*/ 0 : x < y ? /*LT*/ -1 : /*GT*/ 1;
+	}
+
+	/**_UNUSED/
+	if (x instanceof String)
+	{
+		var a = x.valueOf();
+		var b = y.valueOf();
+		return a === b ? 0 : a < b ? -1 : 1;
+	}
+	//*/
+
+	/**/
+	if (typeof x.$ === 'undefined')
+	//*/
+	/**_UNUSED/
+	if (x.$[0] === '#')
+	//*/
+	{
+		return (ord = _Utils_cmp(x.a, y.a))
+			? ord
+			: (ord = _Utils_cmp(x.b, y.b))
+				? ord
+				: _Utils_cmp(x.c, y.c);
+	}
+
+	// traverse conses until end of a list or a mismatch
+	for (; x.b && y.b && !(ord = _Utils_cmp(x.a, y.a)); x = x.b, y = y.b) {} // WHILE_CONSES
+	return ord || (x.b ? /*GT*/ 1 : y.b ? /*LT*/ -1 : /*EQ*/ 0);
+}
+
+var _Utils_lt = F2(function(a, b) { return _Utils_cmp(a, b) < 0; });
+var _Utils_le = F2(function(a, b) { return _Utils_cmp(a, b) < 1; });
+var _Utils_gt = F2(function(a, b) { return _Utils_cmp(a, b) > 0; });
+var _Utils_ge = F2(function(a, b) { return _Utils_cmp(a, b) >= 0; });
+
+var _Utils_compare = F2(function(x, y)
+{
+	var n = _Utils_cmp(x, y);
+	return n < 0 ? $elm$core$Basics$LT : n ? $elm$core$Basics$GT : $elm$core$Basics$EQ;
+});
+
+
+// COMMON VALUES
+
+var _Utils_Tuple0 = 0;
+var _Utils_Tuple0_UNUSED = { $: '#0' };
+
+function _Utils_Tuple2(a, b) { return { a: a, b: b }; }
+function _Utils_Tuple2_UNUSED(a, b) { return { $: '#2', a: a, b: b }; }
+
+function _Utils_Tuple3(a, b, c) { return { a: a, b: b, c: c }; }
+function _Utils_Tuple3_UNUSED(a, b, c) { return { $: '#3', a: a, b: b, c: c }; }
+
+function _Utils_chr(c) { return c; }
+function _Utils_chr_UNUSED(c) { return new String(c); }
+
+
+// RECORDS
+
+function _Utils_update(oldRecord, updatedFields)
+{
+	var newRecord = {};
+
+	for (var key in oldRecord)
+	{
+		newRecord[key] = oldRecord[key];
+	}
+
+	for (var key in updatedFields)
+	{
+		newRecord[key] = updatedFields[key];
+	}
+
+	return newRecord;
+}
+
+
+// APPEND
+
+var _Utils_append = F2(_Utils_ap);
+
+function _Utils_ap(xs, ys)
+{
+	// append Strings
+	if (typeof xs === 'string')
+	{
+		return xs + ys;
+	}
+
+	// append Lists
+	if (!xs.b)
+	{
+		return ys;
+	}
+	var root = _List_Cons(xs.a, ys);
+	xs = xs.b
+	for (var curr = root; xs.b; xs = xs.b) // WHILE_CONS
+	{
+		curr = curr.b = _List_Cons(xs.a, ys);
+	}
+	return root;
+}
+
+
+
+var _List_Nil = { $: 0 };
+var _List_Nil_UNUSED = { $: '[]' };
+
+function _List_Cons(hd, tl) { return { $: 1, a: hd, b: tl }; }
+function _List_Cons_UNUSED(hd, tl) { return { $: '::', a: hd, b: tl }; }
+
+
+var _List_cons = F2(_List_Cons);
+
+function _List_fromArray(arr)
+{
+	var out = _List_Nil;
+	for (var i = arr.length; i--; )
+	{
+		out = _List_Cons(arr[i], out);
+	}
+	return out;
+}
+
+function _List_toArray(xs)
+{
+	for (var out = []; xs.b; xs = xs.b) // WHILE_CONS
+	{
+		out.push(xs.a);
+	}
+	return out;
+}
+
+var _List_map2 = F3(function(f, xs, ys)
+{
+	for (var arr = []; xs.b && ys.b; xs = xs.b, ys = ys.b) // WHILE_CONSES
+	{
+		arr.push(A2(f, xs.a, ys.a));
+	}
+	return _List_fromArray(arr);
+});
+
+var _List_map3 = F4(function(f, xs, ys, zs)
+{
+	for (var arr = []; xs.b && ys.b && zs.b; xs = xs.b, ys = ys.b, zs = zs.b) // WHILE_CONSES
+	{
+		arr.push(A3(f, xs.a, ys.a, zs.a));
+	}
+	return _List_fromArray(arr);
+});
+
+var _List_map4 = F5(function(f, ws, xs, ys, zs)
+{
+	for (var arr = []; ws.b && xs.b && ys.b && zs.b; ws = ws.b, xs = xs.b, ys = ys.b, zs = zs.b) // WHILE_CONSES
+	{
+		arr.push(A4(f, ws.a, xs.a, ys.a, zs.a));
+	}
+	return _List_fromArray(arr);
+});
+
+var _List_map5 = F6(function(f, vs, ws, xs, ys, zs)
+{
+	for (var arr = []; vs.b && ws.b && xs.b && ys.b && zs.b; vs = vs.b, ws = ws.b, xs = xs.b, ys = ys.b, zs = zs.b) // WHILE_CONSES
+	{
+		arr.push(A5(f, vs.a, ws.a, xs.a, ys.a, zs.a));
+	}
+	return _List_fromArray(arr);
+});
+
+var _List_sortBy = F2(function(f, xs)
+{
+	return _List_fromArray(_List_toArray(xs).sort(function(a, b) {
+		return _Utils_cmp(f(a), f(b));
+	}));
+});
+
+var _List_sortWith = F2(function(f, xs)
+{
+	return _List_fromArray(_List_toArray(xs).sort(function(a, b) {
+		var ord = A2(f, a, b);
+		return ord === $elm$core$Basics$EQ ? 0 : ord === $elm$core$Basics$LT ? -1 : 1;
+	}));
+});
+
+
+
+var _JsArray_empty = [];
+
+function _JsArray_singleton(value)
+{
+    return [value];
+}
+
+function _JsArray_length(array)
+{
+    return array.length;
+}
+
+var _JsArray_initialize = F3(function(size, offset, func)
+{
+    var result = new Array(size);
+
+    for (var i = 0; i < size; i++)
+    {
+        result[i] = func(offset + i);
+    }
+
+    return result;
+});
+
+var _JsArray_initializeFromList = F2(function (max, ls)
+{
+    var result = new Array(max);
+
+    for (var i = 0; i < max && ls.b; i++)
+    {
+        result[i] = ls.a;
+        ls = ls.b;
+    }
+
+    result.length = i;
+    return _Utils_Tuple2(result, ls);
+});
+
+var _JsArray_unsafeGet = F2(function(index, array)
+{
+    return array[index];
+});
+
+var _JsArray_unsafeSet = F3(function(index, value, array)
+{
+    var length = array.length;
+    var result = new Array(length);
+
+    for (var i = 0; i < length; i++)
+    {
+        result[i] = array[i];
+    }
+
+    result[index] = value;
+    return result;
+});
+
+var _JsArray_push = F2(function(value, array)
+{
+    var length = array.length;
+    var result = new Array(length + 1);
+
+    for (var i = 0; i < length; i++)
+    {
+        result[i] = array[i];
+    }
+
+    result[length] = value;
+    return result;
+});
+
+var _JsArray_foldl = F3(function(func, acc, array)
+{
+    var length = array.length;
+
+    for (var i = 0; i < length; i++)
+    {
+        acc = A2(func, array[i], acc);
+    }
+
+    return acc;
+});
+
+var _JsArray_foldr = F3(function(func, acc, array)
+{
+    for (var i = array.length - 1; i >= 0; i--)
+    {
+        acc = A2(func, array[i], acc);
+    }
+
+    return acc;
+});
+
+var _JsArray_map = F2(function(func, array)
+{
+    var length = array.length;
+    var result = new Array(length);
+
+    for (var i = 0; i < length; i++)
+    {
+        result[i] = func(array[i]);
+    }
+
+    return result;
+});
+
+var _JsArray_indexedMap = F3(function(func, offset, array)
+{
+    var length = array.length;
+    var result = new Array(length);
+
+    for (var i = 0; i < length; i++)
+    {
+        result[i] = A2(func, offset + i, array[i]);
+    }
+
+    return result;
+});
+
+var _JsArray_slice = F3(function(from, to, array)
+{
+    return array.slice(from, to);
+});
+
+var _JsArray_appendN = F3(function(n, dest, source)
+{
+    var destLen = dest.length;
+    var itemsToCopy = n - destLen;
+
+    if (itemsToCopy > source.length)
+    {
+        itemsToCopy = source.length;
+    }
+
+    var size = destLen + itemsToCopy;
+    var result = new Array(size);
+
+    for (var i = 0; i < destLen; i++)
+    {
+        result[i] = dest[i];
+    }
+
+    for (var i = 0; i < itemsToCopy; i++)
+    {
+        result[i + destLen] = source[i];
+    }
+
+    return result;
+});
+
+
+
+// LOG
+
+var _Debug_log = F2(function(tag, value)
+{
+	return value;
+});
+
+var _Debug_log_UNUSED = F2(function(tag, value)
+{
+	console.log(tag + ': ' + _Debug_toString(value));
+	return value;
+});
+
+
+// TODOS
+
+function _Debug_todo(moduleName, region)
+{
+	return function(message) {
+		_Debug_crash(8, moduleName, region, message);
+	};
+}
+
+function _Debug_todoCase(moduleName, region, value)
+{
+	return function(message) {
+		_Debug_crash(9, moduleName, region, value, message);
+	};
+}
+
+
+// TO STRING
+
+function _Debug_toString(value)
+{
+	return '<internals>';
+}
+
+function _Debug_toString_UNUSED(value)
+{
+	return _Debug_toAnsiString(false, value);
+}
+
+function _Debug_toAnsiString(ansi, value)
+{
+	if (typeof value === 'function')
+	{
+		return _Debug_internalColor(ansi, '<function>');
+	}
+
+	if (typeof value === 'boolean')
+	{
+		return _Debug_ctorColor(ansi, value ? 'True' : 'False');
+	}
+
+	if (typeof value === 'number')
+	{
+		return _Debug_numberColor(ansi, value + '');
+	}
+
+	if (value instanceof String)
+	{
+		return _Debug_charColor(ansi, "'" + _Debug_addSlashes(value, true) + "'");
+	}
+
+	if (typeof value === 'string')
+	{
+		return _Debug_stringColor(ansi, '"' + _Debug_addSlashes(value, false) + '"');
+	}
+
+	if (typeof value === 'object' && '$' in value)
+	{
+		var tag = value.$;
+
+		if (typeof tag === 'number')
+		{
+			return _Debug_internalColor(ansi, '<internals>');
+		}
+
+		if (tag[0] === '#')
+		{
+			var output = [];
+			for (var k in value)
+			{
+				if (k === '$') continue;
+				output.push(_Debug_toAnsiString(ansi, value[k]));
+			}
+			return '(' + output.join(',') + ')';
+		}
+
+		if (tag === 'Set_elm_builtin')
+		{
+			return _Debug_ctorColor(ansi, 'Set')
+				+ _Debug_fadeColor(ansi, '.fromList') + ' '
+				+ _Debug_toAnsiString(ansi, $elm$core$Set$toList(value));
+		}
+
+		if (tag === 'RBNode_elm_builtin' || tag === 'RBEmpty_elm_builtin')
+		{
+			return _Debug_ctorColor(ansi, 'Dict')
+				+ _Debug_fadeColor(ansi, '.fromList') + ' '
+				+ _Debug_toAnsiString(ansi, $elm$core$Dict$toList(value));
+		}
+
+		if (tag === 'Array_elm_builtin')
+		{
+			return _Debug_ctorColor(ansi, 'Array')
+				+ _Debug_fadeColor(ansi, '.fromList') + ' '
+				+ _Debug_toAnsiString(ansi, $elm$core$Array$toList(value));
+		}
+
+		if (tag === '::' || tag === '[]')
+		{
+			var output = '[';
+
+			value.b && (output += _Debug_toAnsiString(ansi, value.a), value = value.b)
+
+			for (; value.b; value = value.b) // WHILE_CONS
+			{
+				output += ',' + _Debug_toAnsiString(ansi, value.a);
+			}
+			return output + ']';
+		}
+
+		var output = '';
+		for (var i in value)
+		{
+			if (i === '$') continue;
+			var str = _Debug_toAnsiString(ansi, value[i]);
+			var c0 = str[0];
+			var parenless = c0 === '{' || c0 === '(' || c0 === '[' || c0 === '<' || c0 === '"' || str.indexOf(' ') < 0;
+			output += ' ' + (parenless ? str : '(' + str + ')');
+		}
+		return _Debug_ctorColor(ansi, tag) + output;
+	}
+
+	if (typeof DataView === 'function' && value instanceof DataView)
+	{
+		return _Debug_stringColor(ansi, '<' + value.byteLength + ' bytes>');
+	}
+
+	if (typeof File !== 'undefined' && value instanceof File)
+	{
+		return _Debug_internalColor(ansi, '<' + value.name + '>');
+	}
+
+	if (typeof value === 'object')
+	{
+		var output = [];
+		for (var key in value)
+		{
+			var field = key[0] === '_' ? key.slice(1) : key;
+			output.push(_Debug_fadeColor(ansi, field) + ' = ' + _Debug_toAnsiString(ansi, value[key]));
+		}
+		if (output.length === 0)
+		{
+			return '{}';
+		}
+		return '{ ' + output.join(', ') + ' }';
+	}
+
+	return _Debug_internalColor(ansi, '<internals>');
+}
+
+function _Debug_addSlashes(str, isChar)
+{
+	var s = str
+		.replace(/\\/g, '\\\\')
+		.replace(/\n/g, '\\n')
+		.replace(/\t/g, '\\t')
+		.replace(/\r/g, '\\r')
+		.replace(/\v/g, '\\v')
+		.replace(/\0/g, '\\0');
+
+	if (isChar)
+	{
+		return s.replace(/\'/g, '\\\'');
+	}
+	else
+	{
+		return s.replace(/\"/g, '\\"');
+	}
+}
+
+function _Debug_ctorColor(ansi, string)
+{
+	return ansi ? '\x1b[96m' + string + '\x1b[0m' : string;
+}
+
+function _Debug_numberColor(ansi, string)
+{
+	return ansi ? '\x1b[95m' + string + '\x1b[0m' : string;
+}
+
+function _Debug_stringColor(ansi, string)
+{
+	return ansi ? '\x1b[93m' + string + '\x1b[0m' : string;
+}
+
+function _Debug_charColor(ansi, string)
+{
+	return ansi ? '\x1b[92m' + string + '\x1b[0m' : string;
+}
+
+function _Debug_fadeColor(ansi, string)
+{
+	return ansi ? '\x1b[37m' + string + '\x1b[0m' : string;
+}
+
+function _Debug_internalColor(ansi, string)
+{
+	return ansi ? '\x1b[36m' + string + '\x1b[0m' : string;
+}
+
+function _Debug_toHexDigit(n)
+{
+	return String.fromCharCode(n < 10 ? 48 + n : 55 + n);
+}
+
+
+// CRASH
+
+
+function _Debug_crash(identifier)
+{
+	throw new Error('https://github.com/elm/core/blob/1.0.0/hints/' + identifier + '.md');
+}
+
+
+function _Debug_crash_UNUSED(identifier, fact1, fact2, fact3, fact4)
+{
+	switch(identifier)
+	{
+		case 0:
+			throw new Error('What node should I take over? In JavaScript I need something like:\n\n    Elm.Main.init({\n        node: document.getElementById("elm-node")\n    })\n\nYou need to do this with any Browser.sandbox or Browser.element program.');
+
+		case 1:
+			throw new Error('Browser.application programs cannot handle URLs like this:\n\n    ' + document.location.href + '\n\nWhat is the root? The root of your file system? Try looking at this program with `elm reactor` or some other server.');
+
+		case 2:
+			var jsonErrorString = fact1;
+			throw new Error('Problem with the flags given to your Elm program on initialization.\n\n' + jsonErrorString);
+
+		case 3:
+			var portName = fact1;
+			throw new Error('There can only be one port named `' + portName + '`, but your program has multiple.');
+
+		case 4:
+			var portName = fact1;
+			var problem = fact2;
+			throw new Error('Trying to send an unexpected type of value through port `' + portName + '`:\n' + problem);
+
+		case 5:
+			throw new Error('Trying to use `(==)` on functions.\nThere is no way to know if functions are "the same" in the Elm sense.\nRead more about this at https://package.elm-lang.org/packages/elm/core/latest/Basics#== which describes why it is this way and what the better version will look like.');
+
+		case 6:
+			var moduleName = fact1;
+			throw new Error('Your page is loading multiple Elm scripts with a module named ' + moduleName + '. Maybe a duplicate script is getting loaded accidentally? If not, rename one of them so I know which is which!');
+
+		case 8:
+			var moduleName = fact1;
+			var region = fact2;
+			var message = fact3;
+			throw new Error('TODO in module `' + moduleName + '` ' + _Debug_regionToString(region) + '\n\n' + message);
+
+		case 9:
+			var moduleName = fact1;
+			var region = fact2;
+			var value = fact3;
+			var message = fact4;
+			throw new Error(
+				'TODO in module `' + moduleName + '` from the `case` expression '
+				+ _Debug_regionToString(region) + '\n\nIt received the following value:\n\n    '
+				+ _Debug_toString(value).replace('\n', '\n    ')
+				+ '\n\nBut the branch that handles it says:\n\n    ' + message.replace('\n', '\n    ')
+			);
+
+		case 10:
+			throw new Error('Bug in https://github.com/elm/virtual-dom/issues');
+
+		case 11:
+			throw new Error('Cannot perform mod 0. Division by zero error.');
+	}
+}
+
+function _Debug_regionToString(region)
+{
+	if (region.I.z === region.N.z)
+	{
+		return 'on line ' + region.I.z;
+	}
+	return 'on lines ' + region.I.z + ' through ' + region.N.z;
+}
+
+
+
+// MATH
+
+var _Basics_add = F2(function(a, b) { return a + b; });
+var _Basics_sub = F2(function(a, b) { return a - b; });
+var _Basics_mul = F2(function(a, b) { return a * b; });
+var _Basics_fdiv = F2(function(a, b) { return a / b; });
+var _Basics_idiv = F2(function(a, b) { return (a / b) | 0; });
+var _Basics_pow = F2(Math.pow);
+
+var _Basics_remainderBy = F2(function(b, a) { return a % b; });
+
+// https://www.microsoft.com/en-us/research/wp-content/uploads/2016/02/divmodnote-letter.pdf
+var _Basics_modBy = F2(function(modulus, x)
+{
+	var answer = x % modulus;
+	return modulus === 0
+		? _Debug_crash(11)
+		:
+	((answer > 0 && modulus < 0) || (answer < 0 && modulus > 0))
+		? answer + modulus
+		: answer;
+});
+
+
+// TRIGONOMETRY
+
+var _Basics_pi = Math.PI;
+var _Basics_e = Math.E;
+var _Basics_cos = Math.cos;
+var _Basics_sin = Math.sin;
+var _Basics_tan = Math.tan;
+var _Basics_acos = Math.acos;
+var _Basics_asin = Math.asin;
+var _Basics_atan = Math.atan;
+var _Basics_atan2 = F2(Math.atan2);
+
+
+// MORE MATH
+
+function _Basics_toFloat(x) { return x; }
+function _Basics_truncate(n) { return n | 0; }
+function _Basics_isInfinite(n) { return n === Infinity || n === -Infinity; }
+
+var _Basics_ceiling = Math.ceil;
+var _Basics_floor = Math.floor;
+var _Basics_round = Math.round;
+var _Basics_sqrt = Math.sqrt;
+var _Basics_log = Math.log;
+var _Basics_isNaN = isNaN;
+
+
+// BOOLEANS
+
+function _Basics_not(bool) { return !bool; }
+var _Basics_and = F2(function(a, b) { return a && b; });
+var _Basics_or  = F2(function(a, b) { return a || b; });
+var _Basics_xor = F2(function(a, b) { return a !== b; });
+
+
+
+var _String_cons = F2(function(chr, str)
+{
+	return chr + str;
+});
+
+function _String_uncons(string)
+{
+	var word = string.charCodeAt(0);
+	return !isNaN(word)
+		? $elm$core$Maybe$Just(
+			0xD800 <= word && word <= 0xDBFF
+				? _Utils_Tuple2(_Utils_chr(string[0] + string[1]), string.slice(2))
+				: _Utils_Tuple2(_Utils_chr(string[0]), string.slice(1))
+		)
+		: $elm$core$Maybe$Nothing;
+}
+
+var _String_append = F2(function(a, b)
+{
+	return a + b;
+});
+
+function _String_length(str)
+{
+	return str.length;
+}
+
+var _String_map = F2(function(func, string)
+{
+	var len = string.length;
+	var array = new Array(len);
+	var i = 0;
+	while (i < len)
+	{
+		var word = string.charCodeAt(i);
+		if (0xD800 <= word && word <= 0xDBFF)
+		{
+			array[i] = func(_Utils_chr(string[i] + string[i+1]));
+			i += 2;
+			continue;
+		}
+		array[i] = func(_Utils_chr(string[i]));
+		i++;
+	}
+	return array.join('');
+});
+
+var _String_filter = F2(function(isGood, str)
+{
+	var arr = [];
+	var len = str.length;
+	var i = 0;
+	while (i < len)
+	{
+		var char = str[i];
+		var word = str.charCodeAt(i);
+		i++;
+		if (0xD800 <= word && word <= 0xDBFF)
+		{
+			char += str[i];
+			i++;
+		}
+
+		if (isGood(_Utils_chr(char)))
+		{
+			arr.push(char);
+		}
+	}
+	return arr.join('');
+});
+
+function _String_reverse(str)
+{
+	var len = str.length;
+	var arr = new Array(len);
+	var i = 0;
+	while (i < len)
+	{
+		var word = str.charCodeAt(i);
+		if (0xD800 <= word && word <= 0xDBFF)
+		{
+			arr[len - i] = str[i + 1];
+			i++;
+			arr[len - i] = str[i - 1];
+			i++;
+		}
+		else
+		{
+			arr[len - i] = str[i];
+			i++;
+		}
+	}
+	return arr.join('');
+}
+
+var _String_foldl = F3(function(func, state, string)
+{
+	var len = string.length;
+	var i = 0;
+	while (i < len)
+	{
+		var char = string[i];
+		var word = string.charCodeAt(i);
+		i++;
+		if (0xD800 <= word && word <= 0xDBFF)
+		{
+			char += string[i];
+			i++;
+		}
+		state = A2(func, _Utils_chr(char), state);
+	}
+	return state;
+});
+
+var _String_foldr = F3(function(func, state, string)
+{
+	var i = string.length;
+	while (i--)
+	{
+		var char = string[i];
+		var word = string.charCodeAt(i);
+		if (0xDC00 <= word && word <= 0xDFFF)
+		{
+			i--;
+			char = string[i] + char;
+		}
+		state = A2(func, _Utils_chr(char), state);
+	}
+	return state;
+});
+
+var _String_split = F2(function(sep, str)
+{
+	return str.split(sep);
+});
+
+var _String_join = F2(function(sep, strs)
+{
+	return strs.join(sep);
+});
+
+var _String_slice = F3(function(start, end, str) {
+	return str.slice(start, end);
+});
+
+function _String_trim(str)
+{
+	return str.trim();
+}
+
+function _String_trimLeft(str)
+{
+	return str.replace(/^\s+/, '');
+}
+
+function _String_trimRight(str)
+{
+	return str.replace(/\s+$/, '');
+}
+
+function _String_words(str)
+{
+	return _List_fromArray(str.trim().split(/\s+/g));
+}
+
+function _String_lines(str)
+{
+	return _List_fromArray(str.split(/\r\n|\r|\n/g));
+}
+
+function _String_toUpper(str)
+{
+	return str.toUpperCase();
+}
+
+function _String_toLower(str)
+{
+	return str.toLowerCase();
+}
+
+var _String_any = F2(function(isGood, string)
+{
+	var i = string.length;
+	while (i--)
+	{
+		var char = string[i];
+		var word = string.charCodeAt(i);
+		if (0xDC00 <= word && word <= 0xDFFF)
+		{
+			i--;
+			char = string[i] + char;
+		}
+		if (isGood(_Utils_chr(char)))
+		{
+			return true;
+		}
+	}
+	return false;
+});
+
+var _String_all = F2(function(isGood, string)
+{
+	var i = string.length;
+	while (i--)
+	{
+		var char = string[i];
+		var word = string.charCodeAt(i);
+		if (0xDC00 <= word && word <= 0xDFFF)
+		{
+			i--;
+			char = string[i] + char;
+		}
+		if (!isGood(_Utils_chr(char)))
+		{
+			return false;
+		}
+	}
+	return true;
+});
+
+var _String_contains = F2(function(sub, str)
+{
+	return str.indexOf(sub) > -1;
+});
+
+var _String_startsWith = F2(function(sub, str)
+{
+	return str.indexOf(sub) === 0;
+});
+
+var _String_endsWith = F2(function(sub, str)
+{
+	return str.length >= sub.length &&
+		str.lastIndexOf(sub) === str.length - sub.length;
+});
+
+var _String_indexes = F2(function(sub, str)
+{
+	var subLen = sub.length;
+
+	if (subLen < 1)
+	{
+		return _List_Nil;
+	}
+
+	var i = 0;
+	var is = [];
+
+	while ((i = str.indexOf(sub, i)) > -1)
+	{
+		is.push(i);
+		i = i + subLen;
+	}
+
+	return _List_fromArray(is);
+});
+
+
+// TO STRING
+
+function _String_fromNumber(number)
+{
+	return number + '';
+}
+
+
+// INT CONVERSIONS
+
+function _String_toInt(str)
+{
+	var total = 0;
+	var code0 = str.charCodeAt(0);
+	var start = code0 == 0x2B /* + */ || code0 == 0x2D /* - */ ? 1 : 0;
+
+	for (var i = start; i < str.length; ++i)
+	{
+		var code = str.charCodeAt(i);
+		if (code < 0x30 || 0x39 < code)
+		{
+			return $elm$core$Maybe$Nothing;
+		}
+		total = 10 * total + code - 0x30;
+	}
+
+	return i == start
+		? $elm$core$Maybe$Nothing
+		: $elm$core$Maybe$Just(code0 == 0x2D ? -total : total);
+}
+
+
+// FLOAT CONVERSIONS
+
+function _String_toFloat(s)
+{
+	// check if it is a hex, octal, or binary number
+	if (s.length === 0 || /[\sxbo]/.test(s))
+	{
+		return $elm$core$Maybe$Nothing;
+	}
+	var n = +s;
+	// faster isNaN check
+	return n === n ? $elm$core$Maybe$Just(n) : $elm$core$Maybe$Nothing;
+}
+
+function _String_fromList(chars)
+{
+	return _List_toArray(chars).join('');
+}
+
+
+
+
+function _Char_toCode(char)
+{
+	var code = char.charCodeAt(0);
+	if (0xD800 <= code && code <= 0xDBFF)
+	{
+		return (code - 0xD800) * 0x400 + char.charCodeAt(1) - 0xDC00 + 0x10000
+	}
+	return code;
+}
+
+function _Char_fromCode(code)
+{
+	return _Utils_chr(
+		(code < 0 || 0x10FFFF < code)
+			? '\uFFFD'
+			:
+		(code <= 0xFFFF)
+			? String.fromCharCode(code)
+			:
+		(code -= 0x10000,
+			String.fromCharCode(Math.floor(code / 0x400) + 0xD800, code % 0x400 + 0xDC00)
+		)
+	);
+}
+
+function _Char_toUpper(char)
+{
+	return _Utils_chr(char.toUpperCase());
+}
+
+function _Char_toLower(char)
+{
+	return _Utils_chr(char.toLowerCase());
+}
+
+function _Char_toLocaleUpper(char)
+{
+	return _Utils_chr(char.toLocaleUpperCase());
+}
+
+function _Char_toLocaleLower(char)
+{
+	return _Utils_chr(char.toLocaleLowerCase());
+}
+
+
+
+/**_UNUSED/
+function _Json_errorToString(error)
+{
+	return $elm$json$Json$Decode$errorToString(error);
+}
+//*/
+
+
+// CORE DECODERS
+
+function _Json_succeed(msg)
+{
+	return {
+		$: 0,
+		a: msg
+	};
+}
+
+function _Json_fail(msg)
+{
+	return {
+		$: 1,
+		a: msg
+	};
+}
+
+function _Json_decodePrim(decoder)
+{
+	return { $: 2, b: decoder };
+}
+
+var _Json_decodeInt = _Json_decodePrim(function(value) {
+	return (typeof value !== 'number')
+		? _Json_expecting('an INT', value)
+		:
+	(-2147483647 < value && value < 2147483647 && (value | 0) === value)
+		? $elm$core$Result$Ok(value)
+		:
+	(isFinite(value) && !(value % 1))
+		? $elm$core$Result$Ok(value)
+		: _Json_expecting('an INT', value);
+});
+
+var _Json_decodeBool = _Json_decodePrim(function(value) {
+	return (typeof value === 'boolean')
+		? $elm$core$Result$Ok(value)
+		: _Json_expecting('a BOOL', value);
+});
+
+var _Json_decodeFloat = _Json_decodePrim(function(value) {
+	return (typeof value === 'number')
+		? $elm$core$Result$Ok(value)
+		: _Json_expecting('a FLOAT', value);
+});
+
+var _Json_decodeValue = _Json_decodePrim(function(value) {
+	return $elm$core$Result$Ok(_Json_wrap(value));
+});
+
+var _Json_decodeString = _Json_decodePrim(function(value) {
+	return (typeof value === 'string')
+		? $elm$core$Result$Ok(value)
+		: (value instanceof String)
+			? $elm$core$Result$Ok(value + '')
+			: _Json_expecting('a STRING', value);
+});
+
+function _Json_decodeList(decoder) { return { $: 3, b: decoder }; }
+function _Json_decodeArray(decoder) { return { $: 4, b: decoder }; }
+
+function _Json_decodeNull(value) { return { $: 5, c: value }; }
+
+var _Json_decodeField = F2(function(field, decoder)
+{
+	return {
+		$: 6,
+		d: field,
+		b: decoder
+	};
+});
+
+var _Json_decodeIndex = F2(function(index, decoder)
+{
+	return {
+		$: 7,
+		e: index,
+		b: decoder
+	};
+});
+
+function _Json_decodeKeyValuePairs(decoder)
+{
+	return {
+		$: 8,
+		b: decoder
+	};
+}
+
+function _Json_mapMany(f, decoders)
+{
+	return {
+		$: 9,
+		f: f,
+		g: decoders
+	};
+}
+
+var _Json_andThen = F2(function(callback, decoder)
+{
+	return {
+		$: 10,
+		b: decoder,
+		h: callback
+	};
+});
+
+function _Json_oneOf(decoders)
+{
+	return {
+		$: 11,
+		g: decoders
+	};
+}
+
+
+// DECODING OBJECTS
+
+var _Json_map1 = F2(function(f, d1)
+{
+	return _Json_mapMany(f, [d1]);
+});
+
+var _Json_map2 = F3(function(f, d1, d2)
+{
+	return _Json_mapMany(f, [d1, d2]);
+});
+
+var _Json_map3 = F4(function(f, d1, d2, d3)
+{
+	return _Json_mapMany(f, [d1, d2, d3]);
+});
+
+var _Json_map4 = F5(function(f, d1, d2, d3, d4)
+{
+	return _Json_mapMany(f, [d1, d2, d3, d4]);
+});
+
+var _Json_map5 = F6(function(f, d1, d2, d3, d4, d5)
+{
+	return _Json_mapMany(f, [d1, d2, d3, d4, d5]);
+});
+
+var _Json_map6 = F7(function(f, d1, d2, d3, d4, d5, d6)
+{
+	return _Json_mapMany(f, [d1, d2, d3, d4, d5, d6]);
+});
+
+var _Json_map7 = F8(function(f, d1, d2, d3, d4, d5, d6, d7)
+{
+	return _Json_mapMany(f, [d1, d2, d3, d4, d5, d6, d7]);
+});
+
+var _Json_map8 = F9(function(f, d1, d2, d3, d4, d5, d6, d7, d8)
+{
+	return _Json_mapMany(f, [d1, d2, d3, d4, d5, d6, d7, d8]);
+});
+
+
+// DECODE
+
+var _Json_runOnString = F2(function(decoder, string)
+{
+	try
+	{
+		var value = JSON.parse(string);
+		return _Json_runHelp(decoder, value);
+	}
+	catch (e)
+	{
+		return $elm$core$Result$Err(A2($elm$json$Json$Decode$Failure, 'This is not valid JSON! ' + e.message, _Json_wrap(string)));
+	}
+});
+
+var _Json_run = F2(function(decoder, value)
+{
+	return _Json_runHelp(decoder, _Json_unwrap(value));
+});
+
+function _Json_runHelp(decoder, value)
+{
+	switch (decoder.$)
+	{
+		case 2:
+			return decoder.b(value);
+
+		case 5:
+			return (value === null)
+				? $elm$core$Result$Ok(decoder.c)
+				: _Json_expecting('null', value);
+
+		case 3:
+			if (!_Json_isArray(value))
+			{
+				return _Json_expecting('a LIST', value);
+			}
+			return _Json_runArrayDecoder(decoder.b, value, _List_fromArray);
+
+		case 4:
+			if (!_Json_isArray(value))
+			{
+				return _Json_expecting('an ARRAY', value);
+			}
+			return _Json_runArrayDecoder(decoder.b, value, _Json_toElmArray);
+
+		case 6:
+			var field = decoder.d;
+			if (typeof value !== 'object' || value === null || !(field in value))
+			{
+				return _Json_expecting('an OBJECT with a field named `' + field + '`', value);
+			}
+			var result = _Json_runHelp(decoder.b, value[field]);
+			return ($elm$core$Result$isOk(result)) ? result : $elm$core$Result$Err(A2($elm$json$Json$Decode$Field, field, result.a));
+
+		case 7:
+			var index = decoder.e;
+			if (!_Json_isArray(value))
+			{
+				return _Json_expecting('an ARRAY', value);
+			}
+			if (index >= value.length)
+			{
+				return _Json_expecting('a LONGER array. Need index ' + index + ' but only see ' + value.length + ' entries', value);
+			}
+			var result = _Json_runHelp(decoder.b, value[index]);
+			return ($elm$core$Result$isOk(result)) ? result : $elm$core$Result$Err(A2($elm$json$Json$Decode$Index, index, result.a));
+
+		case 8:
+			if (typeof value !== 'object' || value === null || _Json_isArray(value))
+			{
+				return _Json_expecting('an OBJECT', value);
+			}
+
+			var keyValuePairs = _List_Nil;
+			// TODO test perf of Object.keys and switch when support is good enough
+			for (var key in value)
+			{
+				if (value.hasOwnProperty(key))
+				{
+					var result = _Json_runHelp(decoder.b, value[key]);
+					if (!$elm$core$Result$isOk(result))
+					{
+						return $elm$core$Result$Err(A2($elm$json$Json$Decode$Field, key, result.a));
+					}
+					keyValuePairs = _List_Cons(_Utils_Tuple2(key, result.a), keyValuePairs);
+				}
+			}
+			return $elm$core$Result$Ok($elm$core$List$reverse(keyValuePairs));
+
+		case 9:
+			var answer = decoder.f;
+			var decoders = decoder.g;
+			for (var i = 0; i < decoders.length; i++)
+			{
+				var result = _Json_runHelp(decoders[i], value);
+				if (!$elm$core$Result$isOk(result))
+				{
+					return result;
+				}
+				answer = answer(result.a);
+			}
+			return $elm$core$Result$Ok(answer);
+
+		case 10:
+			var result = _Json_runHelp(decoder.b, value);
+			return (!$elm$core$Result$isOk(result))
+				? result
+				: _Json_runHelp(decoder.h(result.a), value);
+
+		case 11:
+			var errors = _List_Nil;
+			for (var temp = decoder.g; temp.b; temp = temp.b) // WHILE_CONS
+			{
+				var result = _Json_runHelp(temp.a, value);
+				if ($elm$core$Result$isOk(result))
+				{
+					return result;
+				}
+				errors = _List_Cons(result.a, errors);
+			}
+			return $elm$core$Result$Err($elm$json$Json$Decode$OneOf($elm$core$List$reverse(errors)));
+
+		case 1:
+			return $elm$core$Result$Err(A2($elm$json$Json$Decode$Failure, decoder.a, _Json_wrap(value)));
+
+		case 0:
+			return $elm$core$Result$Ok(decoder.a);
+	}
+}
+
+function _Json_runArrayDecoder(decoder, value, toElmValue)
+{
+	var len = value.length;
+	var array = new Array(len);
+	for (var i = 0; i < len; i++)
+	{
+		var result = _Json_runHelp(decoder, value[i]);
+		if (!$elm$core$Result$isOk(result))
+		{
+			return $elm$core$Result$Err(A2($elm$json$Json$Decode$Index, i, result.a));
+		}
+		array[i] = result.a;
+	}
+	return $elm$core$Result$Ok(toElmValue(array));
+}
+
+function _Json_isArray(value)
+{
+	return Array.isArray(value) || (typeof FileList !== 'undefined' && value instanceof FileList);
+}
+
+function _Json_toElmArray(array)
+{
+	return A2($elm$core$Array$initialize, array.length, function(i) { return array[i]; });
+}
+
+function _Json_expecting(type, value)
+{
+	return $elm$core$Result$Err(A2($elm$json$Json$Decode$Failure, 'Expecting ' + type, _Json_wrap(value)));
+}
+
+
+// EQUALITY
+
+function _Json_equality(x, y)
+{
+	if (x === y)
+	{
+		return true;
+	}
+
+	if (x.$ !== y.$)
+	{
+		return false;
+	}
+
+	switch (x.$)
+	{
+		case 0:
+		case 1:
+			return x.a === y.a;
+
+		case 2:
+			return x.b === y.b;
+
+		case 5:
+			return x.c === y.c;
+
+		case 3:
+		case 4:
+		case 8:
+			return _Json_equality(x.b, y.b);
+
+		case 6:
+			return x.d === y.d && _Json_equality(x.b, y.b);
+
+		case 7:
+			return x.e === y.e && _Json_equality(x.b, y.b);
+
+		case 9:
+			return x.f === y.f && _Json_listEquality(x.g, y.g);
+
+		case 10:
+			return x.h === y.h && _Json_equality(x.b, y.b);
+
+		case 11:
+			return _Json_listEquality(x.g, y.g);
+	}
+}
+
+function _Json_listEquality(aDecoders, bDecoders)
+{
+	var len = aDecoders.length;
+	if (len !== bDecoders.length)
+	{
+		return false;
+	}
+	for (var i = 0; i < len; i++)
+	{
+		if (!_Json_equality(aDecoders[i], bDecoders[i]))
+		{
+			return false;
+		}
+	}
+	return true;
+}
+
+
+// ENCODE
+
+var _Json_encode = F2(function(indentLevel, value)
+{
+	return JSON.stringify(_Json_unwrap(value), null, indentLevel) + '';
+});
+
+function _Json_wrap_UNUSED(value) { return { $: 0, a: value }; }
+function _Json_unwrap_UNUSED(value) { return value.a; }
+
+function _Json_wrap(value) { return value; }
+function _Json_unwrap(value) { return value; }
+
+function _Json_emptyArray() { return []; }
+function _Json_emptyObject() { return {}; }
+
+var _Json_addField = F3(function(key, value, object)
+{
+	object[key] = _Json_unwrap(value);
+	return object;
+});
+
+function _Json_addEntry(func)
+{
+	return F2(function(entry, array)
+	{
+		array.push(_Json_unwrap(func(entry)));
+		return array;
+	});
+}
+
+var _Json_encodeNull = _Json_wrap(null);
+
+
+
+// TASKS
+
+function _Scheduler_succeed(value)
+{
+	return {
+		$: 0,
+		a: value
+	};
+}
+
+function _Scheduler_fail(error)
+{
+	return {
+		$: 1,
+		a: error
+	};
+}
+
+function _Scheduler_binding(callback)
+{
+	return {
+		$: 2,
+		b: callback,
+		c: null
+	};
+}
+
+var _Scheduler_andThen = F2(function(callback, task)
+{
+	return {
+		$: 3,
+		b: callback,
+		d: task
+	};
+});
+
+var _Scheduler_onError = F2(function(callback, task)
+{
+	return {
+		$: 4,
+		b: callback,
+		d: task
+	};
+});
+
+function _Scheduler_receive(callback)
+{
+	return {
+		$: 5,
+		b: callback
+	};
+}
+
+
+// PROCESSES
+
+var _Scheduler_guid = 0;
+
+function _Scheduler_rawSpawn(task)
+{
+	var proc = {
+		$: 0,
+		e: _Scheduler_guid++,
+		f: task,
+		g: null,
+		h: []
+	};
+
+	_Scheduler_enqueue(proc);
+
+	return proc;
+}
+
+function _Scheduler_spawn(task)
+{
+	return _Scheduler_binding(function(callback) {
+		callback(_Scheduler_succeed(_Scheduler_rawSpawn(task)));
+	});
+}
+
+function _Scheduler_rawSend(proc, msg)
+{
+	proc.h.push(msg);
+	_Scheduler_enqueue(proc);
+}
+
+var _Scheduler_send = F2(function(proc, msg)
+{
+	return _Scheduler_binding(function(callback) {
+		_Scheduler_rawSend(proc, msg);
+		callback(_Scheduler_succeed(_Utils_Tuple0));
+	});
+});
+
+function _Scheduler_kill(proc)
+{
+	return _Scheduler_binding(function(callback) {
+		var task = proc.f;
+		if (task.$ === 2 && task.c)
+		{
+			task.c();
+		}
+
+		proc.f = null;
+
+		callback(_Scheduler_succeed(_Utils_Tuple0));
+	});
+}
+
+
+/* STEP PROCESSES
+
+type alias Process =
+  { $ : tag
+  , id : unique_id
+  , root : Task
+  , stack : null | { $: SUCCEED | FAIL, a: callback, b: stack }
+  , mailbox : [msg]
+  }
+
+*/
+
+
+var _Scheduler_working = false;
+var _Scheduler_queue = [];
+
+
+function _Scheduler_enqueue(proc)
+{
+	_Scheduler_queue.push(proc);
+	if (_Scheduler_working)
+	{
+		return;
+	}
+	_Scheduler_working = true;
+	while (proc = _Scheduler_queue.shift())
+	{
+		_Scheduler_step(proc);
+	}
+	_Scheduler_working = false;
+}
+
+
+function _Scheduler_step(proc)
+{
+	while (proc.f)
+	{
+		var rootTag = proc.f.$;
+		if (rootTag === 0 || rootTag === 1)
+		{
+			while (proc.g && proc.g.$ !== rootTag)
+			{
+				proc.g = proc.g.i;
+			}
+			if (!proc.g)
+			{
+				return;
+			}
+			proc.f = proc.g.b(proc.f.a);
+			proc.g = proc.g.i;
+		}
+		else if (rootTag === 2)
+		{
+			proc.f.c = proc.f.b(function(newRoot) {
+				proc.f = newRoot;
+				_Scheduler_enqueue(proc);
+			});
+			return;
+		}
+		else if (rootTag === 5)
+		{
+			if (proc.h.length === 0)
+			{
+				return;
+			}
+			proc.f = proc.f.b(proc.h.shift());
+		}
+		else // if (rootTag === 3 || rootTag === 4)
+		{
+			proc.g = {
+				$: rootTag === 3 ? 0 : 1,
+				b: proc.f.b,
+				i: proc.g
+			};
+			proc.f = proc.f.d;
+		}
+	}
+}
+
+
+
+function _Process_sleep(time)
+{
+	return _Scheduler_binding(function(callback) {
+		var id = setTimeout(function() {
+			callback(_Scheduler_succeed(_Utils_Tuple0));
+		}, time);
+
+		return function() { clearTimeout(id); };
+	});
+}
+
+
+
+
+// PROGRAMS
+
+
+var _Platform_worker = F4(function(impl, flagDecoder, debugMetadata, args)
+{
+	return _Platform_initialize(
+		flagDecoder,
+		args,
+		impl.at,
+		impl.aB,
+		impl.az,
+		function() { return function() {} }
+	);
+});
+
+
+
+// INITIALIZE A PROGRAM
+
+
+function _Platform_initialize(flagDecoder, args, init, update, subscriptions, stepperBuilder)
+{
+	var result = A2(_Json_run, flagDecoder, _Json_wrap(args ? args['flags'] : undefined));
+	$elm$core$Result$isOk(result) || _Debug_crash(2 /**_UNUSED/, _Json_errorToString(result.a) /**/);
+	var managers = {};
+	var initPair = init(result.a);
+	var model = initPair.a;
+	var stepper = stepperBuilder(sendToApp, model);
+	var ports = _Platform_setupEffects(managers, sendToApp);
+
+	function sendToApp(msg, viewMetadata)
+	{
+		var pair = A2(update, msg, model);
+		stepper(model = pair.a, viewMetadata);
+		_Platform_enqueueEffects(managers, pair.b, subscriptions(model));
+	}
+
+	_Platform_enqueueEffects(managers, initPair.b, subscriptions(model));
+
+	return ports ? { ports: ports } : {};
+}
+
+
+
+// TRACK PRELOADS
+//
+// This is used by code in elm/browser and elm/http
+// to register any HTTP requests that are triggered by init.
+//
+
+
+var _Platform_preload;
+
+
+function _Platform_registerPreload(url)
+{
+	_Platform_preload.add(url);
+}
+
+
+
+// EFFECT MANAGERS
+
+
+var _Platform_effectManagers = {};
+
+
+function _Platform_setupEffects(managers, sendToApp)
+{
+	var ports;
+
+	// setup all necessary effect managers
+	for (var key in _Platform_effectManagers)
+	{
+		var manager = _Platform_effectManagers[key];
+
+		if (manager.a)
+		{
+			ports = ports || {};
+			ports[key] = manager.a(key, sendToApp);
+		}
+
+		managers[key] = _Platform_instantiateManager(manager, sendToApp);
+	}
+
+	return ports;
+}
+
+
+function _Platform_createManager(init, onEffects, onSelfMsg, cmdMap, subMap)
+{
+	return {
+		b: init,
+		c: onEffects,
+		d: onSelfMsg,
+		e: cmdMap,
+		f: subMap
+	};
+}
+
+
+function _Platform_instantiateManager(info, sendToApp)
+{
+	var router = {
+		g: sendToApp,
+		h: undefined
+	};
+
+	var onEffects = info.c;
+	var onSelfMsg = info.d;
+	var cmdMap = info.e;
+	var subMap = info.f;
+
+	function loop(state)
+	{
+		return A2(_Scheduler_andThen, loop, _Scheduler_receive(function(msg)
+		{
+			var value = msg.a;
+
+			if (msg.$ === 0)
+			{
+				return A3(onSelfMsg, router, value, state);
+			}
+
+			return cmdMap && subMap
+				? A4(onEffects, router, value.i, value.j, state)
+				: A3(onEffects, router, cmdMap ? value.i : value.j, state);
+		}));
+	}
+
+	return router.h = _Scheduler_rawSpawn(A2(_Scheduler_andThen, loop, info.b));
+}
+
+
+
+// ROUTING
+
+
+var _Platform_sendToApp = F2(function(router, msg)
+{
+	return _Scheduler_binding(function(callback)
+	{
+		router.g(msg);
+		callback(_Scheduler_succeed(_Utils_Tuple0));
+	});
+});
+
+
+var _Platform_sendToSelf = F2(function(router, msg)
+{
+	return A2(_Scheduler_send, router.h, {
+		$: 0,
+		a: msg
+	});
+});
+
+
+
+// BAGS
+
+
+function _Platform_leaf(home)
+{
+	return function(value)
+	{
+		return {
+			$: 1,
+			k: home,
+			l: value
+		};
+	};
+}
+
+
+function _Platform_batch(list)
+{
+	return {
+		$: 2,
+		m: list
+	};
+}
+
+
+var _Platform_map = F2(function(tagger, bag)
+{
+	return {
+		$: 3,
+		n: tagger,
+		o: bag
+	}
+});
+
+
+
+// PIPE BAGS INTO EFFECT MANAGERS
+//
+// Effects must be queued!
+//
+// Say your init contains a synchronous command, like Time.now or Time.here
+//
+//   - This will produce a batch of effects (FX_1)
+//   - The synchronous task triggers the subsequent `update` call
+//   - This will produce a batch of effects (FX_2)
+//
+// If we just start dispatching FX_2, subscriptions from FX_2 can be processed
+// before subscriptions from FX_1. No good! Earlier versions of this code had
+// this problem, leading to these reports:
+//
+//   https://github.com/elm/core/issues/980
+//   https://github.com/elm/core/pull/981
+//   https://github.com/elm/compiler/issues/1776
+//
+// The queue is necessary to avoid ordering issues for synchronous commands.
+
+
+// Why use true/false here? Why not just check the length of the queue?
+// The goal is to detect "are we currently dispatching effects?" If we
+// are, we need to bail and let the ongoing while loop handle things.
+//
+// Now say the queue has 1 element. When we dequeue the final element,
+// the queue will be empty, but we are still actively dispatching effects.
+// So you could get queue jumping in a really tricky category of cases.
+//
+var _Platform_effectsQueue = [];
+var _Platform_effectsActive = false;
+
+
+function _Platform_enqueueEffects(managers, cmdBag, subBag)
+{
+	_Platform_effectsQueue.push({ p: managers, q: cmdBag, r: subBag });
+
+	if (_Platform_effectsActive) return;
+
+	_Platform_effectsActive = true;
+	for (var fx; fx = _Platform_effectsQueue.shift(); )
+	{
+		_Platform_dispatchEffects(fx.p, fx.q, fx.r);
+	}
+	_Platform_effectsActive = false;
+}
+
+
+function _Platform_dispatchEffects(managers, cmdBag, subBag)
+{
+	var effectsDict = {};
+	_Platform_gatherEffects(true, cmdBag, effectsDict, null);
+	_Platform_gatherEffects(false, subBag, effectsDict, null);
+
+	for (var home in managers)
+	{
+		_Scheduler_rawSend(managers[home], {
+			$: 'fx',
+			a: effectsDict[home] || { i: _List_Nil, j: _List_Nil }
+		});
+	}
+}
+
+
+function _Platform_gatherEffects(isCmd, bag, effectsDict, taggers)
+{
+	switch (bag.$)
+	{
+		case 1:
+			var home = bag.k;
+			var effect = _Platform_toEffect(isCmd, home, taggers, bag.l);
+			effectsDict[home] = _Platform_insert(isCmd, effect, effectsDict[home]);
+			return;
+
+		case 2:
+			for (var list = bag.m; list.b; list = list.b) // WHILE_CONS
+			{
+				_Platform_gatherEffects(isCmd, list.a, effectsDict, taggers);
+			}
+			return;
+
+		case 3:
+			_Platform_gatherEffects(isCmd, bag.o, effectsDict, {
+				s: bag.n,
+				t: taggers
+			});
+			return;
+	}
+}
+
+
+function _Platform_toEffect(isCmd, home, taggers, value)
+{
+	function applyTaggers(x)
+	{
+		for (var temp = taggers; temp; temp = temp.t)
+		{
+			x = temp.s(x);
+		}
+		return x;
+	}
+
+	var map = isCmd
+		? _Platform_effectManagers[home].e
+		: _Platform_effectManagers[home].f;
+
+	return A2(map, applyTaggers, value)
+}
+
+
+function _Platform_insert(isCmd, newEffect, effects)
+{
+	effects = effects || { i: _List_Nil, j: _List_Nil };
+
+	isCmd
+		? (effects.i = _List_Cons(newEffect, effects.i))
+		: (effects.j = _List_Cons(newEffect, effects.j));
+
+	return effects;
+}
+
+
+
+// PORTS
+
+
+function _Platform_checkPortName(name)
+{
+	if (_Platform_effectManagers[name])
+	{
+		_Debug_crash(3, name)
+	}
+}
+
+
+
+// OUTGOING PORTS
+
+
+function _Platform_outgoingPort(name, converter)
+{
+	_Platform_checkPortName(name);
+	_Platform_effectManagers[name] = {
+		e: _Platform_outgoingPortMap,
+		u: converter,
+		a: _Platform_setupOutgoingPort
+	};
+	return _Platform_leaf(name);
+}
+
+
+var _Platform_outgoingPortMap = F2(function(tagger, value) { return value; });
+
+
+function _Platform_setupOutgoingPort(name)
+{
+	var subs = [];
+	var converter = _Platform_effectManagers[name].u;
+
+	// CREATE MANAGER
+
+	var init = _Process_sleep(0);
+
+	_Platform_effectManagers[name].b = init;
+	_Platform_effectManagers[name].c = F3(function(router, cmdList, state)
+	{
+		for ( ; cmdList.b; cmdList = cmdList.b) // WHILE_CONS
+		{
+			// grab a separate reference to subs in case unsubscribe is called
+			var currentSubs = subs;
+			var value = _Json_unwrap(converter(cmdList.a));
+			for (var i = 0; i < currentSubs.length; i++)
+			{
+				currentSubs[i](value);
+			}
+		}
+		return init;
+	});
+
+	// PUBLIC API
+
+	function subscribe(callback)
+	{
+		subs.push(callback);
+	}
+
+	function unsubscribe(callback)
+	{
+		// copy subs into a new array in case unsubscribe is called within a
+		// subscribed callback
+		subs = subs.slice();
+		var index = subs.indexOf(callback);
+		if (index >= 0)
+		{
+			subs.splice(index, 1);
+		}
+	}
+
+	return {
+		subscribe: subscribe,
+		unsubscribe: unsubscribe
+	};
+}
+
+
+
+// INCOMING PORTS
+
+
+function _Platform_incomingPort(name, converter)
+{
+	_Platform_checkPortName(name);
+	_Platform_effectManagers[name] = {
+		f: _Platform_incomingPortMap,
+		u: converter,
+		a: _Platform_setupIncomingPort
+	};
+	return _Platform_leaf(name);
+}
+
+
+var _Platform_incomingPortMap = F2(function(tagger, finalTagger)
+{
+	return function(value)
+	{
+		return tagger(finalTagger(value));
+	};
+});
+
+
+function _Platform_setupIncomingPort(name, sendToApp)
+{
+	var subs = _List_Nil;
+	var converter = _Platform_effectManagers[name].u;
+
+	// CREATE MANAGER
+
+	var init = _Scheduler_succeed(null);
+
+	_Platform_effectManagers[name].b = init;
+	_Platform_effectManagers[name].c = F3(function(router, subList, state)
+	{
+		subs = subList;
+		return init;
+	});
+
+	// PUBLIC API
+
+	function send(incomingValue)
+	{
+		var result = A2(_Json_run, converter, _Json_wrap(incomingValue));
+
+		$elm$core$Result$isOk(result) || _Debug_crash(4, name, result.a);
+
+		var value = result.a;
+		for (var temp = subs; temp.b; temp = temp.b) // WHILE_CONS
+		{
+			sendToApp(temp.a(value));
+		}
+	}
+
+	return { send: send };
+}
+
+
+
+// EXPORT ELM MODULES
+//
+// Have DEBUG and PROD versions so that we can (1) give nicer errors in
+// debug mode and (2) not pay for the bits needed for that in prod mode.
+//
+
+
+function _Platform_export(exports)
+{
+	scope['Elm']
+		? _Platform_mergeExportsProd(scope['Elm'], exports)
+		: scope['Elm'] = exports;
+}
+
+
+function _Platform_mergeExportsProd(obj, exports)
+{
+	for (var name in exports)
+	{
+		(name in obj)
+			? (name == 'init')
+				? _Debug_crash(6)
+				: _Platform_mergeExportsProd(obj[name], exports[name])
+			: (obj[name] = exports[name]);
+	}
+}
+
+
+function _Platform_export_UNUSED(exports)
+{
+	scope['Elm']
+		? _Platform_mergeExportsDebug('Elm', scope['Elm'], exports)
+		: scope['Elm'] = exports;
+}
+
+
+function _Platform_mergeExportsDebug(moduleName, obj, exports)
+{
+	for (var name in exports)
+	{
+		(name in obj)
+			? (name == 'init')
+				? _Debug_crash(6, moduleName)
+				: _Platform_mergeExportsDebug(moduleName + '.' + name, obj[name], exports[name])
+			: (obj[name] = exports[name]);
+	}
+}
+
+
+
+
+// HELPERS
+
+
+var _VirtualDom_divertHrefToApp;
+
+var _VirtualDom_doc = typeof document !== 'undefined' ? document : {};
+
+
+function _VirtualDom_appendChild(parent, child)
+{
+	parent.appendChild(child);
+}
+
+var _VirtualDom_init = F4(function(virtualNode, flagDecoder, debugMetadata, args)
+{
+	// NOTE: this function needs _Platform_export available to work
+
+	/**/
+	var node = args['node'];
+	//*/
+	/**_UNUSED/
+	var node = args && args['node'] ? args['node'] : _Debug_crash(0);
+	//*/
+
+	node.parentNode.replaceChild(
+		_VirtualDom_render(virtualNode, function() {}),
+		node
+	);
+
+	return {};
+});
+
+
+
+// TEXT
+
+
+function _VirtualDom_text(string)
+{
+	return {
+		$: 0,
+		a: string
+	};
+}
+
+
+
+// NODE
+
+
+var _VirtualDom_nodeNS = F2(function(namespace, tag)
+{
+	return F2(function(factList, kidList)
+	{
+		for (var kids = [], descendantsCount = 0; kidList.b; kidList = kidList.b) // WHILE_CONS
+		{
+			var kid = kidList.a;
+			descendantsCount += (kid.b || 0);
+			kids.push(kid);
+		}
+		descendantsCount += kids.length;
+
+		return {
+			$: 1,
+			c: tag,
+			d: _VirtualDom_organizeFacts(factList),
+			e: kids,
+			f: namespace,
+			b: descendantsCount
+		};
+	});
+});
+
+
+var _VirtualDom_node = _VirtualDom_nodeNS(undefined);
+
+
+
+// KEYED NODE
+
+
+var _VirtualDom_keyedNodeNS = F2(function(namespace, tag)
+{
+	return F2(function(factList, kidList)
+	{
+		for (var kids = [], descendantsCount = 0; kidList.b; kidList = kidList.b) // WHILE_CONS
+		{
+			var kid = kidList.a;
+			descendantsCount += (kid.b.b || 0);
+			kids.push(kid);
+		}
+		descendantsCount += kids.length;
+
+		return {
+			$: 2,
+			c: tag,
+			d: _VirtualDom_organizeFacts(factList),
+			e: kids,
+			f: namespace,
+			b: descendantsCount
+		};
+	});
+});
+
+
+var _VirtualDom_keyedNode = _VirtualDom_keyedNodeNS(undefined);
+
+
+
+// CUSTOM
+
+
+function _VirtualDom_custom(factList, model, render, diff)
+{
+	return {
+		$: 3,
+		d: _VirtualDom_organizeFacts(factList),
+		g: model,
+		h: render,
+		i: diff
+	};
+}
+
+
+
+// MAP
+
+
+var _VirtualDom_map = F2(function(tagger, node)
+{
+	return {
+		$: 4,
+		j: tagger,
+		k: node,
+		b: 1 + (node.b || 0)
+	};
+});
+
+
+
+// LAZY
+
+
+function _VirtualDom_thunk(refs, thunk)
+{
+	return {
+		$: 5,
+		l: refs,
+		m: thunk,
+		k: undefined
+	};
+}
+
+var _VirtualDom_lazy = F2(function(func, a)
+{
+	return _VirtualDom_thunk([func, a], function() {
+		return func(a);
+	});
+});
+
+var _VirtualDom_lazy2 = F3(function(func, a, b)
+{
+	return _VirtualDom_thunk([func, a, b], function() {
+		return A2(func, a, b);
+	});
+});
+
+var _VirtualDom_lazy3 = F4(function(func, a, b, c)
+{
+	return _VirtualDom_thunk([func, a, b, c], function() {
+		return A3(func, a, b, c);
+	});
+});
+
+var _VirtualDom_lazy4 = F5(function(func, a, b, c, d)
+{
+	return _VirtualDom_thunk([func, a, b, c, d], function() {
+		return A4(func, a, b, c, d);
+	});
+});
+
+var _VirtualDom_lazy5 = F6(function(func, a, b, c, d, e)
+{
+	return _VirtualDom_thunk([func, a, b, c, d, e], function() {
+		return A5(func, a, b, c, d, e);
+	});
+});
+
+var _VirtualDom_lazy6 = F7(function(func, a, b, c, d, e, f)
+{
+	return _VirtualDom_thunk([func, a, b, c, d, e, f], function() {
+		return A6(func, a, b, c, d, e, f);
+	});
+});
+
+var _VirtualDom_lazy7 = F8(function(func, a, b, c, d, e, f, g)
+{
+	return _VirtualDom_thunk([func, a, b, c, d, e, f, g], function() {
+		return A7(func, a, b, c, d, e, f, g);
+	});
+});
+
+var _VirtualDom_lazy8 = F9(function(func, a, b, c, d, e, f, g, h)
+{
+	return _VirtualDom_thunk([func, a, b, c, d, e, f, g, h], function() {
+		return A8(func, a, b, c, d, e, f, g, h);
+	});
+});
+
+
+
+// FACTS
+
+
+var _VirtualDom_on = F2(function(key, handler)
+{
+	return {
+		$: 'a0',
+		n: key,
+		o: handler
+	};
+});
+var _VirtualDom_style = F2(function(key, value)
+{
+	return {
+		$: 'a1',
+		n: key,
+		o: value
+	};
+});
+var _VirtualDom_property = F2(function(key, value)
+{
+	return {
+		$: 'a2',
+		n: key,
+		o: value
+	};
+});
+var _VirtualDom_attribute = F2(function(key, value)
+{
+	return {
+		$: 'a3',
+		n: key,
+		o: value
+	};
+});
+var _VirtualDom_attributeNS = F3(function(namespace, key, value)
+{
+	return {
+		$: 'a4',
+		n: key,
+		o: { f: namespace, o: value }
+	};
+});
+
+
+
+// XSS ATTACK VECTOR CHECKS
+
+
+function _VirtualDom_noScript(tag)
+{
+	return tag == 'script' ? 'p' : tag;
+}
+
+function _VirtualDom_noOnOrFormAction(key)
+{
+	return /^(on|formAction$)/i.test(key) ? 'data-' + key : key;
+}
+
+function _VirtualDom_noInnerHtmlOrFormAction(key)
+{
+	return key == 'innerHTML' || key == 'formAction' ? 'data-' + key : key;
+}
+
+function _VirtualDom_noJavaScriptUri(value)
+{
+	return /^javascript:/i.test(value.replace(/\s/g,'')) ? '' : value;
+}
+
+function _VirtualDom_noJavaScriptUri_UNUSED(value)
+{
+	return /^javascript:/i.test(value.replace(/\s/g,''))
+		? 'javascript:alert("This is an XSS vector. Please use ports or web components instead.")'
+		: value;
+}
+
+function _VirtualDom_noJavaScriptOrHtmlUri(value)
+{
+	return /^\s*(javascript:|data:text\/html)/i.test(value) ? '' : value;
+}
+
+function _VirtualDom_noJavaScriptOrHtmlUri_UNUSED(value)
+{
+	return /^\s*(javascript:|data:text\/html)/i.test(value)
+		? 'javascript:alert("This is an XSS vector. Please use ports or web components instead.")'
+		: value;
+}
+
+
+
+// MAP FACTS
+
+
+var _VirtualDom_mapAttribute = F2(function(func, attr)
+{
+	return (attr.$ === 'a0')
+		? A2(_VirtualDom_on, attr.n, _VirtualDom_mapHandler(func, attr.o))
+		: attr;
+});
+
+function _VirtualDom_mapHandler(func, handler)
+{
+	var tag = $elm$virtual_dom$VirtualDom$toHandlerInt(handler);
+
+	// 0 = Normal
+	// 1 = MayStopPropagation
+	// 2 = MayPreventDefault
+	// 3 = Custom
+
+	return {
+		$: handler.$,
+		a:
+			!tag
+				? A2($elm$json$Json$Decode$map, func, handler.a)
+				:
+			A3($elm$json$Json$Decode$map2,
+				tag < 3
+					? _VirtualDom_mapEventTuple
+					: _VirtualDom_mapEventRecord,
+				$elm$json$Json$Decode$succeed(func),
+				handler.a
+			)
+	};
+}
+
+var _VirtualDom_mapEventTuple = F2(function(func, tuple)
+{
+	return _Utils_Tuple2(func(tuple.a), tuple.b);
+});
+
+var _VirtualDom_mapEventRecord = F2(function(func, record)
+{
+	return {
+		o: func(record.o),
+		J: record.J,
+		G: record.G
+	}
+});
+
+
+
+// ORGANIZE FACTS
+
+
+function _VirtualDom_organizeFacts(factList)
+{
+	for (var facts = {}; factList.b; factList = factList.b) // WHILE_CONS
+	{
+		var entry = factList.a;
+
+		var tag = entry.$;
+		var key = entry.n;
+		var value = entry.o;
+
+		if (tag === 'a2')
+		{
+			(key === 'className')
+				? _VirtualDom_addClass(facts, key, _Json_unwrap(value))
+				: facts[key] = _Json_unwrap(value);
+
+			continue;
+		}
+
+		var subFacts = facts[tag] || (facts[tag] = {});
+		(tag === 'a3' && key === 'class')
+			? _VirtualDom_addClass(subFacts, key, value)
+			: subFacts[key] = value;
+	}
+
+	return facts;
+}
+
+function _VirtualDom_addClass(object, key, newClass)
+{
+	var classes = object[key];
+	object[key] = classes ? classes + ' ' + newClass : newClass;
+}
+
+
+
+// RENDER
+
+
+function _VirtualDom_render(vNode, eventNode)
+{
+	var tag = vNode.$;
+
+	if (tag === 5)
+	{
+		return _VirtualDom_render(vNode.k || (vNode.k = vNode.m()), eventNode);
+	}
+
+	if (tag === 0)
+	{
+		return _VirtualDom_doc.createTextNode(vNode.a);
+	}
+
+	if (tag === 4)
+	{
+		var subNode = vNode.k;
+		var tagger = vNode.j;
+
+		while (subNode.$ === 4)
+		{
+			typeof tagger !== 'object'
+				? tagger = [tagger, subNode.j]
+				: tagger.push(subNode.j);
+
+			subNode = subNode.k;
+		}
+
+		var subEventRoot = { j: tagger, p: eventNode };
+		var domNode = _VirtualDom_render(subNode, subEventRoot);
+		domNode.elm_event_node_ref = subEventRoot;
+		return domNode;
+	}
+
+	if (tag === 3)
+	{
+		var domNode = vNode.h(vNode.g);
+		_VirtualDom_applyFacts(domNode, eventNode, vNode.d);
+		return domNode;
+	}
+
+	// at this point `tag` must be 1 or 2
+
+	var domNode = vNode.f
+		? _VirtualDom_doc.createElementNS(vNode.f, vNode.c)
+		: _VirtualDom_doc.createElement(vNode.c);
+
+	if (_VirtualDom_divertHrefToApp && vNode.c == 'a')
+	{
+		domNode.addEventListener('click', _VirtualDom_divertHrefToApp(domNode));
+	}
+
+	_VirtualDom_applyFacts(domNode, eventNode, vNode.d);
+
+	for (var kids = vNode.e, i = 0; i < kids.length; i++)
+	{
+		_VirtualDom_appendChild(domNode, _VirtualDom_render(tag === 1 ? kids[i] : kids[i].b, eventNode));
+	}
+
+	return domNode;
+}
+
+
+
+// APPLY FACTS
+
+
+function _VirtualDom_applyFacts(domNode, eventNode, facts)
+{
+	for (var key in facts)
+	{
+		var value = facts[key];
+
+		key === 'a1'
+			? _VirtualDom_applyStyles(domNode, value)
+			:
+		key === 'a0'
+			? _VirtualDom_applyEvents(domNode, eventNode, value)
+			:
+		key === 'a3'
+			? _VirtualDom_applyAttrs(domNode, value)
+			:
+		key === 'a4'
+			? _VirtualDom_applyAttrsNS(domNode, value)
+			:
+		((key !== 'value' && key !== 'checked') || domNode[key] !== value) && (domNode[key] = value);
+	}
+}
+
+
+
+// APPLY STYLES
+
+
+function _VirtualDom_applyStyles(domNode, styles)
+{
+	var domNodeStyle = domNode.style;
+
+	for (var key in styles)
+	{
+		domNodeStyle[key] = styles[key];
+	}
+}
+
+
+
+// APPLY ATTRS
+
+
+function _VirtualDom_applyAttrs(domNode, attrs)
+{
+	for (var key in attrs)
+	{
+		var value = attrs[key];
+		typeof value !== 'undefined'
+			? domNode.setAttribute(key, value)
+			: domNode.removeAttribute(key);
+	}
+}
+
+
+
+// APPLY NAMESPACED ATTRS
+
+
+function _VirtualDom_applyAttrsNS(domNode, nsAttrs)
+{
+	for (var key in nsAttrs)
+	{
+		var pair = nsAttrs[key];
+		var namespace = pair.f;
+		var value = pair.o;
+
+		typeof value !== 'undefined'
+			? domNode.setAttributeNS(namespace, key, value)
+			: domNode.removeAttributeNS(namespace, key);
+	}
+}
+
+
+
+// APPLY EVENTS
+
+
+function _VirtualDom_applyEvents(domNode, eventNode, events)
+{
+	var allCallbacks = domNode.elmFs || (domNode.elmFs = {});
+
+	for (var key in events)
+	{
+		var newHandler = events[key];
+		var oldCallback = allCallbacks[key];
+
+		if (!newHandler)
+		{
+			domNode.removeEventListener(key, oldCallback);
+			allCallbacks[key] = undefined;
+			continue;
+		}
+
+		if (oldCallback)
+		{
+			var oldHandler = oldCallback.q;
+			if (oldHandler.$ === newHandler.$)
+			{
+				oldCallback.q = newHandler;
+				continue;
+			}
+			domNode.removeEventListener(key, oldCallback);
+		}
+
+		oldCallback = _VirtualDom_makeCallback(eventNode, newHandler);
+		domNode.addEventListener(key, oldCallback,
+			_VirtualDom_passiveSupported
+			&& { passive: $elm$virtual_dom$VirtualDom$toHandlerInt(newHandler) < 2 }
+		);
+		allCallbacks[key] = oldCallback;
+	}
+}
+
+
+
+// PASSIVE EVENTS
+
+
+var _VirtualDom_passiveSupported;
+
+try
+{
+	window.addEventListener('t', null, Object.defineProperty({}, 'passive', {
+		get: function() { _VirtualDom_passiveSupported = true; }
+	}));
+}
+catch(e) {}
+
+
+
+// EVENT HANDLERS
+
+
+function _VirtualDom_makeCallback(eventNode, initialHandler)
+{
+	function callback(event)
+	{
+		var handler = callback.q;
+		var result = _Json_runHelp(handler.a, event);
+
+		if (!$elm$core$Result$isOk(result))
+		{
+			return;
+		}
+
+		var tag = $elm$virtual_dom$VirtualDom$toHandlerInt(handler);
+
+		// 0 = Normal
+		// 1 = MayStopPropagation
+		// 2 = MayPreventDefault
+		// 3 = Custom
+
+		var value = result.a;
+		var message = !tag ? value : tag < 3 ? value.a : value.o;
+		var stopPropagation = tag == 1 ? value.b : tag == 3 && value.J;
+		var currentEventNode = (
+			stopPropagation && event.stopPropagation(),
+			(tag == 2 ? value.b : tag == 3 && value.G) && event.preventDefault(),
+			eventNode
+		);
+		var tagger;
+		var i;
+		while (tagger = currentEventNode.j)
+		{
+			if (typeof tagger == 'function')
+			{
+				message = tagger(message);
+			}
+			else
+			{
+				for (var i = tagger.length; i--; )
+				{
+					message = tagger[i](message);
+				}
+			}
+			currentEventNode = currentEventNode.p;
+		}
+		currentEventNode(message, stopPropagation); // stopPropagation implies isSync
+	}
+
+	callback.q = initialHandler;
+
+	return callback;
+}
+
+function _VirtualDom_equalEvents(x, y)
+{
+	return x.$ == y.$ && _Json_equality(x.a, y.a);
+}
+
+
+
+// DIFF
+
+
+// TODO: Should we do patches like in iOS?
+//
+// type Patch
+//   = At Int Patch
+//   | Batch (List Patch)
+//   | Change ...
+//
+// How could it not be better?
+//
+function _VirtualDom_diff(x, y)
+{
+	var patches = [];
+	_VirtualDom_diffHelp(x, y, patches, 0);
+	return patches;
+}
+
+
+function _VirtualDom_pushPatch(patches, type, index, data)
+{
+	var patch = {
+		$: type,
+		r: index,
+		s: data,
+		t: undefined,
+		u: undefined
+	};
+	patches.push(patch);
+	return patch;
+}
+
+
+function _VirtualDom_diffHelp(x, y, patches, index)
+{
+	if (x === y)
+	{
+		return;
+	}
+
+	var xType = x.$;
+	var yType = y.$;
+
+	// Bail if you run into different types of nodes. Implies that the
+	// structure has changed significantly and it's not worth a diff.
+	if (xType !== yType)
+	{
+		if (xType === 1 && yType === 2)
+		{
+			y = _VirtualDom_dekey(y);
+			yType = 1;
+		}
+		else
+		{
+			_VirtualDom_pushPatch(patches, 0, index, y);
+			return;
+		}
+	}
+
+	// Now we know that both nodes are the same $.
+	switch (yType)
+	{
+		case 5:
+			var xRefs = x.l;
+			var yRefs = y.l;
+			var i = xRefs.length;
+			var same = i === yRefs.length;
+			while (same && i--)
+			{
+				same = xRefs[i] === yRefs[i];
+			}
+			if (same)
+			{
+				y.k = x.k;
+				return;
+			}
+			y.k = y.m();
+			var subPatches = [];
+			_VirtualDom_diffHelp(x.k, y.k, subPatches, 0);
+			subPatches.length > 0 && _VirtualDom_pushPatch(patches, 1, index, subPatches);
+			return;
+
+		case 4:
+			// gather nested taggers
+			var xTaggers = x.j;
+			var yTaggers = y.j;
+			var nesting = false;
+
+			var xSubNode = x.k;
+			while (xSubNode.$ === 4)
+			{
+				nesting = true;
+
+				typeof xTaggers !== 'object'
+					? xTaggers = [xTaggers, xSubNode.j]
+					: xTaggers.push(xSubNode.j);
+
+				xSubNode = xSubNode.k;
+			}
+
+			var ySubNode = y.k;
+			while (ySubNode.$ === 4)
+			{
+				nesting = true;
+
+				typeof yTaggers !== 'object'
+					? yTaggers = [yTaggers, ySubNode.j]
+					: yTaggers.push(ySubNode.j);
+
+				ySubNode = ySubNode.k;
+			}
+
+			// Just bail if different numbers of taggers. This implies the
+			// structure of the virtual DOM has changed.
+			if (nesting && xTaggers.length !== yTaggers.length)
+			{
+				_VirtualDom_pushPatch(patches, 0, index, y);
+				return;
+			}
+
+			// check if taggers are "the same"
+			if (nesting ? !_VirtualDom_pairwiseRefEqual(xTaggers, yTaggers) : xTaggers !== yTaggers)
+			{
+				_VirtualDom_pushPatch(patches, 2, index, yTaggers);
+			}
+
+			// diff everything below the taggers
+			_VirtualDom_diffHelp(xSubNode, ySubNode, patches, index + 1);
+			return;
+
+		case 0:
+			if (x.a !== y.a)
+			{
+				_VirtualDom_pushPatch(patches, 3, index, y.a);
+			}
+			return;
+
+		case 1:
+			_VirtualDom_diffNodes(x, y, patches, index, _VirtualDom_diffKids);
+			return;
+
+		case 2:
+			_VirtualDom_diffNodes(x, y, patches, index, _VirtualDom_diffKeyedKids);
+			return;
+
+		case 3:
+			if (x.h !== y.h)
+			{
+				_VirtualDom_pushPatch(patches, 0, index, y);
+				return;
+			}
+
+			var factsDiff = _VirtualDom_diffFacts(x.d, y.d);
+			factsDiff && _VirtualDom_pushPatch(patches, 4, index, factsDiff);
+
+			var patch = y.i(x.g, y.g);
+			patch && _VirtualDom_pushPatch(patches, 5, index, patch);
+
+			return;
+	}
+}
+
+// assumes the incoming arrays are the same length
+function _VirtualDom_pairwiseRefEqual(as, bs)
+{
+	for (var i = 0; i < as.length; i++)
+	{
+		if (as[i] !== bs[i])
+		{
+			return false;
+		}
+	}
+
+	return true;
+}
+
+function _VirtualDom_diffNodes(x, y, patches, index, diffKids)
+{
+	// Bail if obvious indicators have changed. Implies more serious
+	// structural changes such that it's not worth it to diff.
+	if (x.c !== y.c || x.f !== y.f)
+	{
+		_VirtualDom_pushPatch(patches, 0, index, y);
+		return;
+	}
+
+	var factsDiff = _VirtualDom_diffFacts(x.d, y.d);
+	factsDiff && _VirtualDom_pushPatch(patches, 4, index, factsDiff);
+
+	diffKids(x, y, patches, index);
+}
+
+
+
+// DIFF FACTS
+
+
+// TODO Instead of creating a new diff object, it's possible to just test if
+// there *is* a diff. During the actual patch, do the diff again and make the
+// modifications directly. This way, there's no new allocations. Worth it?
+function _VirtualDom_diffFacts(x, y, category)
+{
+	var diff;
+
+	// look for changes and removals
+	for (var xKey in x)
+	{
+		if (xKey === 'a1' || xKey === 'a0' || xKey === 'a3' || xKey === 'a4')
+		{
+			var subDiff = _VirtualDom_diffFacts(x[xKey], y[xKey] || {}, xKey);
+			if (subDiff)
+			{
+				diff = diff || {};
+				diff[xKey] = subDiff;
+			}
+			continue;
+		}
+
+		// remove if not in the new facts
+		if (!(xKey in y))
+		{
+			diff = diff || {};
+			diff[xKey] =
+				!category
+					? (typeof x[xKey] === 'string' ? '' : null)
+					:
+				(category === 'a1')
+					? ''
+					:
+				(category === 'a0' || category === 'a3')
+					? undefined
+					:
+				{ f: x[xKey].f, o: undefined };
+
+			continue;
+		}
+
+		var xValue = x[xKey];
+		var yValue = y[xKey];
+
+		// reference equal, so don't worry about it
+		if (xValue === yValue && xKey !== 'value' && xKey !== 'checked'
+			|| category === 'a0' && _VirtualDom_equalEvents(xValue, yValue))
+		{
+			continue;
+		}
+
+		diff = diff || {};
+		diff[xKey] = yValue;
+	}
+
+	// add new stuff
+	for (var yKey in y)
+	{
+		if (!(yKey in x))
+		{
+			diff = diff || {};
+			diff[yKey] = y[yKey];
+		}
+	}
+
+	return diff;
+}
+
+
+
+// DIFF KIDS
+
+
+function _VirtualDom_diffKids(xParent, yParent, patches, index)
+{
+	var xKids = xParent.e;
+	var yKids = yParent.e;
+
+	var xLen = xKids.length;
+	var yLen = yKids.length;
+
+	// FIGURE OUT IF THERE ARE INSERTS OR REMOVALS
+
+	if (xLen > yLen)
+	{
+		_VirtualDom_pushPatch(patches, 6, index, {
+			v: yLen,
+			i: xLen - yLen
+		});
+	}
+	else if (xLen < yLen)
+	{
+		_VirtualDom_pushPatch(patches, 7, index, {
+			v: xLen,
+			e: yKids
+		});
+	}
+
+	// PAIRWISE DIFF EVERYTHING ELSE
+
+	for (var minLen = xLen < yLen ? xLen : yLen, i = 0; i < minLen; i++)
+	{
+		var xKid = xKids[i];
+		_VirtualDom_diffHelp(xKid, yKids[i], patches, ++index);
+		index += xKid.b || 0;
+	}
+}
+
+
+
+// KEYED DIFF
+
+
+function _VirtualDom_diffKeyedKids(xParent, yParent, patches, rootIndex)
+{
+	var localPatches = [];
+
+	var changes = {}; // Dict String Entry
+	var inserts = []; // Array { index : Int, entry : Entry }
+	// type Entry = { tag : String, vnode : VNode, index : Int, data : _ }
+
+	var xKids = xParent.e;
+	var yKids = yParent.e;
+	var xLen = xKids.length;
+	var yLen = yKids.length;
+	var xIndex = 0;
+	var yIndex = 0;
+
+	var index = rootIndex;
+
+	while (xIndex < xLen && yIndex < yLen)
+	{
+		var x = xKids[xIndex];
+		var y = yKids[yIndex];
+
+		var xKey = x.a;
+		var yKey = y.a;
+		var xNode = x.b;
+		var yNode = y.b;
+
+		var newMatch = undefined;
+		var oldMatch = undefined;
+
+		// check if keys match
+
+		if (xKey === yKey)
+		{
+			index++;
+			_VirtualDom_diffHelp(xNode, yNode, localPatches, index);
+			index += xNode.b || 0;
+
+			xIndex++;
+			yIndex++;
+			continue;
+		}
+
+		// look ahead 1 to detect insertions and removals.
+
+		var xNext = xKids[xIndex + 1];
+		var yNext = yKids[yIndex + 1];
+
+		if (xNext)
+		{
+			var xNextKey = xNext.a;
+			var xNextNode = xNext.b;
+			oldMatch = yKey === xNextKey;
+		}
+
+		if (yNext)
+		{
+			var yNextKey = yNext.a;
+			var yNextNode = yNext.b;
+			newMatch = xKey === yNextKey;
+		}
+
+
+		// swap x and y
+		if (newMatch && oldMatch)
+		{
+			index++;
+			_VirtualDom_diffHelp(xNode, yNextNode, localPatches, index);
+			_VirtualDom_insertNode(changes, localPatches, xKey, yNode, yIndex, inserts);
+			index += xNode.b || 0;
+
+			index++;
+			_VirtualDom_removeNode(changes, localPatches, xKey, xNextNode, index);
+			index += xNextNode.b || 0;
+
+			xIndex += 2;
+			yIndex += 2;
+			continue;
+		}
+
+		// insert y
+		if (newMatch)
+		{
+			index++;
+			_VirtualDom_insertNode(changes, localPatches, yKey, yNode, yIndex, inserts);
+			_VirtualDom_diffHelp(xNode, yNextNode, localPatches, index);
+			index += xNode.b || 0;
+
+			xIndex += 1;
+			yIndex += 2;
+			continue;
+		}
+
+		// remove x
+		if (oldMatch)
+		{
+			index++;
+			_VirtualDom_removeNode(changes, localPatches, xKey, xNode, index);
+			index += xNode.b || 0;
+
+			index++;
+			_VirtualDom_diffHelp(xNextNode, yNode, localPatches, index);
+			index += xNextNode.b || 0;
+
+			xIndex += 2;
+			yIndex += 1;
+			continue;
+		}
+
+		// remove x, insert y
+		if (xNext && xNextKey === yNextKey)
+		{
+			index++;
+			_VirtualDom_removeNode(changes, localPatches, xKey, xNode, index);
+			_VirtualDom_insertNode(changes, localPatches, yKey, yNode, yIndex, inserts);
+			index += xNode.b || 0;
+
+			index++;
+			_VirtualDom_diffHelp(xNextNode, yNextNode, localPatches, index);
+			index += xNextNode.b || 0;
+
+			xIndex += 2;
+			yIndex += 2;
+			continue;
+		}
+
+		break;
+	}
+
+	// eat up any remaining nodes with removeNode and insertNode
+
+	while (xIndex < xLen)
+	{
+		index++;
+		var x = xKids[xIndex];
+		var xNode = x.b;
+		_VirtualDom_removeNode(changes, localPatches, x.a, xNode, index);
+		index += xNode.b || 0;
+		xIndex++;
+	}
+
+	while (yIndex < yLen)
+	{
+		var endInserts = endInserts || [];
+		var y = yKids[yIndex];
+		_VirtualDom_insertNode(changes, localPatches, y.a, y.b, undefined, endInserts);
+		yIndex++;
+	}
+
+	if (localPatches.length > 0 || inserts.length > 0 || endInserts)
+	{
+		_VirtualDom_pushPatch(patches, 8, rootIndex, {
+			w: localPatches,
+			x: inserts,
+			y: endInserts
+		});
+	}
+}
+
+
+
+// CHANGES FROM KEYED DIFF
+
+
+var _VirtualDom_POSTFIX = '_elmW6BL';
+
+
+function _VirtualDom_insertNode(changes, localPatches, key, vnode, yIndex, inserts)
+{
+	var entry = changes[key];
+
+	// never seen this key before
+	if (!entry)
+	{
+		entry = {
+			c: 0,
+			z: vnode,
+			r: yIndex,
+			s: undefined
+		};
+
+		inserts.push({ r: yIndex, A: entry });
+		changes[key] = entry;
+
+		return;
+	}
+
+	// this key was removed earlier, a match!
+	if (entry.c === 1)
+	{
+		inserts.push({ r: yIndex, A: entry });
+
+		entry.c = 2;
+		var subPatches = [];
+		_VirtualDom_diffHelp(entry.z, vnode, subPatches, entry.r);
+		entry.r = yIndex;
+		entry.s.s = {
+			w: subPatches,
+			A: entry
+		};
+
+		return;
+	}
+
+	// this key has already been inserted or moved, a duplicate!
+	_VirtualDom_insertNode(changes, localPatches, key + _VirtualDom_POSTFIX, vnode, yIndex, inserts);
+}
+
+
+function _VirtualDom_removeNode(changes, localPatches, key, vnode, index)
+{
+	var entry = changes[key];
+
+	// never seen this key before
+	if (!entry)
+	{
+		var patch = _VirtualDom_pushPatch(localPatches, 9, index, undefined);
+
+		changes[key] = {
+			c: 1,
+			z: vnode,
+			r: index,
+			s: patch
+		};
+
+		return;
+	}
+
+	// this key was inserted earlier, a match!
+	if (entry.c === 0)
+	{
+		entry.c = 2;
+		var subPatches = [];
+		_VirtualDom_diffHelp(vnode, entry.z, subPatches, index);
+
+		_VirtualDom_pushPatch(localPatches, 9, index, {
+			w: subPatches,
+			A: entry
+		});
+
+		return;
+	}
+
+	// this key has already been removed or moved, a duplicate!
+	_VirtualDom_removeNode(changes, localPatches, key + _VirtualDom_POSTFIX, vnode, index);
+}
+
+
+
+// ADD DOM NODES
+//
+// Each DOM node has an "index" assigned in order of traversal. It is important
+// to minimize our crawl over the actual DOM, so these indexes (along with the
+// descendantsCount of virtual nodes) let us skip touching entire subtrees of
+// the DOM if we know there are no patches there.
+
+
+function _VirtualDom_addDomNodes(domNode, vNode, patches, eventNode)
+{
+	_VirtualDom_addDomNodesHelp(domNode, vNode, patches, 0, 0, vNode.b, eventNode);
+}
+
+
+// assumes `patches` is non-empty and indexes increase monotonically.
+function _VirtualDom_addDomNodesHelp(domNode, vNode, patches, i, low, high, eventNode)
+{
+	var patch = patches[i];
+	var index = patch.r;
+
+	while (index === low)
+	{
+		var patchType = patch.$;
+
+		if (patchType === 1)
+		{
+			_VirtualDom_addDomNodes(domNode, vNode.k, patch.s, eventNode);
+		}
+		else if (patchType === 8)
+		{
+			patch.t = domNode;
+			patch.u = eventNode;
+
+			var subPatches = patch.s.w;
+			if (subPatches.length > 0)
+			{
+				_VirtualDom_addDomNodesHelp(domNode, vNode, subPatches, 0, low, high, eventNode);
+			}
+		}
+		else if (patchType === 9)
+		{
+			patch.t = domNode;
+			patch.u = eventNode;
+
+			var data = patch.s;
+			if (data)
+			{
+				data.A.s = domNode;
+				var subPatches = data.w;
+				if (subPatches.length > 0)
+				{
+					_VirtualDom_addDomNodesHelp(domNode, vNode, subPatches, 0, low, high, eventNode);
+				}
+			}
+		}
+		else
+		{
+			patch.t = domNode;
+			patch.u = eventNode;
+		}
+
+		i++;
+
+		if (!(patch = patches[i]) || (index = patch.r) > high)
+		{
+			return i;
+		}
+	}
+
+	var tag = vNode.$;
+
+	if (tag === 4)
+	{
+		var subNode = vNode.k;
+
+		while (subNode.$ === 4)
+		{
+			subNode = subNode.k;
+		}
+
+		return _VirtualDom_addDomNodesHelp(domNode, subNode, patches, i, low + 1, high, domNode.elm_event_node_ref);
+	}
+
+	// tag must be 1 or 2 at this point
+
+	var vKids = vNode.e;
+	var childNodes = domNode.childNodes;
+	for (var j = 0; j < vKids.length; j++)
+	{
+		low++;
+		var vKid = tag === 1 ? vKids[j] : vKids[j].b;
+		var nextLow = low + (vKid.b || 0);
+		if (low <= index && index <= nextLow)
+		{
+			i = _VirtualDom_addDomNodesHelp(childNodes[j], vKid, patches, i, low, nextLow, eventNode);
+			if (!(patch = patches[i]) || (index = patch.r) > high)
+			{
+				return i;
+			}
+		}
+		low = nextLow;
+	}
+	return i;
+}
+
+
+
+// APPLY PATCHES
+
+
+function _VirtualDom_applyPatches(rootDomNode, oldVirtualNode, patches, eventNode)
+{
+	if (patches.length === 0)
+	{
+		return rootDomNode;
+	}
+
+	_VirtualDom_addDomNodes(rootDomNode, oldVirtualNode, patches, eventNode);
+	return _VirtualDom_applyPatchesHelp(rootDomNode, patches);
+}
+
+function _VirtualDom_applyPatchesHelp(rootDomNode, patches)
+{
+	for (var i = 0; i < patches.length; i++)
+	{
+		var patch = patches[i];
+		var localDomNode = patch.t
+		var newNode = _VirtualDom_applyPatch(localDomNode, patch);
+		if (localDomNode === rootDomNode)
+		{
+			rootDomNode = newNode;
+		}
+	}
+	return rootDomNode;
+}
+
+function _VirtualDom_applyPatch(domNode, patch)
+{
+	switch (patch.$)
+	{
+		case 0:
+			return _VirtualDom_applyPatchRedraw(domNode, patch.s, patch.u);
+
+		case 4:
+			_VirtualDom_applyFacts(domNode, patch.u, patch.s);
+			return domNode;
+
+		case 3:
+			domNode.replaceData(0, domNode.length, patch.s);
+			return domNode;
+
+		case 1:
+			return _VirtualDom_applyPatchesHelp(domNode, patch.s);
+
+		case 2:
+			if (domNode.elm_event_node_ref)
+			{
+				domNode.elm_event_node_ref.j = patch.s;
+			}
+			else
+			{
+				domNode.elm_event_node_ref = { j: patch.s, p: patch.u };
+			}
+			return domNode;
+
+		case 6:
+			var data = patch.s;
+			for (var i = 0; i < data.i; i++)
+			{
+				domNode.removeChild(domNode.childNodes[data.v]);
+			}
+			return domNode;
+
+		case 7:
+			var data = patch.s;
+			var kids = data.e;
+			var i = data.v;
+			var theEnd = domNode.childNodes[i];
+			for (; i < kids.length; i++)
+			{
+				domNode.insertBefore(_VirtualDom_render(kids[i], patch.u), theEnd);
+			}
+			return domNode;
+
+		case 9:
+			var data = patch.s;
+			if (!data)
+			{
+				domNode.parentNode.removeChild(domNode);
+				return domNode;
+			}
+			var entry = data.A;
+			if (typeof entry.r !== 'undefined')
+			{
+				domNode.parentNode.removeChild(domNode);
+			}
+			entry.s = _VirtualDom_applyPatchesHelp(domNode, data.w);
+			return domNode;
+
+		case 8:
+			return _VirtualDom_applyPatchReorder(domNode, patch);
+
+		case 5:
+			return patch.s(domNode);
+
+		default:
+			_Debug_crash(10); // 'Ran into an unknown patch!'
+	}
+}
+
+
+function _VirtualDom_applyPatchRedraw(domNode, vNode, eventNode)
+{
+	var parentNode = domNode.parentNode;
+	var newNode = _VirtualDom_render(vNode, eventNode);
+
+	if (!newNode.elm_event_node_ref)
+	{
+		newNode.elm_event_node_ref = domNode.elm_event_node_ref;
+	}
+
+	if (parentNode && newNode !== domNode)
+	{
+		parentNode.replaceChild(newNode, domNode);
+	}
+	return newNode;
+}
+
+
+function _VirtualDom_applyPatchReorder(domNode, patch)
+{
+	var data = patch.s;
+
+	// remove end inserts
+	var frag = _VirtualDom_applyPatchReorderEndInsertsHelp(data.y, patch);
+
+	// removals
+	domNode = _VirtualDom_applyPatchesHelp(domNode, data.w);
+
+	// inserts
+	var inserts = data.x;
+	for (var i = 0; i < inserts.length; i++)
+	{
+		var insert = inserts[i];
+		var entry = insert.A;
+		var node = entry.c === 2
+			? entry.s
+			: _VirtualDom_render(entry.z, patch.u);
+		domNode.insertBefore(node, domNode.childNodes[insert.r]);
+	}
+
+	// add end inserts
+	if (frag)
+	{
+		_VirtualDom_appendChild(domNode, frag);
+	}
+
+	return domNode;
+}
+
+
+function _VirtualDom_applyPatchReorderEndInsertsHelp(endInserts, patch)
+{
+	if (!endInserts)
+	{
+		return;
+	}
+
+	var frag = _VirtualDom_doc.createDocumentFragment();
+	for (var i = 0; i < endInserts.length; i++)
+	{
+		var insert = endInserts[i];
+		var entry = insert.A;
+		_VirtualDom_appendChild(frag, entry.c === 2
+			? entry.s
+			: _VirtualDom_render(entry.z, patch.u)
+		);
+	}
+	return frag;
+}
+
+
+function _VirtualDom_virtualize(node)
+{
+	// TEXT NODES
+
+	if (node.nodeType === 3)
+	{
+		return _VirtualDom_text(node.textContent);
+	}
+
+
+	// WEIRD NODES
+
+	if (node.nodeType !== 1)
+	{
+		return _VirtualDom_text('');
+	}
+
+
+	// ELEMENT NODES
+
+	var attrList = _List_Nil;
+	var attrs = node.attributes;
+	for (var i = attrs.length; i--; )
+	{
+		var attr = attrs[i];
+		var name = attr.name;
+		var value = attr.value;
+		attrList = _List_Cons( A2(_VirtualDom_attribute, name, value), attrList );
+	}
+
+	var tag = node.tagName.toLowerCase();
+	var kidList = _List_Nil;
+	var kids = node.childNodes;
+
+	for (var i = kids.length; i--; )
+	{
+		kidList = _List_Cons(_VirtualDom_virtualize(kids[i]), kidList);
+	}
+	return A3(_VirtualDom_node, tag, attrList, kidList);
+}
+
+function _VirtualDom_dekey(keyedNode)
+{
+	var keyedKids = keyedNode.e;
+	var len = keyedKids.length;
+	var kids = new Array(len);
+	for (var i = 0; i < len; i++)
+	{
+		kids[i] = keyedKids[i].b;
+	}
+
+	return {
+		$: 1,
+		c: keyedNode.c,
+		d: keyedNode.d,
+		e: kids,
+		f: keyedNode.f,
+		b: keyedNode.b
+	};
+}
+
+
+
+
+// ELEMENT
+
+
+var _Debugger_element;
+
+var _Browser_element = _Debugger_element || F4(function(impl, flagDecoder, debugMetadata, args)
+{
+	return _Platform_initialize(
+		flagDecoder,
+		args,
+		impl.at,
+		impl.aB,
+		impl.az,
+		function(sendToApp, initialModel) {
+			var view = impl.aC;
+			/**/
+			var domNode = args['node'];
+			//*/
+			/**_UNUSED/
+			var domNode = args && args['node'] ? args['node'] : _Debug_crash(0);
+			//*/
+			var currNode = _VirtualDom_virtualize(domNode);
+
+			return _Browser_makeAnimator(initialModel, function(model)
+			{
+				var nextNode = view(model);
+				var patches = _VirtualDom_diff(currNode, nextNode);
+				domNode = _VirtualDom_applyPatches(domNode, currNode, patches, sendToApp);
+				currNode = nextNode;
+			});
+		}
+	);
+});
+
+
+
+// DOCUMENT
+
+
+var _Debugger_document;
+
+var _Browser_document = _Debugger_document || F4(function(impl, flagDecoder, debugMetadata, args)
+{
+	return _Platform_initialize(
+		flagDecoder,
+		args,
+		impl.at,
+		impl.aB,
+		impl.az,
+		function(sendToApp, initialModel) {
+			var divertHrefToApp = impl.H && impl.H(sendToApp)
+			var view = impl.aC;
+			var title = _VirtualDom_doc.title;
+			var bodyNode = _VirtualDom_doc.body;
+			var currNode = _VirtualDom_virtualize(bodyNode);
+			return _Browser_makeAnimator(initialModel, function(model)
+			{
+				_VirtualDom_divertHrefToApp = divertHrefToApp;
+				var doc = view(model);
+				var nextNode = _VirtualDom_node('body')(_List_Nil)(doc.am);
+				var patches = _VirtualDom_diff(currNode, nextNode);
+				bodyNode = _VirtualDom_applyPatches(bodyNode, currNode, patches, sendToApp);
+				currNode = nextNode;
+				_VirtualDom_divertHrefToApp = 0;
+				(title !== doc.aA) && (_VirtualDom_doc.title = title = doc.aA);
+			});
+		}
+	);
+});
+
+
+
+// ANIMATION
+
+
+var _Browser_cancelAnimationFrame =
+	typeof cancelAnimationFrame !== 'undefined'
+		? cancelAnimationFrame
+		: function(id) { clearTimeout(id); };
+
+var _Browser_requestAnimationFrame =
+	typeof requestAnimationFrame !== 'undefined'
+		? requestAnimationFrame
+		: function(callback) { return setTimeout(callback, 1000 / 60); };
+
+
+function _Browser_makeAnimator(model, draw)
+{
+	draw(model);
+
+	var state = 0;
+
+	function updateIfNeeded()
+	{
+		state = state === 1
+			? 0
+			: ( _Browser_requestAnimationFrame(updateIfNeeded), draw(model), 1 );
+	}
+
+	return function(nextModel, isSync)
+	{
+		model = nextModel;
+
+		isSync
+			? ( draw(model),
+				state === 2 && (state = 1)
+				)
+			: ( state === 0 && _Browser_requestAnimationFrame(updateIfNeeded),
+				state = 2
+				);
+	};
+}
+
+
+
+// APPLICATION
+
+
+function _Browser_application(impl)
+{
+	var onUrlChange = impl.av;
+	var onUrlRequest = impl.aw;
+	var key = function() { key.a(onUrlChange(_Browser_getUrl())); };
+
+	return _Browser_document({
+		H: function(sendToApp)
+		{
+			key.a = sendToApp;
+			_Browser_window.addEventListener('popstate', key);
+			_Browser_window.navigator.userAgent.indexOf('Trident') < 0 || _Browser_window.addEventListener('hashchange', key);
+
+			return F2(function(domNode, event)
+			{
+				if (!event.ctrlKey && !event.metaKey && !event.shiftKey && event.button < 1 && !domNode.target && !domNode.hasAttribute('download'))
+				{
+					event.preventDefault();
+					var href = domNode.href;
+					var curr = _Browser_getUrl();
+					var next = $elm$url$Url$fromString(href).a;
+					sendToApp(onUrlRequest(
+						(next
+							&& curr._ === next._
+							&& curr.R === next.R
+							&& curr.X.a === next.X.a
+						)
+							? $elm$browser$Browser$Internal(next)
+							: $elm$browser$Browser$External(href)
+					));
+				}
+			});
+		},
+		at: function(flags)
+		{
+			return A3(impl.at, flags, _Browser_getUrl(), key);
+		},
+		aC: impl.aC,
+		aB: impl.aB,
+		az: impl.az
+	});
+}
+
+function _Browser_getUrl()
+{
+	return $elm$url$Url$fromString(_VirtualDom_doc.location.href).a || _Debug_crash(1);
+}
+
+var _Browser_go = F2(function(key, n)
+{
+	return A2($elm$core$Task$perform, $elm$core$Basics$never, _Scheduler_binding(function() {
+		n && history.go(n);
+		key();
+	}));
+});
+
+var _Browser_pushUrl = F2(function(key, url)
+{
+	return A2($elm$core$Task$perform, $elm$core$Basics$never, _Scheduler_binding(function() {
+		history.pushState({}, '', url);
+		key();
+	}));
+});
+
+var _Browser_replaceUrl = F2(function(key, url)
+{
+	return A2($elm$core$Task$perform, $elm$core$Basics$never, _Scheduler_binding(function() {
+		history.replaceState({}, '', url);
+		key();
+	}));
+});
+
+
+
+// GLOBAL EVENTS
+
+
+var _Browser_fakeNode = { addEventListener: function() {}, removeEventListener: function() {} };
+var _Browser_doc = typeof document !== 'undefined' ? document : _Browser_fakeNode;
+var _Browser_window = typeof window !== 'undefined' ? window : _Browser_fakeNode;
+
+var _Browser_on = F3(function(node, eventName, sendToSelf)
+{
+	return _Scheduler_spawn(_Scheduler_binding(function(callback)
+	{
+		function handler(event)	{ _Scheduler_rawSpawn(sendToSelf(event)); }
+		node.addEventListener(eventName, handler, _VirtualDom_passiveSupported && { passive: true });
+		return function() { node.removeEventListener(eventName, handler); };
+	}));
+});
+
+var _Browser_decodeEvent = F2(function(decoder, event)
+{
+	var result = _Json_runHelp(decoder, event);
+	return $elm$core$Result$isOk(result) ? $elm$core$Maybe$Just(result.a) : $elm$core$Maybe$Nothing;
+});
+
+
+
+// PAGE VISIBILITY
+
+
+function _Browser_visibilityInfo()
+{
+	return (typeof _VirtualDom_doc.hidden !== 'undefined')
+		? { ar: 'hidden', an: 'visibilitychange' }
+		:
+	(typeof _VirtualDom_doc.mozHidden !== 'undefined')
+		? { ar: 'mozHidden', an: 'mozvisibilitychange' }
+		:
+	(typeof _VirtualDom_doc.msHidden !== 'undefined')
+		? { ar: 'msHidden', an: 'msvisibilitychange' }
+		:
+	(typeof _VirtualDom_doc.webkitHidden !== 'undefined')
+		? { ar: 'webkitHidden', an: 'webkitvisibilitychange' }
+		: { ar: 'hidden', an: 'visibilitychange' };
+}
+
+
+
+// ANIMATION FRAMES
+
+
+function _Browser_rAF()
+{
+	return _Scheduler_binding(function(callback)
+	{
+		var id = _Browser_requestAnimationFrame(function() {
+			callback(_Scheduler_succeed(Date.now()));
+		});
+
+		return function() {
+			_Browser_cancelAnimationFrame(id);
+		};
+	});
+}
+
+
+function _Browser_now()
+{
+	return _Scheduler_binding(function(callback)
+	{
+		callback(_Scheduler_succeed(Date.now()));
+	});
+}
+
+
+
+// DOM STUFF
+
+
+function _Browser_withNode(id, doStuff)
+{
+	return _Scheduler_binding(function(callback)
+	{
+		_Browser_requestAnimationFrame(function() {
+			var node = document.getElementById(id);
+			callback(node
+				? _Scheduler_succeed(doStuff(node))
+				: _Scheduler_fail($elm$browser$Browser$Dom$NotFound(id))
+			);
+		});
+	});
+}
+
+
+function _Browser_withWindow(doStuff)
+{
+	return _Scheduler_binding(function(callback)
+	{
+		_Browser_requestAnimationFrame(function() {
+			callback(_Scheduler_succeed(doStuff()));
+		});
+	});
+}
+
+
+// FOCUS and BLUR
+
+
+var _Browser_call = F2(function(functionName, id)
+{
+	return _Browser_withNode(id, function(node) {
+		node[functionName]();
+		return _Utils_Tuple0;
+	});
+});
+
+
+
+// WINDOW VIEWPORT
+
+
+function _Browser_getViewport()
+{
+	return {
+		ad: _Browser_getScene(),
+		ag: {
+			ai: _Browser_window.pageXOffset,
+			aj: _Browser_window.pageYOffset,
+			ah: _Browser_doc.documentElement.clientWidth,
+			Q: _Browser_doc.documentElement.clientHeight
+		}
+	};
+}
+
+function _Browser_getScene()
+{
+	var body = _Browser_doc.body;
+	var elem = _Browser_doc.documentElement;
+	return {
+		ah: Math.max(body.scrollWidth, body.offsetWidth, elem.scrollWidth, elem.offsetWidth, elem.clientWidth),
+		Q: Math.max(body.scrollHeight, body.offsetHeight, elem.scrollHeight, elem.offsetHeight, elem.clientHeight)
+	};
+}
+
+var _Browser_setViewport = F2(function(x, y)
+{
+	return _Browser_withWindow(function()
+	{
+		_Browser_window.scroll(x, y);
+		return _Utils_Tuple0;
+	});
+});
+
+
+
+// ELEMENT VIEWPORT
+
+
+function _Browser_getViewportOf(id)
+{
+	return _Browser_withNode(id, function(node)
+	{
+		return {
+			ad: {
+				ah: node.scrollWidth,
+				Q: node.scrollHeight
+			},
+			ag: {
+				ai: node.scrollLeft,
+				aj: node.scrollTop,
+				ah: node.clientWidth,
+				Q: node.clientHeight
+			}
+		};
+	});
+}
+
+
+var _Browser_setViewportOf = F3(function(id, x, y)
+{
+	return _Browser_withNode(id, function(node)
+	{
+		node.scrollLeft = x;
+		node.scrollTop = y;
+		return _Utils_Tuple0;
+	});
+});
+
+
+
+// ELEMENT
+
+
+function _Browser_getElement(id)
+{
+	return _Browser_withNode(id, function(node)
+	{
+		var rect = node.getBoundingClientRect();
+		var x = _Browser_window.pageXOffset;
+		var y = _Browser_window.pageYOffset;
+		return {
+			ad: _Browser_getScene(),
+			ag: {
+				ai: x,
+				aj: y,
+				ah: _Browser_doc.documentElement.clientWidth,
+				Q: _Browser_doc.documentElement.clientHeight
+			},
+			ap: {
+				ai: x + rect.left,
+				aj: y + rect.top,
+				ah: rect.width,
+				Q: rect.height
+			}
+		};
+	});
+}
+
+
+
+// LOAD and RELOAD
+
+
+function _Browser_reload(skipCache)
+{
+	return A2($elm$core$Task$perform, $elm$core$Basics$never, _Scheduler_binding(function(callback)
+	{
+		_VirtualDom_doc.location.reload(skipCache);
+	}));
+}
+
+function _Browser_load(url)
+{
+	return A2($elm$core$Task$perform, $elm$core$Basics$never, _Scheduler_binding(function(callback)
+	{
+		try
+		{
+			_Browser_window.location = url;
+		}
+		catch(err)
+		{
+			// Only Firefox can throw a NS_ERROR_MALFORMED_URI exception here.
+			// Other browsers reload the page, so let's be consistent about that.
+			_VirtualDom_doc.location.reload(false);
+		}
+	}));
+}
+var $author$project$Main$init = 0;
+var $elm$core$Basics$EQ = 1;
+var $elm$core$Basics$GT = 2;
+var $elm$core$Basics$LT = 0;
+var $elm$core$List$cons = _List_cons;
+var $elm$core$Dict$foldr = F3(
+	function (func, acc, t) {
+		foldr:
+		while (true) {
+			if (t.$ === -2) {
+				return acc;
+			} else {
+				var key = t.b;
+				var value = t.c;
+				var left = t.d;
+				var right = t.e;
+				var $temp$func = func,
+					$temp$acc = A3(
+					func,
+					key,
+					value,
+					A3($elm$core$Dict$foldr, func, acc, right)),
+					$temp$t = left;
+				func = $temp$func;
+				acc = $temp$acc;
+				t = $temp$t;
+				continue foldr;
+			}
+		}
+	});
+var $elm$core$Dict$toList = function (dict) {
+	return A3(
+		$elm$core$Dict$foldr,
+		F3(
+			function (key, value, list) {
+				return A2(
+					$elm$core$List$cons,
+					_Utils_Tuple2(key, value),
+					list);
+			}),
+		_List_Nil,
+		dict);
+};
+var $elm$core$Dict$keys = function (dict) {
+	return A3(
+		$elm$core$Dict$foldr,
+		F3(
+			function (key, value, keyList) {
+				return A2($elm$core$List$cons, key, keyList);
+			}),
+		_List_Nil,
+		dict);
+};
+var $elm$core$Set$toList = function (_v0) {
+	var dict = _v0;
+	return $elm$core$Dict$keys(dict);
+};
+var $elm$core$Elm$JsArray$foldr = _JsArray_foldr;
+var $elm$core$Array$foldr = F3(
+	function (func, baseCase, _v0) {
+		var tree = _v0.c;
+		var tail = _v0.d;
+		var helper = F2(
+			function (node, acc) {
+				if (!node.$) {
+					var subTree = node.a;
+					return A3($elm$core$Elm$JsArray$foldr, helper, acc, subTree);
+				} else {
+					var values = node.a;
+					return A3($elm$core$Elm$JsArray$foldr, func, acc, values);
+				}
+			});
+		return A3(
+			$elm$core$Elm$JsArray$foldr,
+			helper,
+			A3($elm$core$Elm$JsArray$foldr, func, baseCase, tail),
+			tree);
+	});
+var $elm$core$Array$toList = function (array) {
+	return A3($elm$core$Array$foldr, $elm$core$List$cons, _List_Nil, array);
+};
+var $elm$core$Result$Err = function (a) {
+	return {$: 1, a: a};
+};
+var $elm$json$Json$Decode$Failure = F2(
+	function (a, b) {
+		return {$: 3, a: a, b: b};
+	});
+var $elm$json$Json$Decode$Field = F2(
+	function (a, b) {
+		return {$: 0, a: a, b: b};
+	});
+var $elm$json$Json$Decode$Index = F2(
+	function (a, b) {
+		return {$: 1, a: a, b: b};
+	});
+var $elm$core$Result$Ok = function (a) {
+	return {$: 0, a: a};
+};
+var $elm$json$Json$Decode$OneOf = function (a) {
+	return {$: 2, a: a};
+};
+var $elm$core$Basics$False = 1;
+var $elm$core$Basics$add = _Basics_add;
+var $elm$core$Maybe$Just = function (a) {
+	return {$: 0, a: a};
+};
+var $elm$core$Maybe$Nothing = {$: 1};
+var $elm$core$String$all = _String_all;
+var $elm$core$Basics$and = _Basics_and;
+var $elm$core$Basics$append = _Utils_append;
+var $elm$json$Json$Encode$encode = _Json_encode;
+var $elm$core$String$fromInt = _String_fromNumber;
+var $elm$core$String$join = F2(
+	function (sep, chunks) {
+		return A2(
+			_String_join,
+			sep,
+			_List_toArray(chunks));
+	});
+var $elm$core$String$split = F2(
+	function (sep, string) {
+		return _List_fromArray(
+			A2(_String_split, sep, string));
+	});
+var $elm$json$Json$Decode$indent = function (str) {
+	return A2(
+		$elm$core$String$join,
+		'\n    ',
+		A2($elm$core$String$split, '\n', str));
+};
+var $elm$core$List$foldl = F3(
+	function (func, acc, list) {
+		foldl:
+		while (true) {
+			if (!list.b) {
+				return acc;
+			} else {
+				var x = list.a;
+				var xs = list.b;
+				var $temp$func = func,
+					$temp$acc = A2(func, x, acc),
+					$temp$list = xs;
+				func = $temp$func;
+				acc = $temp$acc;
+				list = $temp$list;
+				continue foldl;
+			}
+		}
+	});
+var $elm$core$List$length = function (xs) {
+	return A3(
+		$elm$core$List$foldl,
+		F2(
+			function (_v0, i) {
+				return i + 1;
+			}),
+		0,
+		xs);
+};
+var $elm$core$List$map2 = _List_map2;
+var $elm$core$Basics$le = _Utils_le;
+var $elm$core$Basics$sub = _Basics_sub;
+var $elm$core$List$rangeHelp = F3(
+	function (lo, hi, list) {
+		rangeHelp:
+		while (true) {
+			if (_Utils_cmp(lo, hi) < 1) {
+				var $temp$lo = lo,
+					$temp$hi = hi - 1,
+					$temp$list = A2($elm$core$List$cons, hi, list);
+				lo = $temp$lo;
+				hi = $temp$hi;
+				list = $temp$list;
+				continue rangeHelp;
+			} else {
+				return list;
+			}
+		}
+	});
+var $elm$core$List$range = F2(
+	function (lo, hi) {
+		return A3($elm$core$List$rangeHelp, lo, hi, _List_Nil);
+	});
+var $elm$core$List$indexedMap = F2(
+	function (f, xs) {
+		return A3(
+			$elm$core$List$map2,
+			f,
+			A2(
+				$elm$core$List$range,
+				0,
+				$elm$core$List$length(xs) - 1),
+			xs);
+	});
+var $elm$core$Char$toCode = _Char_toCode;
+var $elm$core$Char$isLower = function (_char) {
+	var code = $elm$core$Char$toCode(_char);
+	return (97 <= code) && (code <= 122);
+};
+var $elm$core$Char$isUpper = function (_char) {
+	var code = $elm$core$Char$toCode(_char);
+	return (code <= 90) && (65 <= code);
+};
+var $elm$core$Basics$or = _Basics_or;
+var $elm$core$Char$isAlpha = function (_char) {
+	return $elm$core$Char$isLower(_char) || $elm$core$Char$isUpper(_char);
+};
+var $elm$core$Char$isDigit = function (_char) {
+	var code = $elm$core$Char$toCode(_char);
+	return (code <= 57) && (48 <= code);
+};
+var $elm$core$Char$isAlphaNum = function (_char) {
+	return $elm$core$Char$isLower(_char) || ($elm$core$Char$isUpper(_char) || $elm$core$Char$isDigit(_char));
+};
+var $elm$core$List$reverse = function (list) {
+	return A3($elm$core$List$foldl, $elm$core$List$cons, _List_Nil, list);
+};
+var $elm$core$String$uncons = _String_uncons;
+var $elm$json$Json$Decode$errorOneOf = F2(
+	function (i, error) {
+		return '\n\n(' + ($elm$core$String$fromInt(i + 1) + (') ' + $elm$json$Json$Decode$indent(
+			$elm$json$Json$Decode$errorToString(error))));
+	});
+var $elm$json$Json$Decode$errorToString = function (error) {
+	return A2($elm$json$Json$Decode$errorToStringHelp, error, _List_Nil);
+};
+var $elm$json$Json$Decode$errorToStringHelp = F2(
+	function (error, context) {
+		errorToStringHelp:
+		while (true) {
+			switch (error.$) {
+				case 0:
+					var f = error.a;
+					var err = error.b;
+					var isSimple = function () {
+						var _v1 = $elm$core$String$uncons(f);
+						if (_v1.$ === 1) {
+							return false;
+						} else {
+							var _v2 = _v1.a;
+							var _char = _v2.a;
+							var rest = _v2.b;
+							return $elm$core$Char$isAlpha(_char) && A2($elm$core$String$all, $elm$core$Char$isAlphaNum, rest);
+						}
+					}();
+					var fieldName = isSimple ? ('.' + f) : ('[\'' + (f + '\']'));
+					var $temp$error = err,
+						$temp$context = A2($elm$core$List$cons, fieldName, context);
+					error = $temp$error;
+					context = $temp$context;
+					continue errorToStringHelp;
+				case 1:
+					var i = error.a;
+					var err = error.b;
+					var indexName = '[' + ($elm$core$String$fromInt(i) + ']');
+					var $temp$error = err,
+						$temp$context = A2($elm$core$List$cons, indexName, context);
+					error = $temp$error;
+					context = $temp$context;
+					continue errorToStringHelp;
+				case 2:
+					var errors = error.a;
+					if (!errors.b) {
+						return 'Ran into a Json.Decode.oneOf with no possibilities' + function () {
+							if (!context.b) {
+								return '!';
+							} else {
+								return ' at json' + A2(
+									$elm$core$String$join,
+									'',
+									$elm$core$List$reverse(context));
+							}
+						}();
+					} else {
+						if (!errors.b.b) {
+							var err = errors.a;
+							var $temp$error = err,
+								$temp$context = context;
+							error = $temp$error;
+							context = $temp$context;
+							continue errorToStringHelp;
+						} else {
+							var starter = function () {
+								if (!context.b) {
+									return 'Json.Decode.oneOf';
+								} else {
+									return 'The Json.Decode.oneOf at json' + A2(
+										$elm$core$String$join,
+										'',
+										$elm$core$List$reverse(context));
+								}
+							}();
+							var introduction = starter + (' failed in the following ' + ($elm$core$String$fromInt(
+								$elm$core$List$length(errors)) + ' ways:'));
+							return A2(
+								$elm$core$String$join,
+								'\n\n',
+								A2(
+									$elm$core$List$cons,
+									introduction,
+									A2($elm$core$List$indexedMap, $elm$json$Json$Decode$errorOneOf, errors)));
+						}
+					}
+				default:
+					var msg = error.a;
+					var json = error.b;
+					var introduction = function () {
+						if (!context.b) {
+							return 'Problem with the given value:\n\n';
+						} else {
+							return 'Problem with the value at json' + (A2(
+								$elm$core$String$join,
+								'',
+								$elm$core$List$reverse(context)) + ':\n\n    ');
+						}
+					}();
+					return introduction + ($elm$json$Json$Decode$indent(
+						A2($elm$json$Json$Encode$encode, 4, json)) + ('\n\n' + msg));
+			}
+		}
+	});
+var $elm$core$Array$branchFactor = 32;
+var $elm$core$Array$Array_elm_builtin = F4(
+	function (a, b, c, d) {
+		return {$: 0, a: a, b: b, c: c, d: d};
+	});
+var $elm$core$Elm$JsArray$empty = _JsArray_empty;
+var $elm$core$Basics$ceiling = _Basics_ceiling;
+var $elm$core$Basics$fdiv = _Basics_fdiv;
+var $elm$core$Basics$logBase = F2(
+	function (base, number) {
+		return _Basics_log(number) / _Basics_log(base);
+	});
+var $elm$core$Basics$toFloat = _Basics_toFloat;
+var $elm$core$Array$shiftStep = $elm$core$Basics$ceiling(
+	A2($elm$core$Basics$logBase, 2, $elm$core$Array$branchFactor));
+var $elm$core$Array$empty = A4($elm$core$Array$Array_elm_builtin, 0, $elm$core$Array$shiftStep, $elm$core$Elm$JsArray$empty, $elm$core$Elm$JsArray$empty);
+var $elm$core$Elm$JsArray$initialize = _JsArray_initialize;
+var $elm$core$Array$Leaf = function (a) {
+	return {$: 1, a: a};
+};
+var $elm$core$Basics$apL = F2(
+	function (f, x) {
+		return f(x);
+	});
+var $elm$core$Basics$apR = F2(
+	function (x, f) {
+		return f(x);
+	});
+var $elm$core$Basics$eq = _Utils_equal;
+var $elm$core$Basics$floor = _Basics_floor;
+var $elm$core$Elm$JsArray$length = _JsArray_length;
+var $elm$core$Basics$gt = _Utils_gt;
+var $elm$core$Basics$max = F2(
+	function (x, y) {
+		return (_Utils_cmp(x, y) > 0) ? x : y;
+	});
+var $elm$core$Basics$mul = _Basics_mul;
+var $elm$core$Array$SubTree = function (a) {
+	return {$: 0, a: a};
+};
+var $elm$core$Elm$JsArray$initializeFromList = _JsArray_initializeFromList;
+var $elm$core$Array$compressNodes = F2(
+	function (nodes, acc) {
+		compressNodes:
+		while (true) {
+			var _v0 = A2($elm$core$Elm$JsArray$initializeFromList, $elm$core$Array$branchFactor, nodes);
+			var node = _v0.a;
+			var remainingNodes = _v0.b;
+			var newAcc = A2(
+				$elm$core$List$cons,
+				$elm$core$Array$SubTree(node),
+				acc);
+			if (!remainingNodes.b) {
+				return $elm$core$List$reverse(newAcc);
+			} else {
+				var $temp$nodes = remainingNodes,
+					$temp$acc = newAcc;
+				nodes = $temp$nodes;
+				acc = $temp$acc;
+				continue compressNodes;
+			}
+		}
+	});
+var $elm$core$Tuple$first = function (_v0) {
+	var x = _v0.a;
+	return x;
+};
+var $elm$core$Array$treeFromBuilder = F2(
+	function (nodeList, nodeListSize) {
+		treeFromBuilder:
+		while (true) {
+			var newNodeSize = $elm$core$Basics$ceiling(nodeListSize / $elm$core$Array$branchFactor);
+			if (newNodeSize === 1) {
+				return A2($elm$core$Elm$JsArray$initializeFromList, $elm$core$Array$branchFactor, nodeList).a;
+			} else {
+				var $temp$nodeList = A2($elm$core$Array$compressNodes, nodeList, _List_Nil),
+					$temp$nodeListSize = newNodeSize;
+				nodeList = $temp$nodeList;
+				nodeListSize = $temp$nodeListSize;
+				continue treeFromBuilder;
+			}
+		}
+	});
+var $elm$core$Array$builderToArray = F2(
+	function (reverseNodeList, builder) {
+		if (!builder.a) {
+			return A4(
+				$elm$core$Array$Array_elm_builtin,
+				$elm$core$Elm$JsArray$length(builder.c),
+				$elm$core$Array$shiftStep,
+				$elm$core$Elm$JsArray$empty,
+				builder.c);
+		} else {
+			var treeLen = builder.a * $elm$core$Array$branchFactor;
+			var depth = $elm$core$Basics$floor(
+				A2($elm$core$Basics$logBase, $elm$core$Array$branchFactor, treeLen - 1));
+			var correctNodeList = reverseNodeList ? $elm$core$List$reverse(builder.d) : builder.d;
+			var tree = A2($elm$core$Array$treeFromBuilder, correctNodeList, builder.a);
+			return A4(
+				$elm$core$Array$Array_elm_builtin,
+				$elm$core$Elm$JsArray$length(builder.c) + treeLen,
+				A2($elm$core$Basics$max, 5, depth * $elm$core$Array$shiftStep),
+				tree,
+				builder.c);
+		}
+	});
+var $elm$core$Basics$idiv = _Basics_idiv;
+var $elm$core$Basics$lt = _Utils_lt;
+var $elm$core$Array$initializeHelp = F5(
+	function (fn, fromIndex, len, nodeList, tail) {
+		initializeHelp:
+		while (true) {
+			if (fromIndex < 0) {
+				return A2(
+					$elm$core$Array$builderToArray,
+					false,
+					{d: nodeList, a: (len / $elm$core$Array$branchFactor) | 0, c: tail});
+			} else {
+				var leaf = $elm$core$Array$Leaf(
+					A3($elm$core$Elm$JsArray$initialize, $elm$core$Array$branchFactor, fromIndex, fn));
+				var $temp$fn = fn,
+					$temp$fromIndex = fromIndex - $elm$core$Array$branchFactor,
+					$temp$len = len,
+					$temp$nodeList = A2($elm$core$List$cons, leaf, nodeList),
+					$temp$tail = tail;
+				fn = $temp$fn;
+				fromIndex = $temp$fromIndex;
+				len = $temp$len;
+				nodeList = $temp$nodeList;
+				tail = $temp$tail;
+				continue initializeHelp;
+			}
+		}
+	});
+var $elm$core$Basics$remainderBy = _Basics_remainderBy;
+var $elm$core$Array$initialize = F2(
+	function (len, fn) {
+		if (len <= 0) {
+			return $elm$core$Array$empty;
+		} else {
+			var tailLen = len % $elm$core$Array$branchFactor;
+			var tail = A3($elm$core$Elm$JsArray$initialize, tailLen, len - tailLen, fn);
+			var initialFromIndex = (len - tailLen) - $elm$core$Array$branchFactor;
+			return A5($elm$core$Array$initializeHelp, fn, initialFromIndex, len, _List_Nil, tail);
+		}
+	});
+var $elm$core$Basics$True = 0;
+var $elm$core$Result$isOk = function (result) {
+	if (!result.$) {
+		return true;
+	} else {
+		return false;
+	}
+};
+var $elm$json$Json$Decode$map = _Json_map1;
+var $elm$json$Json$Decode$map2 = _Json_map2;
+var $elm$json$Json$Decode$succeed = _Json_succeed;
+var $elm$virtual_dom$VirtualDom$toHandlerInt = function (handler) {
+	switch (handler.$) {
+		case 0:
+			return 0;
+		case 1:
+			return 1;
+		case 2:
+			return 2;
+		default:
+			return 3;
+	}
+};
+var $elm$browser$Browser$External = function (a) {
+	return {$: 1, a: a};
+};
+var $elm$browser$Browser$Internal = function (a) {
+	return {$: 0, a: a};
+};
+var $elm$core$Basics$identity = function (x) {
+	return x;
+};
+var $elm$browser$Browser$Dom$NotFound = $elm$core$Basics$identity;
+var $elm$url$Url$Http = 0;
+var $elm$url$Url$Https = 1;
+var $elm$url$Url$Url = F6(
+	function (protocol, host, port_, path, query, fragment) {
+		return {P: fragment, R: host, V: path, X: port_, _: protocol, aa: query};
+	});
+var $elm$core$String$contains = _String_contains;
+var $elm$core$String$length = _String_length;
+var $elm$core$String$slice = _String_slice;
+var $elm$core$String$dropLeft = F2(
+	function (n, string) {
+		return (n < 1) ? string : A3(
+			$elm$core$String$slice,
+			n,
+			$elm$core$String$length(string),
+			string);
+	});
+var $elm$core$String$indexes = _String_indexes;
+var $elm$core$String$isEmpty = function (string) {
+	return string === '';
+};
+var $elm$core$String$left = F2(
+	function (n, string) {
+		return (n < 1) ? '' : A3($elm$core$String$slice, 0, n, string);
+	});
+var $elm$core$String$toInt = _String_toInt;
+var $elm$url$Url$chompBeforePath = F5(
+	function (protocol, path, params, frag, str) {
+		if ($elm$core$String$isEmpty(str) || A2($elm$core$String$contains, '@', str)) {
+			return $elm$core$Maybe$Nothing;
+		} else {
+			var _v0 = A2($elm$core$String$indexes, ':', str);
+			if (!_v0.b) {
+				return $elm$core$Maybe$Just(
+					A6($elm$url$Url$Url, protocol, str, $elm$core$Maybe$Nothing, path, params, frag));
+			} else {
+				if (!_v0.b.b) {
+					var i = _v0.a;
+					var _v1 = $elm$core$String$toInt(
+						A2($elm$core$String$dropLeft, i + 1, str));
+					if (_v1.$ === 1) {
+						return $elm$core$Maybe$Nothing;
+					} else {
+						var port_ = _v1;
+						return $elm$core$Maybe$Just(
+							A6(
+								$elm$url$Url$Url,
+								protocol,
+								A2($elm$core$String$left, i, str),
+								port_,
+								path,
+								params,
+								frag));
+					}
+				} else {
+					return $elm$core$Maybe$Nothing;
+				}
+			}
+		}
+	});
+var $elm$url$Url$chompBeforeQuery = F4(
+	function (protocol, params, frag, str) {
+		if ($elm$core$String$isEmpty(str)) {
+			return $elm$core$Maybe$Nothing;
+		} else {
+			var _v0 = A2($elm$core$String$indexes, '/', str);
+			if (!_v0.b) {
+				return A5($elm$url$Url$chompBeforePath, protocol, '/', params, frag, str);
+			} else {
+				var i = _v0.a;
+				return A5(
+					$elm$url$Url$chompBeforePath,
+					protocol,
+					A2($elm$core$String$dropLeft, i, str),
+					params,
+					frag,
+					A2($elm$core$String$left, i, str));
+			}
+		}
+	});
+var $elm$url$Url$chompBeforeFragment = F3(
+	function (protocol, frag, str) {
+		if ($elm$core$String$isEmpty(str)) {
+			return $elm$core$Maybe$Nothing;
+		} else {
+			var _v0 = A2($elm$core$String$indexes, '?', str);
+			if (!_v0.b) {
+				return A4($elm$url$Url$chompBeforeQuery, protocol, $elm$core$Maybe$Nothing, frag, str);
+			} else {
+				var i = _v0.a;
+				return A4(
+					$elm$url$Url$chompBeforeQuery,
+					protocol,
+					$elm$core$Maybe$Just(
+						A2($elm$core$String$dropLeft, i + 1, str)),
+					frag,
+					A2($elm$core$String$left, i, str));
+			}
+		}
+	});
+var $elm$url$Url$chompAfterProtocol = F2(
+	function (protocol, str) {
+		if ($elm$core$String$isEmpty(str)) {
+			return $elm$core$Maybe$Nothing;
+		} else {
+			var _v0 = A2($elm$core$String$indexes, '#', str);
+			if (!_v0.b) {
+				return A3($elm$url$Url$chompBeforeFragment, protocol, $elm$core$Maybe$Nothing, str);
+			} else {
+				var i = _v0.a;
+				return A3(
+					$elm$url$Url$chompBeforeFragment,
+					protocol,
+					$elm$core$Maybe$Just(
+						A2($elm$core$String$dropLeft, i + 1, str)),
+					A2($elm$core$String$left, i, str));
+			}
+		}
+	});
+var $elm$core$String$startsWith = _String_startsWith;
+var $elm$url$Url$fromString = function (str) {
+	return A2($elm$core$String$startsWith, 'http://', str) ? A2(
+		$elm$url$Url$chompAfterProtocol,
+		0,
+		A2($elm$core$String$dropLeft, 7, str)) : (A2($elm$core$String$startsWith, 'https://', str) ? A2(
+		$elm$url$Url$chompAfterProtocol,
+		1,
+		A2($elm$core$String$dropLeft, 8, str)) : $elm$core$Maybe$Nothing);
+};
+var $elm$core$Basics$never = function (_v0) {
+	never:
+	while (true) {
+		var nvr = _v0;
+		var $temp$_v0 = nvr;
+		_v0 = $temp$_v0;
+		continue never;
+	}
+};
+var $elm$core$Task$Perform = $elm$core$Basics$identity;
+var $elm$core$Task$succeed = _Scheduler_succeed;
+var $elm$core$Task$init = $elm$core$Task$succeed(0);
+var $elm$core$List$foldrHelper = F4(
+	function (fn, acc, ctr, ls) {
+		if (!ls.b) {
+			return acc;
+		} else {
+			var a = ls.a;
+			var r1 = ls.b;
+			if (!r1.b) {
+				return A2(fn, a, acc);
+			} else {
+				var b = r1.a;
+				var r2 = r1.b;
+				if (!r2.b) {
+					return A2(
+						fn,
+						a,
+						A2(fn, b, acc));
+				} else {
+					var c = r2.a;
+					var r3 = r2.b;
+					if (!r3.b) {
+						return A2(
+							fn,
+							a,
+							A2(
+								fn,
+								b,
+								A2(fn, c, acc)));
+					} else {
+						var d = r3.a;
+						var r4 = r3.b;
+						var res = (ctr > 500) ? A3(
+							$elm$core$List$foldl,
+							fn,
+							acc,
+							$elm$core$List$reverse(r4)) : A4($elm$core$List$foldrHelper, fn, acc, ctr + 1, r4);
+						return A2(
+							fn,
+							a,
+							A2(
+								fn,
+								b,
+								A2(
+									fn,
+									c,
+									A2(fn, d, res))));
+					}
+				}
+			}
+		}
+	});
+var $elm$core$List$foldr = F3(
+	function (fn, acc, ls) {
+		return A4($elm$core$List$foldrHelper, fn, acc, 0, ls);
+	});
+var $elm$core$List$map = F2(
+	function (f, xs) {
+		return A3(
+			$elm$core$List$foldr,
+			F2(
+				function (x, acc) {
+					return A2(
+						$elm$core$List$cons,
+						f(x),
+						acc);
+				}),
+			_List_Nil,
+			xs);
+	});
+var $elm$core$Task$andThen = _Scheduler_andThen;
+var $elm$core$Task$map = F2(
+	function (func, taskA) {
+		return A2(
+			$elm$core$Task$andThen,
+			function (a) {
+				return $elm$core$Task$succeed(
+					func(a));
+			},
+			taskA);
+	});
+var $elm$core$Task$map2 = F3(
+	function (func, taskA, taskB) {
+		return A2(
+			$elm$core$Task$andThen,
+			function (a) {
+				return A2(
+					$elm$core$Task$andThen,
+					function (b) {
+						return $elm$core$Task$succeed(
+							A2(func, a, b));
+					},
+					taskB);
+			},
+			taskA);
+	});
+var $elm$core$Task$sequence = function (tasks) {
+	return A3(
+		$elm$core$List$foldr,
+		$elm$core$Task$map2($elm$core$List$cons),
+		$elm$core$Task$succeed(_List_Nil),
+		tasks);
+};
+var $elm$core$Platform$sendToApp = _Platform_sendToApp;
+var $elm$core$Task$spawnCmd = F2(
+	function (router, _v0) {
+		var task = _v0;
+		return _Scheduler_spawn(
+			A2(
+				$elm$core$Task$andThen,
+				$elm$core$Platform$sendToApp(router),
+				task));
+	});
+var $elm$core$Task$onEffects = F3(
+	function (router, commands, state) {
+		return A2(
+			$elm$core$Task$map,
+			function (_v0) {
+				return 0;
+			},
+			$elm$core$Task$sequence(
+				A2(
+					$elm$core$List$map,
+					$elm$core$Task$spawnCmd(router),
+					commands)));
+	});
+var $elm$core$Task$onSelfMsg = F3(
+	function (_v0, _v1, _v2) {
+		return $elm$core$Task$succeed(0);
+	});
+var $elm$core$Task$cmdMap = F2(
+	function (tagger, _v0) {
+		var task = _v0;
+		return A2($elm$core$Task$map, tagger, task);
+	});
+_Platform_effectManagers['Task'] = _Platform_createManager($elm$core$Task$init, $elm$core$Task$onEffects, $elm$core$Task$onSelfMsg, $elm$core$Task$cmdMap);
+var $elm$core$Task$command = _Platform_leaf('Task');
+var $elm$core$Task$perform = F2(
+	function (toMessage, task) {
+		return $elm$core$Task$command(
+			A2($elm$core$Task$map, toMessage, task));
+	});
+var $elm$core$Platform$Cmd$batch = _Platform_batch;
+var $elm$core$Platform$Cmd$none = $elm$core$Platform$Cmd$batch(_List_Nil);
+var $elm$core$Platform$Sub$batch = _Platform_batch;
+var $elm$core$Platform$Sub$none = $elm$core$Platform$Sub$batch(_List_Nil);
+var $elm$browser$Browser$sandbox = function (impl) {
+	return _Browser_element(
+		{
+			at: function (_v0) {
+				return _Utils_Tuple2(impl.at, $elm$core$Platform$Cmd$none);
+			},
+			az: function (_v1) {
+				return $elm$core$Platform$Sub$none;
+			},
+			aB: F2(
+				function (msg, model) {
+					return _Utils_Tuple2(
+						A2(impl.aB, msg, model),
+						$elm$core$Platform$Cmd$none);
+				}),
+			aC: impl.aC
+		});
+};
+var $author$project$Main$update = F2(
+	function (msg, model) {
+		if (!msg) {
+			return model + 1;
+		} else {
+			return model - 1;
+		}
+	});
+var $author$project$Main$Decrement = 1;
+var $author$project$Main$Increment = 0;
+var $elm$html$Html$button = _VirtualDom_node('button');
+var $elm$html$Html$div = _VirtualDom_node('div');
+var $elm$virtual_dom$VirtualDom$Normal = function (a) {
+	return {$: 0, a: a};
+};
+var $elm$virtual_dom$VirtualDom$on = _VirtualDom_on;
+var $elm$html$Html$Events$on = F2(
+	function (event, decoder) {
+		return A2(
+			$elm$virtual_dom$VirtualDom$on,
+			event,
+			$elm$virtual_dom$VirtualDom$Normal(decoder));
+	});
+var $elm$html$Html$Events$onClick = function (msg) {
+	return A2(
+		$elm$html$Html$Events$on,
+		'click',
+		$elm$json$Json$Decode$succeed(msg));
+};
+var $elm$virtual_dom$VirtualDom$text = _VirtualDom_text;
+var $elm$html$Html$text = $elm$virtual_dom$VirtualDom$text;
+var $author$project$Main$view = function (model) {
+	return A2(
+		$elm$html$Html$div,
+		_List_Nil,
+		_List_fromArray(
+			[
+				A2(
+				$elm$html$Html$button,
+				_List_fromArray(
+					[
+						$elm$html$Html$Events$onClick(1)
+					]),
+				_List_fromArray(
+					[
+						$elm$html$Html$text('-')
+					])),
+				A2(
+				$elm$html$Html$div,
+				_List_Nil,
+				_List_fromArray(
+					[
+						$elm$html$Html$text(
+						$elm$core$String$fromInt(model))
+					])),
+				A2(
+				$elm$html$Html$button,
+				_List_fromArray(
+					[
+						$elm$html$Html$Events$onClick(0)
+					]),
+				_List_fromArray(
+					[
+						$elm$html$Html$text('+')
+					]))
+			]));
+};
+var $author$project$Main$main = $elm$browser$Browser$sandbox(
+	{at: $author$project$Main$init, aB: $author$project$Main$update, aC: $author$project$Main$view});
+_Platform_export({'Main':{'init':$author$project$Main$main(
+	$elm$json$Json$Decode$succeed(0))(0)}});}(this));
+
+  var app = Elm.Main.init({ node: document.getElementById("elm") });
+}
+catch (e)
+{
+  // display initialization errors (e.g. bad flags, infinite recursion)
+  var header = document.createElement("h1");
+  header.style.fontFamily = "monospace";
+  header.innerText = "Initialization Error";
+  var pre = document.getElementById("elm");
+  document.body.insertBefore(header, pre);
+  pre.innerText = e;
+  throw e;
+}
+</script>
+
+</body>
+</html>
\ No newline at end of file
diff --git a/src/Main.elm b/src/Main.elm
new file mode 100644
index 0000000..90045ac
--- /dev/null
+++ b/src/Main.elm
@@ -0,0 +1,64 @@
+module Main exposing (..)
+
+-- Press buttons to increment and decrement a counter.
+--
+-- Read how it works:
+--   https://guide.elm-lang.org/architecture/buttons.html
+--
+
+
+import Browser
+import Html exposing (Html, button, div, text)
+import Html.Events exposing (onClick)
+
+
+
+-- MAIN
+
+
+main =
+  Browser.sandbox { init = init, update = update, view = view }
+
+
+
+-- MODEL
+
+
+type alias Model = Int
+
+
+init : Model
+init =
+  0
+
+
+
+-- UPDATE
+
+
+type Msg
+  = Increment
+  | Decrement
+
+
+update : Msg -> Model -> Model
+update msg model =
+  case msg of
+    Increment ->
+      model + 1
+
+    Decrement ->
+      model - 1
+
+
+
+-- VIEW
+
+
+view : Model -> Html Msg
+view model =
+  div []
+    [ button [ onClick Decrement ] [ text "-" ]
+    , div [] [ text (String.fromInt model) ]
+    , button [ onClick Increment ] [ text "+" ]
+    ]
\ No newline at end of file
diff --git a/src/QCM.elm b/src/QCM.elm
new file mode 100644
index 0000000..185fab2
--- /dev/null
+++ b/src/QCM.elm
@@ -0,0 +1,702 @@
+module QCM exposing (..)
+
+import Browser
+import Parser as P exposing (Parser, (|.), (|=), succeed, symbol, float, spaces)
+import List as L
+import String as S
+import Html exposing (Html, Attribute, button, div, input, text, p)
+import Html.Attributes exposing (..)
+import Html.Events exposing (onInput, onClick)
+
+{-
+        ███    ███  █████  ██ ███    ██ 
+        ████  ████ ██   ██ ██ ████   ██ 
+        ██ ████ ██ ███████ ██ ██ ██  ██ 
+        ██  ██  ██ ██   ██ ██ ██  ██ ██ 
+        ██      ██ ██   ██ ██ ██   ████ 
+-}
+
+main =
+  Browser.sandbox { init = init, update = update, view = view }
+
+
+{-
+        ███    ███  ██████  ██████  ███████ ██      
+        ████  ████ ██    ██ ██   ██ ██      ██      
+        ██ ████ ██ ██    ██ ██   ██ █████   ██      
+        ██  ██  ██ ██    ██ ██   ██ ██      ██      
+        ██      ██  ██████  ██████  ███████ ███████ 
+-}
+
+type alias Model =
+  { question : String
+  , questions : List String
+  }
+
+
+init : Model
+init =
+  { question = ""
+  , questions = [ "" ]
+  }
+
+
+{-
+        ██    ██ ██████  ██████   █████  ████████ ███████ 
+        ██    ██ ██   ██ ██   ██ ██   ██    ██    ██      
+        ██    ██ ██████  ██   ██ ███████    ██    █████   
+        ██    ██ ██      ██   ██ ██   ██    ██    ██      
+         ██████  ██      ██████  ██   ██    ██    ███████ 
+-}
+
+type Msg
+  = Question String
+  | GenererQuestion
+
+update : Msg -> Model -> Model
+update msg model =
+  case msg of
+    Question nouvelleQuestion ->
+      { model | question = nouvelleQuestion }
+    GenererQuestion ->
+      { model | questions = [
+        case P.run questions model.question of
+          Ok macro -> voirMacro macro
+          Err _ -> "Y a un truc qui cloche !"
+      ] }
+
+
+{-
+
+        ██    ██ ██ ███████ ██     ██ 
+        ██    ██ ██ ██      ██     ██ 
+        ██    ██ ██ █████   ██  █  ██ 
+         ██  ██  ██ ██      ██ ███ ██ 
+          ████   ██ ███████  ███ ███  
+-}
+
+view : Model -> Html Msg
+view model =
+  div []
+    <| input [ placeholder "Format de la question", value model.question, onInput Question ] []
+    :: button [ onClick GenererQuestion ] [ text "Générer les questions" ]
+    :: ( p [] <| L.map text model.questions )
+
+    {-
+    , [ dl05 [0, 4, 2] 5 ]
+    , [ text ( poly [0, 0, 7, -3, 0 , 2, 1 , -1 , 3 , 1, 1, 1, 5] ) ]
+    , [ primitLn01 [-5,-6] ]
+    , [ primitPoly01 [2,-5,1,7] ] -- J'ai oublié de les générer !!!!!!!
+    , [ equaDiff01 -5 ]
+    , [ equaDiff02 [4, -5] ]
+    , [ equaDiff03 [4, -5] ]
+    , [ derivPoly01 [4, -5, 3, 5, 13] ]
+    , [ derivPoly02 [-3, -4, 2, 7, -13] ]
+    , [ dl01 [-5, -2, 2, -1] ]
+    , [ dl02 [-5, 0, -2, -1] ]
+    , [ dl03 [0, -8, 0, 7] ]
+    , [ dl04 [-1, 2, 0, -3] ]
+    , List.map equaDiff01 <| List.range -99 -2 -- 98 possibilités OK
+    , List.map equaDiff02 ( mix [ [3,5,9,11,13,17,27,15,25,27], [-2,-4,-7,-8,-14,-16,-19,-23,-28,-29] ] )  -- 100 possibilités OK
+    , List.map equaDiff03 ( mix [ [3,5,9,11,13,17,27,15,25,27], [-2,-4,-7,-8,-14,-16,-19,-23,-28,-29] ] )  -- 100 possibilités OK
+      -- Pourries par un List.range -2 1 ++ List.range 1 2 qui passe à 900 et 768 possibilités dans evalbox, dont répétitions
+    , List.map derivPoly01 ( mix [ [2,4,6], List.range -6 -2, List.range 2 6, List.range -2 -1 ++ List.range 1 2, List.range 11 12 ] )  -- 600 possibilités
+    , List.map derivPoly02 ( mix [ [-9,-7,-5,-3], [-8,-6,-4,-2], [2,4,6,8], List.range -2 -1 ++ List.range 1 2, List.range -12 -11 ] )  -- 512 possibilités
+    , List.map primitLn01 ( mix [ List.range -9 -2 ++ List.range 2 9, List.range -9 -2 ++ List.range 2 9 ] )  -- 256 possibilités OK
+    , List.map dl01 ( mix [ [-5,-3,-1,1,3,5], [-6,-4,-2,2,4,6], [1,2,3], [-3,-2,-1,1,2,3] ] )  -- 648 possibilités OK
+    , List.map dl02 ( mix [ [-5,-4,-3,-2,-1,1,2,3,4,5], [0], [-1,-2,-3,-4,-5], [-3,-2,-1,1,2,3] ] )  -- 300 possibilités (toutes les questions en double because import pourri)
+    , List.map dl03 ( mix [ [0], [-9,-8,-7,-6,-5,-4,-3,-2,-1,1,2,3,4,5,6,7,8,9], [0], [1,2,3,4,5,6,7,8,9] ] )  -- 162 possibilités OK
+    , List.map dl04 ( mix [ [-5,-3,-1,1,3,5], [-6,-4,-2,2,4,6], [0], [-9,-8,-7,-6,-5,-4,-3,-2,-1] ] )  --324 possibilités Ok
+    , List.concat <| List.map ( mapTwist [3,5,9] ) ( List.map dl05 ( mix [ [0], [2,4,7,8,11,13,16,17], [2,4,7,8,11,13,16,17] ] ) )  -- 192 possibilités OK
+    , d3 -- 512 possibilités OK
+    -}
+    :: ( List.map primitPoly01 <| mix [ List.range -3 -2 ++ List.range 2 3, List.range -3 -2 ++ List.range 2 3, List.range -3 -2 ++ List.range 2 3, List.range -3 -2 ++ List.range 2 3 ] ) -- 256 possibilités OK
+
+
+{-
+        ██████   █████  ██████  ███████ ███████ ██████  
+        ██   ██ ██   ██ ██   ██ ██      ██      ██   ██ 
+        ██████  ███████ ██████  ███████ █████   ██████  
+        ██      ██   ██ ██   ██      ██ ██      ██   ██ 
+        ██      ██   ██ ██   ██ ███████ ███████ ██   ██ 
+-}
+
+type TexteVariable
+  = Texte String
+  | Variable String
+
+type alias Macro
+  = List TexteVariable
+
+voirMacro macro
+  = S.concat <| L.map voirTexteVariable macro
+
+voirTexteVariable txtvar
+  = case txtvar of
+    Texte txt -> txt
+    Variable var -> var
+
+questionOld : Parser Macro
+questionOld =
+    succeed (\x -> x :: [])
+    |= P.oneOf [ expressionVariable , texteSansVariables ]
+    {--
+    |= succeed Texte
+      |= (
+        P.getChompedString
+        <| succeed ()
+        |. P.chompUntilEndOr "\n"
+      )
+    --}
+
+texteSansVariables : Parser TexteVariable
+texteSansVariables
+  = succeed Texte
+  |= P.getChompedString (
+    succeed ()
+    |. P.chompIf ( (/=) '#' )
+    |. P.chompWhile ( (/=) '#' )
+  )
+
+expressionVariable : Parser TexteVariable
+expressionVariable
+  = succeed Variable
+  |. symbol "#("
+  |= (P.getChompedString <|
+    succeed ()
+    |. P.chompUntil "#")
+
+{--
+testDeChomp
+  = succeed ( (::) )
+    (
+      P.getChompedString
+      <| succeed ()
+      |. P.chompUntil "truc"
+    )
+    |= P.int
+--}
+
+parserBis : Parser Macro
+parserBis
+  = succeed (\x y-> Texte x :: y :: [])
+  |= P.getChompedString ( P.chompWhile ( (/=) '#' ) )
+  |= P.oneOf [ expressionVariable , texteSansVariables ]
+  --|= question
+
+questions : Parser Macro
+questions =
+  P.loop [] questionsBis
+
+questionsBis : Macro -> Parser (P.Step Macro Macro)
+questionsBis ls =
+  P.oneOf
+    [ succeed (\l -> P.Loop (l :: ls))
+        |= P.oneOf [ expressionVariable , texteSansVariables ]
+    , succeed ()
+        |> P.map (\_ -> P.Done (List.reverse ls))
+    ]
+
+
+
+
+
+
+
+
+
+
+type Expr num
+  = Const num
+  | Var String
+  | Poly ( List num )
+  | Exp ( Expr num )
+  | Ln ( Expr num )
+  | Sin ( Expr num )
+  | Cos ( Expr num )
+  | Prod ( Expr num ) ( Expr num )
+  | Quot ( Expr num ) ( Expr num )
+  | Sum ( Expr num ) ( Expr num )
+  | Diff ( Expr num ) ( Expr num )
+  | Power ( Expr num ) num
+
+
+mathTeX a = "$" ++ a ++ "$"
+
+fonction a = "x\\mapsto " ++ a
+
+affineExp a b c
+  = if (a,b) == (0,0) then "0"
+    else if (a,c) == (0,1) then String.fromInt b ++ "e^x"
+    else if a == 0 then String.fromInt b ++ "e^{" ++ (String.fromInt c) ++ "x}"
+    else if (a,b,c) == (1,0,1) then "xe^x"
+    else if (b,c) == (0,1) then (String.fromInt a) ++ "x" ++ "e^x"
+    else if b == 0 then (String.fromInt a) ++ "x" ++ "e^{" ++ (String.fromInt c) ++ "x}"
+    else if c == 1 then "\\left(" ++ (String.fromInt a) ++ "x+" ++ (String.fromInt b) ++ "\\right)e^x"
+    else "\\left(" ++ (String.fromInt a) ++ "x+" ++ (String.fromInt b) ++ "\\right)e^{" ++ (String.fromInt c) ++ "x}"
+
+derivExp01 a b c =
+  let
+    f aa bb cc = mathTeX ( fonction ( affineExp aa bb cc ) )
+    vr aa bb cc = p [] [ text ( "+" ++ ( f aa bb cc) ) ]
+    fx aa bb cc = p [] [ text ( "-" ++ ( f aa bb cc) ) ]
+  in
+  div []
+    [ p [] [ text ("Donner la dérivée de la fonction " ++ f a b c) ]
+    , vr (a*c) (a+b*c) c
+    , fx (a+b) a c
+    , fx (a+b) a c
+    , fx (a+b*c) (a*c) c
+    , fx (a-b*c) (a*c) c
+    , fx (a-b*c) (a*c) c
+    , fx a 0 c
+    , fx (a*c) 0 c
+    , fx a 0 1
+    , fx (a*c) 0 1
+    {--
+    , p [] [ text ("----") ]
+    , p [] [ text ("Avant toute chose, il faut bien voir que $\\left(" ++ (String.fromInt a) ++ "x+" ++ (String.fromInt b) ++ "\\right)e^{" ++ (String.fromInt c) ++ "x}$ est de la forme $uv$ avec $u=ax+b$ et $v=e^{cx}$.") ],
+    , p [] [ text ("Ensuite, il faut savoir que la dérivée de $uv$ est donnée par $u'v+uv'$, et que la dérivée de $e^{u}$ est donnée par $e^{u}\\cdot u'$, ce qui dans notre cas nous donne que la dérivée de $e^{" ++ (String.fromInt c) ++ "x}$ est donnée par $" ++ (String.fromInt c) ++ "e^{" ++ (String.fromInt c) ++ "x}$.") ]
+    , p [] [ text ("Nous avons donc que la dérivée de la fonction est :") ]
+    , p [] [ text ("$\\begin{array}{rl} x\\mapsto & " ++ (String.fromInt (a)) ++ "e^{" ++ (String.fromInt c) ++ "x}+\\left(" ++ (String.fromInt (a)) ++ "x+" ++ (String.fromInt (b)) ++ "\\right)ce^{" ++ (String.fromInt (c)) ++ "x}\\\\& =" ++ (String.fromInt (a)) ++ "e^{" ++ (String.fromInt (c)) ++ "x}+\\left(" ++ (String.fromInt (a*c)) ++ "x+" ++ (String.fromInt (b*c)) ++ "\\right)e^{" ++ (String.fromInt (c)) ++ "x}\\\\ & =\\left(" ++ (String.fromInt (a)) ++ "+" ++ (String.fromInt (a*c)) ++ "x+" ++ (String.fromInt (b*c)) ++ "\\right)e^{" ++ (String.fromInt (c)) ++ "x}\\\\ & =\\left(" ++ (String.fromInt (a+b*c)) ++ "+" ++ (String.fromInt (a*c)) ++ "x\\right)e^{" ++ (String.fromInt (c)) ++ "x} \\end{array}$") ]
+    --}
+    , p [] [ text ("==== Dérivées, Exponentielle, derivExp01") ]
+    ]
+
+
+
+-- Des DL
+
+monome a n =
+  if a == 0 then ""
+  else if n == 0 then ( String.fromInt a )
+  else if (n,a) == (1,1) then "x"
+  else if (n,a) == (1,-1) then "-x"
+  else if n == 1 then ( String.fromInt a ) ++ "x"
+  else if a == 1 then "x^{" ++ ( String.fromInt n ) ++ "}"
+  else if a == -1 then "-x^{" ++ ( String.fromInt n ) ++ "}"
+  else ( String.fromInt a ) ++ "x^{" ++ ( String.fromInt n ) ++ "}"
+
+poly a_ks =
+  if a_ks == [] then "0"
+  else polyBis a_ks ( List.length a_ks - 1 )
+
+polyBis a_ks n =
+  case a_ks of
+    [] -> ""
+    a_n :: a_kss ->
+      if a_n == 0 then polyBis a_kss ( n - 1 )
+      else ( monome a_n n ) ++ ( polyGen a_kss ( n - 1 ) )
+
+polyGen a_ks n =
+  case a_ks of
+    [] -> ""
+    a_i :: a_is ->
+      if a_i <= 0 then ( monome a_i n ) ++ ( polyGen a_is ( n - 1 ) )
+      else "+" ++ ( monome a_i n ) ++ ( polyGen a_is ( n - 1 ) )
+
+dl a_ks =
+  if a_ks == [] then "0"
+  else dlBis a_ks 0
+
+dlBis a_ks n =
+  case a_ks of
+    [] -> ""
+    premierCoef :: suite ->
+      if premierCoef == 0 then dlBis suite ( n + 1 )
+      else ( monome premierCoef n ) ++ ( dlGen suite ( n + 1 ) )
+
+dlGen a_ks n =
+  case a_ks of
+    [] -> ""
+    a_i :: a_is ->
+      if a_i <= 0 then ( monome a_i n ) ++ ( dlGen a_is ( n + 1 ) )
+      else "+" ++ ( monome a_i n ) ++ ( dlGen a_is ( n + 1 ) )
+
+dl01 a_k =
+  let
+    vr texte = p [] [ text ( "+" ++ texte ) ]
+    fx texte = p [] [ text ( "-" ++ texte ) ]
+  in
+  div []
+    [ p [] [ text ( "On considère une fonction $f$ dont le développement limité à l'ordre 3 au voisinage de $0$ est " ++ mathTeX ( dl a_k ) ++ "." ) ]
+    , p [] [ text ( "On note $C$ la courbe représentative de $f$ et $T_0$ sa tangente en son point d'abscisse $0$." ) ]
+    , p [] [ text ( "Cocher la ou les réponses correctes." ) ]
+    , vr <| "L'équation de $T_0$ est $y=" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$"
+    , fx <| "L'équation de $T_0$ est $y=" ++ poly ( List.take 2 a_k ) ++"$" -- ATTENTION à éviter les cas où a_0 = a_1
+    , fx <| "L'équation de $T_0$ est $" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$"
+    , fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$"
+    , fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.take 2 a_k ) ++"$"
+    , fx <| "L'équation de $T_0$ est $" ++ poly ( List.take 2 a_k ) ++"$"
+    , vr "$C$ est au-dessus de $T_0$."
+    , fx "$C$ est au-dessous de $T_0$."
+    , fx "$C$ est au-dessous puis au-dessus de $T_0$."
+    , fx "$C$ est au-dessus puis au-dessous de $T_0$."
+    {--
+    , p [] [ text ("----") ]
+    --}
+    , p [] [ text ("==== Développements limités, Tangentes, dl01") ]
+    ]
+
+
+dl02 a_k =
+  let
+    vr texte = p [] [ text ( "+" ++ texte ) ]
+    fx texte = p [] [ text ( "-" ++ texte ) ]
+  in
+  div []
+    [ p [] [ text ( "On considère une fonction $f$ dont le développement limité à l'ordre 3 au voisinage de $0$ est " ++ mathTeX ( dl a_k ) ++ "." ) ]
+    , p [] [ text ( "On note $C$ la courbe représentative de $f$ et $T_0$ sa tangente en son point d'abscisse $0$." ) ]
+    , p [] [ text ( "Cocher la ou les réponses correctes." ) ]
+    , vr <| "L'équation de $T_0$ est $y=" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$"
+    , fx <| "L'équation de $T_0$ est $y=" ++ poly ( List.reverse <| List.take 3 a_k ) ++"$"
+    , fx <| "L'équation de $T_0$ est $y=" ++ poly ( List.take 2 a_k ) ++"$"
+    , fx <| "L'équation de $T_0$ est $" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$"
+    , fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.reverse <| List.take 3 a_k ) ++"x$"
+    , fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.take 2 a_k ) ++"$"
+    , fx <| "L'équation de $T_0$ est $" ++ poly ( List.take 2 a_k ) ++"$"
+    , fx "$C$ est au-dessus de $T_0$."
+    , vr "$C$ est au-dessous de $T_0$."
+    , fx "$C$ est au-dessous puis au-dessus de $T_0$."
+    , fx "$C$ est au-dessus puis au-dessous de $T_0$."
+    {--
+    , p [] [ text ("----") ]
+    --}
+    , p [] [ text ("==== Développements limités, Tangentes, dl02") ]
+    ]
+
+
+dl03 a_k =
+  let
+    vr texte = p [] [ text ( "+" ++ texte ) ]
+    fx texte = p [] [ text ( "-" ++ texte ) ]
+  in
+  div []
+    [ p [] [ text ( "On considère une fonction $f$ dont le développement limité à l'ordre 3 au voisinage de $0$ est " ++ mathTeX ( dl a_k ) ++ "." ) ]
+    , p [] [ text ( "On note $C$ la courbe représentative de $f$ et $T_0$ sa tangente en son point d'abscisse $0$." ) ]
+    , p [] [ text ( "Cocher la ou les réponses correctes." ) ]
+    , vr <| "L'équation de $T_0$ est $y=" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$"
+    , fx <| "L'équation de $T_0$ est $y=" ++ poly ( List.take 2 a_k ) ++"$" -- ATTENTION à éviter les cas où a_0 = a_1
+    , fx <| "L'équation de $T_0$ est $" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$"
+    , fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$"
+    , fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.take 2 a_k ) ++"$"
+    , fx <| "L'équation de $T_0$ est $" ++ poly ( List.take 2 a_k ) ++"$"
+    , fx "$C$ est au-dessus de $T_0$."
+    , fx "$C$ est au-dessous de $T_0$."
+    , vr "$C$ est au-dessous puis au-dessus de $T_0$."
+    , fx "$C$ est au-dessus puis au-dessous de $T_0$."
+    {--
+    , p [] [ text ("----") ]
+    --}
+    , p [] [ text ("==== Développements limités, Tangentes, dl03") ]
+    ]
+
+
+dl04 a_k =
+  let
+    vr texte = p [] [ text ( "+" ++ texte ) ]
+    fx texte = p [] [ text ( "-" ++ texte ) ]
+  in
+  div []
+    [ p [] [ text ( "On considère une fonction $f$ dont le développement limité à l'ordre 3 au voisinage de $0$ est " ++ mathTeX ( dl a_k ) ++ "." ) ]
+    , p [] [ text ( "On note $C$ la courbe représentative de $f$ et $T_0$ sa tangente en son point d'abscisse $0$." ) ]
+    , p [] [ text ( "Cocher la ou les réponses correctes." ) ]
+    , vr <| "L'équation de $T_0$ est $y=" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$"
+    , fx <| "L'équation de $T_0$ est $y=" ++ poly ( List.take 2 a_k ) ++"$" -- ATTENTION à éviter les cas où a_0 = a_1
+    , fx <| "L'équation de $T_0$ est $" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$"
+    , fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$"
+    , fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.take 2 a_k ) ++"$"
+    , fx <| "L'équation de $T_0$ est $" ++ poly ( List.take 2 a_k ) ++"$"
+    , fx "$C$ est au-dessus de $T_0$."
+    , fx "$C$ est au-dessous de $T_0$."
+    , fx "$C$ est au-dessous puis au-dessus de $T_0$."
+    , vr "$C$ est au-dessus puis au-dessous de $T_0$."
+    {--
+    , p [] [ text ("----") ]
+    --}
+    , p [] [ text ("==== Développements limités, Tangentes, dl04") ]
+    ]
+
+
+dl05 a_k k = -- À n'utiliser qu'avec a_0 = 0 !!!
+  let
+    coefLin =
+      case a_k of
+        [] -> 0
+        a_0 :: [] -> 0
+        a_0 :: a_1 :: a_ks -> a_1
+    coefQuad =
+      case a_k of
+        [] -> 0
+        a_0 :: [] -> 0
+        a_0 :: a_1 :: [] -> 0
+        a_0 :: a_1 :: a_2 :: a_ks -> a_2
+    vr a b = p [] [ text <| "+$\\frac{" ++ String.fromInt a ++ "}{" ++ String.fromInt b ++ "}$" ]
+    ffx a b = p [] [ text <| "-$\\frac{" ++ String.fromInt a ++ "}{" ++ String.fromInt b ++ "}$" ]
+    fx a = p [] [ text <| "-$" ++ String.fromInt a ++ "$" ]
+  in
+  div []
+    [ p [] [ text ( "On considère une fonction $f$ dont le développement limité à l'ordre 2 au voisinage de $0$ est " ++ mathTeX ( dl a_k ) ++ "." ) ]
+    , p [] [ text <| "Que vaut $\\lim\\limits_{x\\to0}\\frac{f\\left(x\\right)}{" ++ (String.fromInt k) ++ "x}$" ]
+    , vr coefLin k
+    , ffx 1 coefLin
+    , ffx 1 coefQuad
+    , ffx 1 k
+    , ffx coefQuad k
+    , ffx k coefQuad
+    , fx coefLin
+    , fx coefQuad
+    , fx k
+    , fx 1
+    {--
+    , p [] [ text ("----") ]
+    --}
+    , p [] [ text ("==== Développements limités, Tangentes, dl05") ]
+    ]
+
+
+mapTwist a b = List.map b a
+
+entiers = List.range 2 9
+
+d1 = List.map derivExp01 entiers
+
+d2 = List.concat ( List.map (mapTwist entiers) d1 )
+
+d3 = List.concat ( List.map (mapTwist entiers) d2 )
+
+mix lls =
+  case lls of
+    [] -> []
+    [] :: llss -> []
+    l :: [] -> List.map List.singleton l
+    (a :: ls) :: llss -> ( List.map ( (::) a ) ( mix llss ) ) ++ mix ( ls :: llss )
+
+derivPoly01 param = -- on donne a pair et positif, les deux racines x_1 < x_2, d, et m > x_2
+  case param of
+    [] -> div [] []
+    a :: [] -> div [] []
+    a :: b :: [] -> div [] []
+    a :: b :: c :: [] -> div [] []
+    a :: b :: c :: d :: [] -> div [] []
+    a :: b :: c :: d :: e :: a_ks -> derivPoly01Bis a b c d e
+
+derivPoly01Bis a x_1 x_2 d m =
+  let
+    b = 0 - 3*a*(x_1 + x_2)//2
+    c = 3*a*x_1*x_2
+    a_k = [a,b,c,d]
+    vr texte = p [] [ text ( "+" ++ texte ) ]
+    fx texte = p [] [ text ( "-" ++ texte ) ]
+  in
+  div []
+    [ p [] [ text ( "On considère la fonction $f:x\\mapsto " ++ ( poly a_k ) ++ "$." ) ]
+    , p [] [ text ( "Cocher la ou les réponses correctes." ) ]
+    , vr <| "La dérivée de $f$ est la fonction $f\\prime:x\\mapsto " ++ ( poly <| polyD a_k ) ++ "$."
+    , fx <| "La dérivée de $f$ est la fonction $f\\prime:x\\mapsto " ++ ( poly [3*a, 2*b, c + d] ) ++ "$."
+    , fx <| "la fonction $f$ est croissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";" ++ String.fromInt x_2 ++ "\\right]$"
+    , vr <| "la fonction $f$ est décroissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";" ++ String.fromInt x_2 ++ "\\right]$"
+    , fx <| "la fonction $f$ est décroissante sur l'intervalle $\\left[" ++ String.fromInt m ++ ";+\\infty\\right[$"
+    , vr <| "la fonction $f$ est croissante sur l'intervalle $\\left[" ++ String.fromInt m ++ ";+\\infty\\right[$"
+    , fx <| "la fonction $f$ est croissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";+\\infty\\right[$"
+    , fx <| "la fonction $f$ est décroissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";+\\infty\\right[$"
+    {--
+    , p [] [ text ("----") ]
+    --}
+    , p [] [ text ("==== Dérivée, Polynômes, derivPoly01") ]
+    ]
+
+derivPoly02 param = -- on donne a impair et négatif, les deux racines x_1 < x_2 pairs distincs, d, et m < x_1
+  case param of
+    [] -> div [] []
+    a :: [] -> div [] []
+    a :: b :: [] -> div [] []
+    a :: b :: c :: [] -> div [] []
+    a :: b :: c :: d :: [] -> div [] []
+    a :: b :: c :: d :: e :: a_ks -> derivPoly02Bis a b c d e
+
+derivPoly02Bis a x_1 x_2 d m =
+  let
+    b = 0 - 3*a*(x_1 + x_2)//2
+    c = 3*a*x_1*x_2
+    a_k = [a,b,c,d]
+    vr texte = p [] [ text ( "+" ++ texte ) ]
+    fx texte = p [] [ text ( "-" ++ texte ) ]
+  in
+  div []
+    [ p [] [ text ( "On considère la fonction $f:x\\mapsto " ++ ( poly a_k ) ++ "$." ) ]
+    , p [] [ text ( "Cocher la ou les réponses correctes." ) ]
+    , vr <| "La dérivée de $f$ est la fonction $f\\prime:x\\mapsto " ++ ( poly <| polyD a_k ) ++ "$."
+    , fx <| "La dérivée de $f$ est la fonction $f\\prime:x\\mapsto " ++ ( poly [3*a, 2*b, c + d] ) ++ "$."
+    , vr <| "la fonction $f$ est croissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";" ++ String.fromInt x_2 ++ "\\right]$"
+    , fx <| "la fonction $f$ est décroissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";" ++ String.fromInt x_2 ++ "\\right]$"
+    , vr <| "la fonction $f$ est décroissante sur l'intervalle $\\left]-\\infty;" ++ String.fromInt m ++ "\\right]$"
+    , fx <| "la fonction $f$ est croissante sur l'intervalle $\\left]-\\infty;" ++ String.fromInt m ++ "\\right[$"
+    , fx <| "la fonction $f$ est croissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";+\\infty\\right[$"
+    , fx <| "la fonction $f$ est décroissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";+\\infty\\right[$"
+    {--
+    , p [] [ text ("----") ]
+    --}
+    , p [] [ text ("==== Dérivée, Polynômes, derivPoly02") ]
+    ]
+
+polyD a_ks = polyDbis a_ks ( List.length a_ks - 1 )
+
+polyDbis a_ks n =
+  case a_ks of
+    [] -> []
+    a_0 :: [] -> []
+    a_k :: a_kss -> ( n*a_k ) :: polyDbis a_kss ( n - 1 ) 
+
+equaDiff01 a = -- a négatif
+  let
+    f aa = mathTeX ( fonction ( aa ) )
+    vr aa = p [] [ text ( "+" ++ ( f aa ) ) ]
+    fx aa = p [] [ text ( "-" ++ ( f aa ) ) ]
+  in
+  div []
+    [ p [] [ text <| "Parmi les fonctions ci-dessous, lesquelles sont des solutions de l'équation différentielle $y'=" ++ String.fromInt a ++ "y$ ?" ]
+    , vr <| String.fromInt ( a - 1 ) ++ "e^{" ++ String.fromInt a ++ "x}"
+    , vr <| String.fromInt ( a + 4 ) ++ "e^{" ++ String.fromInt a ++ "x}"
+    , vr <| String.fromInt a ++ "e^{" ++ String.fromInt a ++ "x}"
+    , fx <| String.fromInt a ++ "e^{" ++ String.fromInt (a-1) ++ "x}"
+    , fx <| String.fromInt ( a - 3 ) ++ "e^x"
+    , fx <| String.fromInt ( a + 7 ) ++ "e^x" ++ String.fromInt a
+    , fx <| String.fromInt a ++ "e^x"
+    , fx <| String.fromInt a ++ "e^x+" ++ String.fromInt ( a + 100)
+    , fx <| String.fromInt ( a - 1 ) ++ "e^x+" ++ String.fromInt ( a + 100)
+    , fx <| String.fromInt ( a - 8 ) ++ "e^{" ++ String.fromInt (a-1) ++ "x}" ++ String.fromInt a
+    {--
+    , p [] [ text ("----") ]
+    --}
+    , p [] [ text ("==== Équations différentielles, equaDiff01") ]
+    ]
+
+equaDiff02 param =
+  case param of
+    [] -> div [] []
+    a :: [] -> div [] []
+    a :: b :: c -> equaDiff02Bis a b
+
+equaDiff02Bis a b = -- a positif, b négatif, pas de simplification
+  let
+    f aa = mathTeX ( fonction ( aa ) )
+    vr aa = p [] [ text ( "+" ++ ( f aa ) ) ]
+    fx aa = p [] [ text ( "-" ++ ( f aa ) ) ]
+  in
+  div []
+    [ p [] [ text <| "Parmi les fonctions ci-dessous, lesquelles sont des solutions de l'équation différentielle $" ++ String.fromInt a ++"y'=" ++ String.fromInt b ++ "y$ ?" ]
+    , vr <| String.fromInt ( a - 17 ) ++ "e^{-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}x}"
+    , vr <| String.fromInt ( a + 23 ) ++ "e^{-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}x}"
+    , fx <| String.fromInt ( a + 3 ) ++ "e^{\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}x}"
+    , fx <| String.fromInt ( a - 17 ) ++ "e^{\\frac{" ++ String.fromInt a ++ "}{" ++ String.fromInt (0 - b) ++ "}x}"
+    , fx <| String.fromInt ( a + 23 ) ++ "e^{-\\frac{" ++ String.fromInt a ++ "}{" ++ String.fromInt (0 - b) ++ "}x}"
+    , fx <| String.fromInt a ++ "e^{" ++ String.fromInt b ++ "x}-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}"
+    , fx <| String.fromInt a ++ "e^{" ++ String.fromInt b ++ "x}+\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}"
+    , fx <| String.fromInt b ++ "e^{" ++ String.fromInt b ++ "x}-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}"
+    , fx <| String.fromInt b ++ "e^{" ++ String.fromInt b ++ "x}+\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}"
+    , fx <| "e^x+\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}"
+    {--
+    , p [] [ text ("----") ]
+    --}
+    , p [] [ text ("==== Équations différentielles, equaDiff02") ]
+    ]
+
+equaDiff03 param =
+  case param of
+    [] -> div [] []
+    a :: [] -> div [] []
+    a :: b :: c -> equaDiff03Bis a b
+
+equaDiff03Bis a b = -- a positif, b négatif, pas de simplification
+  let
+    f aa = mathTeX ( fonction ( aa ) )
+    vr aa = p [] [ text ( "+" ++ ( f aa ) ) ]
+    fx aa = p [] [ text ( "-" ++ ( f aa ) ) ]
+  in
+  div []
+    [ p [] [ text <| "Parmi les fonctions ci-dessous, lesquelles sont des solutions de l'équation différentielle $y'=" ++ String.fromInt a ++ "y" ++ String.fromInt b ++"$ ?" ]
+    , fx <| String.fromInt ( a - 17 ) ++ "e^{-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}x}"
+    , fx <| String.fromInt ( a + 23 ) ++ "e^{-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}x}"
+    , fx <| String.fromInt ( a + 3 ) ++ "e^{\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}x}"
+    , fx <| String.fromInt ( a - 17 ) ++ "e^{\\frac{" ++ String.fromInt a ++ "}{" ++ String.fromInt (0 - b) ++ "}x}"
+    , fx <| String.fromInt ( a + 23 ) ++ "e^{-\\frac{" ++ String.fromInt a ++ "}{" ++ String.fromInt (0 - b) ++ "}x}"
+    , fx <| String.fromInt a ++ "e^{" ++ String.fromInt a ++ "x}-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}"
+    , vr <| String.fromInt a ++ "e^{" ++ String.fromInt a ++ "x}+\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}"
+    , fx <| String.fromInt b ++ "e^{" ++ String.fromInt a ++ "x}-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}"
+    , vr <| String.fromInt b ++ "e^{" ++ String.fromInt a ++ "x}+\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}"
+    , fx <| "e^x+\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}"
+    {--
+    , p [] [ text ("----") ]
+    --}
+    , p [] [ text ("==== Équations différentielles, equaDiff03") ]
+    ]
+
+primitLn01 a_k =
+  case a_k of
+    [] -> div [] []
+    a :: [] -> div [] []
+    a :: b :: c -> primitLn01Bis a b
+
+primitLn01Bis a b =
+  let
+    f aa = mathTeX ( fonction ( aa ) )
+    vr aa = p [] [ text ( "+" ++ ( f aa ) ) ]
+    fx aa = p [] [ text ( "-" ++ ( f aa ) ) ]
+    axpb = poly [a,b]
+  in
+  div []
+    [ p [] [ text <| "Parmi les fonctions ci-dessous, lesquelles sont des primitives de la fonction " ++ ( f <| "\\frac{" ++ String.fromInt a ++ "}{" ++ axpb ++ "}" ) ++ " ?" ]
+    , vr <| "\\ln\\left(" ++ axpb ++ "\\right)"
+    , vr <| "\\ln\\left(" ++ axpb ++ "\\right)+" ++ String.fromInt ( b + 30 )
+    , vr <| "\\ln\\left(" ++ axpb ++ "\\right)" ++ String.fromInt ( a - 20)
+    , fx <| "\\frac{" ++ String.fromInt (a*a) ++ "}{\\left(" ++ axpb ++ "\\right)^2}"
+    , fx <| "\\frac{" ++ String.fromInt (a*a) ++ "}{" ++ axpb ++ "}" ++ String.fromInt ( b + 30 )
+    , fx <| "\\frac{" ++ String.fromInt (0 - a*a) ++ "}{\\left(" ++ axpb ++ "\\right)^2}"
+    , fx <| "\\frac{" ++ String.fromInt (0 - a*a) ++ "}{" ++ axpb ++ "}+" ++ String.fromInt ( b + 30 )
+    , fx <| "\\frac{" ++ String.fromInt (0 - a*a) ++ "}{" ++ axpb ++ "}" ++ String.fromInt ( a - 20)
+    , fx <| "\\frac{" ++ poly [a*a, a*b+a*a] ++ "}{\\left(" ++ axpb ++ "\\right)^2}"
+    , fx <| "\\frac{" ++ poly [a*a, a*b-a*a] ++ "}{\\left(" ++ axpb ++ "\\right)^2}"
+    {--
+    , p [] [ text ("----") ]
+    --}
+    , p [] [ text ("==== Primitives, Logarithme, primitLn01") ]
+    ]
+
+primitPoly01 a_k =
+  case a_k of
+    [] -> div [] []
+    a :: [] -> div [] []
+    a :: b :: [] -> div [] []
+    a :: b :: c :: [] -> div [] []
+    a :: b :: c :: d :: e -> primitPoly01Bis a b c d
+
+primitPoly01Bis a b c d =
+  let
+    pol = [a,b,c,d,0]
+    polD = polyD pol
+    polDD = polyD polD
+    f a_k = mathTeX ( fonction ( poly a_k ) )
+    vr a_k = p [] [ text ( "+" ++ ( f a_k ) ) ]
+    fx a_k = p [] [ text ( "-" ++ ( f a_k ) ) ]
+  in
+  div []
+    [ p [] [ text <| "Parmi les fonctions ci-dessous, lesquelles sont des primitives de la fonction " ++ ( f polD ) ++ " ?" ]
+    , vr <| List.map2 (+) pol [0,0,0,0,5]
+    , vr <| List.map2 (+) pol [0,0,0,0,-8]
+    , vr <| List.map2 (+) pol [0,0,0,0,8]
+    , fx <| List.map2 (+) polD [0,0,0,8]
+    , fx <| List.map2 (+) polD [0,0,0,-5]
+    , fx <| List.map2 (+) polD [0,0,0,-8]
+    , fx <| List.map2 (+) polDD [0,0,8]
+    , fx <| List.map2 (+) polDD [0,0,-5]
+    , fx <| List.map2 (+) polDD [0,0,-8]
+    {--
+    , p [] [ text ("----") ]
+    --}
+    , p [] [ text ("==== Primitives, Polynômes, primitPoly01") ]
+    ]
+
+
+
+
diff --git a/src/QCMbis.elm b/src/QCMbis.elm
new file mode 100644
index 0000000..a806beb
--- /dev/null
+++ b/src/QCMbis.elm
@@ -0,0 +1,583 @@
+module QCMbis exposing (..)
+
+-- Press buttons to increment and decrement a counter.
+--
+-- Read how it works:
+--   https://guide.elm-lang.org/architecture/buttons.html
+--
+
+
+import Browser
+import Html exposing (Html, button, div, text, p)
+import Html.Events exposing (onClick)
+
+
+
+-- MAIN
+
+
+main =
+  Browser.sandbox { init = init, update = update, view = view }
+
+
+
+-- MODEL
+
+
+type alias Model = Int
+
+
+init : Model
+init =
+  0
+
+
+
+-- UPDATE
+
+
+type Msg
+  = Increment
+  | Decrement
+
+
+update : Msg -> Model -> Model
+update msg model =
+  case msg of
+    Increment ->
+      model + 1
+
+    Decrement ->
+      model - 1
+
+
+
+-- VIEW
+
+
+view : Model -> Html Msg
+view model =
+  div [] ( List.concat
+    [
+    {--
+    , [ dl10 [0, 4, 2] 5 ]
+    , [ text ( poly [0, 0, 7, -3, 0 , 2, 1 , -1 , 3 , 1, 1, 1, 5] ) ]
+    , [ primitPoly02 [2,-5,1,7] ]
+    , [ primitLn02 [-5,-6] ]
+    , [ equaDiff04 -5 ]
+    , [ equaDiff05 [4, -5] ]
+    , [ equaDiff06 [4, -5] ]
+    , [ derivPoly03 [4, -5, 3, 5, 13] ]
+    , [ derivPoly04 [-3, -4, 2, 7, -13] ]
+    , [ dl06 [-5, -2, 2, -1] ]
+    , [ dl07 [-5, 0, -2, -1] ]
+    , [ dl08 [0, -8, 0, 7] ]
+    , [ dl09 [-1, 2, 0, -3] ]
+    --}
+      List.map equaDiff04 <| List.range -9 -2 -- 98 possibilités
+    , List.map equaDiff05 ( mix [ [3,5,7], [-2,-4,-7,-8] ] )  -- 99 possibilités
+    , List.map equaDiff06 ( mix [ [3,5,7], [-2,-4,-7,-8] ] )  -- 99 possibilités
+    , List.map derivPoly03 ( mix [ [4,6], List.range -7 -6, List.range 2 3, List.range 11 12 ] )  -- 576 possibilités
+    , List.map derivPoly04 ( mix [ [-5,-3], [-4,-2], [2,6], List.range -14 -13 ] )  -- 256 possibilités
+    , List.map primitLn02 ( mix [ List.range -3 -2 ++ List.range 2 3, List.range -5 -4 ++ List.range 5 6 ] )  -- 256 possibilités
+    , List.map primitPoly02 ( mix [ List.range -3 -2 , List.range 2 3, List.range -5 -4 , List.range 6 7 ] )  -- 256 possibilités
+    , List.map dl06 ( mix [ [-3,5], [-2,6], [2,3], [-2,3] ] )  -- 648 possibilités
+    , List.map dl07 ( mix [ [-5,-2,2], [0], [-3,-4], [-2,3] ] )  -- 300 possibilités
+    , List.map dl08 ( mix [ [0], [-3,-2,2,3], [0], [2,3,4,5] ] )  -- 162 possibilités
+    , List.map dl09 ( mix [ [-5,3,5], [-6,4], [0], [-5,-3] ] )  --324 possibilités
+    , List.concat <| List.map ( mapTwist [3,5,9] ) ( List.map dl10 ( mix [ [0], [2,4], [7,8] ] ) )  -- 192 possibilités
+    , d3 -- 729 possibilités
+    ] 
+  )
+
+{--
+type Fonction num
+  = Const num
+  | X
+  | Poly List num
+  | Exp Fonction
+  | Ln Fonction
+  | Sin Fonction
+  | Cos Fonction
+--}
+
+
+mathTeX a = "$" ++ a ++ "$"
+
+fonction a = "x\\mapsto " ++ a
+
+affineExp a b c
+  = if (a,b) == (0,0) then "0"
+    else if (a,c) == (0,1) then String.fromInt b ++ "e^x"
+    else if a == 0 then String.fromInt b ++ "e^{" ++ (String.fromInt c) ++ "x}"
+    else if (a,b,c) == (1,0,1) then "xe^x"
+    else if (b,c) == (0,1) then (String.fromInt a) ++ "x" ++ "e^x"
+    else if b == 0 then (String.fromInt a) ++ "x" ++ "e^{" ++ (String.fromInt c) ++ "x}"
+    else if c == 1 then "\\left(" ++ (String.fromInt a) ++ "x+" ++ (String.fromInt b) ++ "\\right)e^x"
+    else "\\left(" ++ (String.fromInt a) ++ "x+" ++ (String.fromInt b) ++ "\\right)e^{" ++ (String.fromInt c) ++ "x}"
+
+derivExp02 a b c =
+  let
+    f aa bb cc = mathTeX ( fonction ( affineExp aa bb cc ) )
+    vr aa bb cc = p [] [ text ( "+" ++ ( f aa bb cc) ) ]
+    fx aa bb cc = p [] [ text ( "-" ++ ( f aa bb cc) ) ]
+  in
+  div []
+    [ p [] [ text ("Donner la dérivée de la fonction " ++ f a b c) ]
+    , vr (a*c) (a+b*c) c
+    , fx (a+b) a c
+    , fx (a+b) a c
+    , fx (a+b*c) (a*c) c
+    , fx (a-b*c) (a*c) c
+    , fx (a-b*c) (a*c) c
+    , fx a 0 c
+    , fx (a*c) 0 c
+    , fx a 0 1
+    , fx (a*c) 0 1
+    {--
+    , p [] [ text ("----") ]
+    , p [] [ text ("Avant toute chose, il faut bien voir que $\\left(" ++ (String.fromInt a) ++ "x+" ++ (String.fromInt b) ++ "\\right)e^{" ++ (String.fromInt c) ++ "x}$ est de la forme $uv$ avec $u=ax+b$ et $v=e^{cx}$.") ],
+    , p [] [ text ("Ensuite, il faut savoir que la dérivée de $uv$ est donnée par $u'v+uv'$, et que la dérivée de $e^{u}$ est donnée par $e^{u}\\cdot u'$, ce qui dans notre cas nous donne que la dérivée de $e^{" ++ (String.fromInt c) ++ "x}$ est donnée par $" ++ (String.fromInt c) ++ "e^{" ++ (String.fromInt c) ++ "x}$.") ]
+    , p [] [ text ("Nous avons donc que la dérivée de la fonction est :") ]
+    , p [] [ text ("$\\begin{array}{rl} x\\mapsto & " ++ (String.fromInt (a)) ++ "e^{" ++ (String.fromInt c) ++ "x}+\\left(" ++ (String.fromInt (a)) ++ "x+" ++ (String.fromInt (b)) ++ "\\right)ce^{" ++ (String.fromInt (c)) ++ "x}\\\\& =" ++ (String.fromInt (a)) ++ "e^{" ++ (String.fromInt (c)) ++ "x}+\\left(" ++ (String.fromInt (a*c)) ++ "x+" ++ (String.fromInt (b*c)) ++ "\\right)e^{" ++ (String.fromInt (c)) ++ "x}\\\\ & =\\left(" ++ (String.fromInt (a)) ++ "+" ++ (String.fromInt (a*c)) ++ "x+" ++ (String.fromInt (b*c)) ++ "\\right)e^{" ++ (String.fromInt (c)) ++ "x}\\\\ & =\\left(" ++ (String.fromInt (a+b*c)) ++ "+" ++ (String.fromInt (a*c)) ++ "x\\right)e^{" ++ (String.fromInt (c)) ++ "x} \\end{array}$") ]
+    --}
+    , p [] [ text ("==== Dérivées, Exponentielle, derivExp02") ]
+    ]
+
+
+
+-- Des DL
+
+monome a n =
+  if a == 0 then ""
+  else if n == 0 then ( String.fromInt a )
+  else if (n,a) == (1,1) then "x"
+  else if (n,a) == (1,-1) then "-x"
+  else if n == 1 then ( String.fromInt a ) ++ "x"
+  else if a == 1 then "x^{" ++ ( String.fromInt n ) ++ "}"
+  else if a == -1 then "-x^{" ++ ( String.fromInt n ) ++ "}"
+  else ( String.fromInt a ) ++ "x^{" ++ ( String.fromInt n ) ++ "}"
+
+poly a_ks =
+  if a_ks == [] then "0"
+  else polyBis a_ks ( List.length a_ks - 1 )
+
+polyBis a_ks n =
+  case a_ks of
+    [] -> ""
+    a_n :: a_kss ->
+      if a_n == 0 then polyBis a_kss ( n - 1 )
+      else ( monome a_n n ) ++ ( polyGen a_kss ( n - 1 ) )
+
+polyGen a_ks n =
+  case a_ks of
+    [] -> ""
+    a_i :: a_is ->
+      if a_i <= 0 then ( monome a_i n ) ++ ( polyGen a_is ( n - 1 ) )
+      else "+" ++ ( monome a_i n ) ++ ( polyGen a_is ( n - 1 ) )
+
+dl a_ks =
+  if a_ks == [] then "0"
+  else dlBis a_ks 0
+
+dlBis a_ks n =
+  case a_ks of
+    [] -> ""
+    premierCoef :: suite ->
+      if premierCoef == 0 then dlBis suite ( n + 1 )
+      else ( monome premierCoef n ) ++ ( dlGen suite ( n + 1 ) )
+
+dlGen a_ks n =
+  case a_ks of
+    [] -> ""
+    a_i :: a_is ->
+      if a_i <= 0 then ( monome a_i n ) ++ ( dlGen a_is ( n + 1 ) )
+      else "+" ++ ( monome a_i n ) ++ ( dlGen a_is ( n + 1 ) )
+
+dl06 a_k =
+  let
+    vr texte = p [] [ text ( "+" ++ texte ) ]
+    fx texte = p [] [ text ( "-" ++ texte ) ]
+  in
+  div []
+    [ p [] [ text ( "On considère une fonction $f$ dont le développement limité à l'ordre 3 au voisinage de $0$ est " ++ mathTeX ( dl a_k ) ++ "." ) ]
+    , p [] [ text ( "On note $C$ la courbe représentative de $f$ et $T_0$ sa tangente en son point d'abscisse $0$." ) ]
+    , p [] [ text ( "Cocher la ou les réponses correctes." ) ]
+    , vr <| "L'équation de $T_0$ est $y=" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$"
+    , fx <| "L'équation de $T_0$ est $y=" ++ poly ( List.take 2 a_k ) ++"$" -- ATTENTION à éviter les cas où a_0 = a_1
+    , fx <| "L'équation de $T_0$ est $" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$"
+    , fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$"
+    , fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.take 2 a_k ) ++"$"
+    , fx <| "L'équation de $T_0$ est $" ++ poly ( List.take 2 a_k ) ++"$"
+    , vr "$C$ est au-dessus de $T_0$."
+    , fx "$C$ est au-dessous de $T_0$."
+    , fx "$C$ est au-dessous puis au-dessus de $T_0$."
+    , fx "$C$ est au-dessus puis au-dessous de $T_0$."
+    {--
+    , p [] [ text ("----") ]
+    --}
+    , p [] [ text ("==== Développements limités, Tangentes, dl06") ]
+    ]
+
+
+dl07 a_k =
+  let
+    vr texte = p [] [ text ( "+" ++ texte ) ]
+    fx texte = p [] [ text ( "-" ++ texte ) ]
+  in
+  div []
+    [ p [] [ text ( "On considère une fonction $f$ dont le développement limité à l'ordre 3 au voisinage de $0$ est " ++ mathTeX ( dl a_k ) ++ "." ) ]
+    , p [] [ text ( "On note $C$ la courbe représentative de $f$ et $T_0$ sa tangente en son point d'abscisse $0$." ) ]
+    , p [] [ text ( "Cocher la ou les réponses correctes." ) ]
+    , vr <| "L'équation de $T_0$ est $y=" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$"
+    , vr <| "L'équation de $T_0$ est $y=" ++ poly ( List.reverse <| List.take 3 a_k ) ++"$"
+    , fx <| "L'équation de $T_0$ est $y=" ++ poly ( List.take 2 a_k ) ++"$"
+    , fx <| "L'équation de $T_0$ est $" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$"
+    , fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.reverse <| List.take 3 a_k ) ++"x$"
+    , fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.take 2 a_k ) ++"$"
+    , fx <| "L'équation de $T_0$ est $" ++ poly ( List.take 2 a_k ) ++"$"
+    , fx "$C$ est au-dessus de $T_0$."
+    , vr "$C$ est au-dessous de $T_0$."
+    , fx "$C$ est au-dessous puis au-dessus de $T_0$."
+    , fx "$C$ est au-dessus puis au-dessous de $T_0$."
+    {--
+    , p [] [ text ("----") ]
+    --}
+    , p [] [ text ("==== Développements limités, Tangentes, dl07") ]
+    ]
+
+
+dl08 a_k =
+  let
+    vr texte = p [] [ text ( "+" ++ texte ) ]
+    fx texte = p [] [ text ( "-" ++ texte ) ]
+  in
+  div []
+    [ p [] [ text ( "On considère une fonction $f$ dont le développement limité à l'ordre 3 au voisinage de $0$ est " ++ mathTeX ( dl a_k ) ++ "." ) ]
+    , p [] [ text ( "On note $C$ la courbe représentative de $f$ et $T_0$ sa tangente en son point d'abscisse $0$." ) ]
+    , p [] [ text ( "Cocher la ou les réponses correctes." ) ]
+    , vr <| "L'équation de $T_0$ est $y=" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$"
+    , fx <| "L'équation de $T_0$ est $y=" ++ poly ( List.take 2 a_k ) ++"$" -- ATTENTION à éviter les cas où a_0 = a_1
+    , fx <| "L'équation de $T_0$ est $" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$"
+    , fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$"
+    , fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.take 2 a_k ) ++"$"
+    , fx <| "L'équation de $T_0$ est $" ++ poly ( List.take 2 a_k ) ++"$"
+    , fx "$C$ est au-dessus de $T_0$."
+    , fx "$C$ est au-dessous de $T_0$."
+    , vr "$C$ est au-dessous puis au-dessus de $T_0$."
+    , fx "$C$ est au-dessus puis au-dessous de $T_0$."
+    {--
+    , p [] [ text ("----") ]
+    --}
+    , p [] [ text ("==== Développements limités, Tangentes, dl08") ]
+    ]
+
+
+dl09 a_k =
+  let
+    vr texte = p [] [ text ( "+" ++ texte ) ]
+    fx texte = p [] [ text ( "-" ++ texte ) ]
+  in
+  div []
+    [ p [] [ text ( "On considère une fonction $f$ dont le développement limité à l'ordre 3 au voisinage de $0$ est " ++ mathTeX ( dl a_k ) ++ "." ) ]
+    , p [] [ text ( "On note $C$ la courbe représentative de $f$ et $T_0$ sa tangente en son point d'abscisse $0$." ) ]
+    , p [] [ text ( "Cocher la ou les réponses correctes." ) ]
+    , vr <| "L'équation de $T_0$ est $y=" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$"
+    , fx <| "L'équation de $T_0$ est $y=" ++ poly ( List.take 2 a_k ) ++"$" -- ATTENTION à éviter les cas où a_0 = a_1
+    , fx <| "L'équation de $T_0$ est $" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$"
+    , fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$"
+    , fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.take 2 a_k ) ++"$"
+    , fx <| "L'équation de $T_0$ est $" ++ poly ( List.take 2 a_k ) ++"$"
+    , fx "$C$ est au-dessus de $T_0$."
+    , fx "$C$ est au-dessous de $T_0$."
+    , fx "$C$ est au-dessous puis au-dessus de $T_0$."
+    , vr "$C$ est au-dessus puis au-dessous de $T_0$."
+    {--
+    , p [] [ text ("----") ]
+    --}
+    , p [] [ text ("==== Développements limités, Tangentes, dl09") ]
+    ]
+
+
+dl10 a_k k = -- À n'utiliser qu'avec a_0 = 0 !!!
+  let
+    coefLin =
+      case a_k of
+        [] -> 0
+        a_0 :: [] -> 0
+        a_0 :: a_1 :: a_ks -> a_1
+    coefQuad =
+      case a_k of
+        [] -> 0
+        a_0 :: [] -> 0
+        a_0 :: a_1 :: [] -> 0
+        a_0 :: a_1 :: a_2 :: a_ks -> a_2
+    vr a b = p [] [ text <| "+$\\frac{" ++ String.fromInt a ++ "}{" ++ String.fromInt b ++ "}$" ]
+    ffx a b = p [] [ text <| "-$\\frac{" ++ String.fromInt a ++ "}{" ++ String.fromInt b ++ "}$" ]
+    fx a = p [] [ text <| "-$" ++ String.fromInt a ++ "$" ]
+  in
+  div []
+    [ p [] [ text ( "On considère une fonction $f$ dont le développement limité à l'ordre 2 au voisinage de $0$ est " ++ mathTeX ( dl a_k ) ++ "." ) ]
+    , p [] [ text <| "Que vaut $\\lim\\limits_{x\\to0}\\frac{f\\left(x\\right)}{" ++ (String.fromInt k) ++ "x}$" ]
+    , vr coefLin k
+    , ffx 1 coefLin
+    , ffx 1 coefQuad
+    , ffx 1 k
+    , ffx coefQuad k
+    , ffx k coefQuad
+    , fx coefLin
+    , fx coefQuad
+    , fx k
+    , fx 1
+    {--
+    , p [] [ text ("----") ]
+    --}
+    , p [] [ text ("==== Développements limités, Tangentes, dl10") ]
+    ]
+
+
+mapTwist a b = List.map b a
+
+entiers = List.range 2 4
+
+d1 = List.map derivExp02 entiers
+
+d2 = List.concat ( List.map (mapTwist entiers) d1 )
+
+d3 = List.concat ( List.map (mapTwist entiers) d2 )
+
+mix lls =
+  case lls of
+    [] -> []
+    [] :: llss -> []
+    l :: [] -> List.map List.singleton l
+    (a :: ls) :: llss -> ( List.map ( (::) a ) ( mix llss ) ) ++ mix ( ls :: llss )
+
+derivPoly03 param = -- on donne a pair et positif, les deux racines x_1 < x_2, d, et m > x_2
+  case param of
+    [] -> div [] []
+    a :: [] -> div [] []
+    a :: b :: [] -> div [] []
+    a :: b :: c :: [] -> div [] []
+    a :: b :: c :: d :: [] -> div [] []
+    a :: b :: c :: d :: e :: a_ks -> derivPoly03Bis a b c d e
+
+derivPoly03Bis a x_1 x_2 d m =
+  let
+    b = 0 - 3*a*(x_1 + x_2)//2
+    c = 3*a*x_1*x_2
+    a_k = [a,b,c,d]
+    vr texte = p [] [ text ( "+" ++ texte ) ]
+    fx texte = p [] [ text ( "-" ++ texte ) ]
+  in
+  div []
+    [ p [] [ text ( "On considère la fonction $f:x\\mapsto " ++ ( poly a_k ) ++ "$." ) ]
+    , p [] [ text ( "Cocher la ou les réponses correctes." ) ]
+    , vr <| "La dérivée de $f$ est la fonction $f\\prime:x\\mapsto " ++ ( poly <| polyD a_k ) ++ "$."
+    , fx <| "La dérivée de $f$ est la fonction $f\\prime:x\\mapsto " ++ ( poly [3*a, 2*b, c + d] ) ++ "$."
+    , fx <| "la fonction $f$ est croissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";" ++ String.fromInt x_2 ++ "\\right]$"
+    , vr <| "la fonction $f$ est décroissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";" ++ String.fromInt x_2 ++ "\\right]$"
+    , fx <| "la fonction $f$ est décroissante sur l'intervalle $\\left[" ++ String.fromInt m ++ ";+\\infty\\right[$"
+    , vr <| "la fonction $f$ est croissante sur l'intervalle $\\left[" ++ String.fromInt m ++ ";+\\infty\\right[$"
+    , fx <| "la fonction $f$ est croissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";+\\infty\\right[$"
+    , fx <| "la fonction $f$ est décroissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";+\\infty\\right[$"
+    {--
+    , p [] [ text ("----") ]
+    --}
+    , p [] [ text ("==== Dérivée, Polynômes, derivPoly03") ]
+    ]
+
+derivPoly04 param = -- on donne a impair et négatif, les deux racines x_1 < x_2 pairs distincs, d, et m < x_1
+  case param of
+    [] -> div [] []
+    a :: [] -> div [] []
+    a :: b :: [] -> div [] []
+    a :: b :: c :: [] -> div [] []
+    a :: b :: c :: d :: [] -> div [] []
+    a :: b :: c :: d :: e :: a_ks -> derivPoly04Bis a b c d e
+
+derivPoly04Bis a x_1 x_2 d m =
+  let
+    b = 0 - 3*a*(x_1 + x_2)//2
+    c = 3*a*x_1*x_2
+    a_k = [a,b,c,d]
+    vr texte = p [] [ text ( "+" ++ texte ) ]
+    fx texte = p [] [ text ( "-" ++ texte ) ]
+  in
+  div []
+    [ p [] [ text ( "On considère la fonction $f:x\\mapsto " ++ ( poly a_k ) ++ "$." ) ]
+    , p [] [ text ( "Cocher la ou les réponses correctes." ) ]
+    , vr <| "La dérivée de $f$ est la fonction $f\\prime:x\\mapsto " ++ ( poly <| polyD a_k ) ++ "$."
+    , fx <| "La dérivée de $f$ est la fonction $f\\prime:x\\mapsto " ++ ( poly [3*a, 2*b, c + d] ) ++ "$."
+    , vr <| "la fonction $f$ est croissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";" ++ String.fromInt x_2 ++ "\\right]$"
+    , fx <| "la fonction $f$ est décroissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";" ++ String.fromInt x_2 ++ "\\right]$"
+    , vr <| "la fonction $f$ est décroissante sur l'intervalle $\\left]-\\infty;" ++ String.fromInt m ++ "\\right]$"
+    , fx <| "la fonction $f$ est croissante sur l'intervalle $\\left]-\\infty;" ++ String.fromInt m ++ "\\right[$"
+    , fx <| "la fonction $f$ est croissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";+\\infty\\right[$"
+    , fx <| "la fonction $f$ est décroissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";+\\infty\\right[$"
+    {--
+    , p [] [ text ("----") ]
+    --}
+    , p [] [ text ("==== Dérivée, Polynômes, derivPoly04") ]
+    ]
+
+polyD a_ks = polyDbis a_ks ( List.length a_ks - 1 )
+
+polyDbis a_ks n =
+  case a_ks of
+    [] -> []
+    a_0 :: [] -> []
+    a_k :: a_kss -> ( n*a_k ) :: polyDbis a_kss ( n - 1 ) 
+
+equaDiff04 a = -- a négatif
+  let
+    f aa = mathTeX ( fonction ( aa ) )
+    vr aa = p [] [ text ( "+" ++ ( f aa ) ) ]
+    fx aa = p [] [ text ( "-" ++ ( f aa ) ) ]
+  in
+  div []
+    [ p [] [ text <| "Parmi les fonctions ci-dessous, lesquelles sont des solutions de l'équation différentielle $y'=" ++ String.fromInt a ++ "y$ ?" ]
+    , vr <| String.fromInt ( a - 1 ) ++ "e^{" ++ String.fromInt a ++ "x}"
+    , vr <| String.fromInt ( a + 4 ) ++ "e^{" ++ String.fromInt a ++ "x}"
+    , vr <| String.fromInt a ++ "e^{" ++ String.fromInt a ++ "x}"
+    , fx <| String.fromInt a ++ "e^{" ++ String.fromInt (a-1) ++ "x}"
+    , fx <| String.fromInt ( a - 3 ) ++ "e^x"
+    , fx <| String.fromInt ( a + 7 ) ++ "e^x" ++ String.fromInt a
+    , fx <| String.fromInt a ++ "e^x"
+    , fx <| String.fromInt a ++ "e^x+" ++ String.fromInt ( a + 100)
+    , fx <| String.fromInt ( a - 1 ) ++ "e^x+" ++ String.fromInt ( a + 100)
+    , fx <| String.fromInt ( a - 8 ) ++ "e^{" ++ String.fromInt (a-1) ++ "x}" ++ String.fromInt a
+    {--
+    , p [] [ text ("----") ]
+    --}
+    , p [] [ text ("==== Équations différentielles, equaDiff04") ]
+    ]
+
+equaDiff05 param =
+  case param of
+    [] -> div [] []
+    a :: [] -> div [] []
+    a :: b :: c -> equaDiff05Bis a b
+
+equaDiff05Bis a b = -- a positif, b négatif, pas de simplification
+  let
+    f aa = mathTeX ( fonction ( aa ) )
+    vr aa = p [] [ text ( "+" ++ ( f aa ) ) ]
+    fx aa = p [] [ text ( "-" ++ ( f aa ) ) ]
+  in
+  div []
+    [ p [] [ text <| "Parmi les fonctions ci-dessous, lesquelles sont des solutions de l'équation différentielle $" ++ String.fromInt a ++"y'=" ++ String.fromInt b ++ "y$ ?" ]
+    , vr <| String.fromInt ( a - 17 ) ++ "e^{-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}x}"
+    , vr <| String.fromInt ( a + 23 ) ++ "e^{-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}x}"
+    , fx <| String.fromInt ( a + 3 ) ++ "e^{\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}x}"
+    , fx <| String.fromInt ( a - 17 ) ++ "e^{\\frac{" ++ String.fromInt a ++ "}{" ++ String.fromInt (0 - b) ++ "}x}"
+    , fx <| String.fromInt ( a + 23 ) ++ "e^{-\\frac{" ++ String.fromInt a ++ "}{" ++ String.fromInt (0 - b) ++ "}x}"
+    , fx <| String.fromInt a ++ "e^{" ++ String.fromInt b ++ "x}-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}"
+    , fx <| String.fromInt a ++ "e^{" ++ String.fromInt b ++ "x}+\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}"
+    , fx <| String.fromInt b ++ "e^{" ++ String.fromInt b ++ "x}-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}"
+    , fx <| String.fromInt b ++ "e^{" ++ String.fromInt b ++ "x}+\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}"
+    , fx <| "e^x+\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}"
+    {--
+    , p [] [ text ("----") ]
+    --}
+    , p [] [ text ("==== Équations différentielles, equaDiff05") ]
+    ]
+
+equaDiff06 param =
+  case param of
+    [] -> div [] []
+    a :: [] -> div [] []
+    a :: b :: c -> equaDiff06Bis a b
+
+equaDiff06Bis a b = -- a positif, b négatif, pas de simplification
+  let
+    f aa = mathTeX ( fonction ( aa ) )
+    vr aa = p [] [ text ( "+" ++ ( f aa ) ) ]
+    fx aa = p [] [ text ( "-" ++ ( f aa ) ) ]
+  in
+  div []
+    [ p [] [ text <| "Parmi les fonctions ci-dessous, lesquelles sont des solutions de l'équation différentielle $y'=" ++ String.fromInt a ++ "y" ++ String.fromInt b ++"$ ?" ]
+    , fx <| String.fromInt ( a - 17 ) ++ "e^{-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}x}"
+    , fx <| String.fromInt ( a + 23 ) ++ "e^{-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}x}"
+    , fx <| String.fromInt ( a + 3 ) ++ "e^{\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}x}"
+    , fx <| String.fromInt ( a - 17 ) ++ "e^{\\frac{" ++ String.fromInt a ++ "}{" ++ String.fromInt (0 - b) ++ "}x}"
+    , fx <| String.fromInt ( a + 23 ) ++ "e^{-\\frac{" ++ String.fromInt a ++ "}{" ++ String.fromInt (0 - b) ++ "}x}"
+    , fx <| String.fromInt a ++ "e^{" ++ String.fromInt a ++ "x}-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}"
+    , vr <| String.fromInt a ++ "e^{" ++ String.fromInt a ++ "x}+\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}"
+    , fx <| String.fromInt b ++ "e^{" ++ String.fromInt a ++ "x}-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}"
+    , vr <| String.fromInt b ++ "e^{" ++ String.fromInt a ++ "x}+\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}"
+    , fx <| "e^x+\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}"
+    {--
+    , p [] [ text ("----") ]
+    --}
+    , p [] [ text ("==== Équations différentielles, equaDiff06") ]
+    ]
+
+primitLn02 a_k =
+  case a_k of
+    [] -> div [] []
+    a :: [] -> div [] []
+    a :: b :: c -> primitLn02Bis a b
+
+primitLn02Bis a b =
+  let
+    f aa = mathTeX ( fonction ( aa ) )
+    vr aa = p [] [ text ( "+" ++ ( f aa ) ) ]
+    fx aa = p [] [ text ( "-" ++ ( f aa ) ) ]
+    axpb = poly [a,b]
+  in
+  div []
+    [ p [] [ text <| "Parmi les fonctions ci-dessous, lesquelles sont des primitives de la fonction " ++ ( f <| "\\frac{" ++ String.fromInt a ++ "}{" ++ axpb ++ "}" ) ++ " ?" ]
+    , vr <| "\\ln\\left(" ++ axpb ++ "\\right)"
+    , vr <| "\\ln\\left(" ++ axpb ++ "\\right)+" ++ String.fromInt ( b + 30 )
+    , vr <| "\\ln\\left(" ++ axpb ++ "\\right)" ++ String.fromInt ( a - 20)
+    , fx <| "\\frac{" ++ String.fromInt (a*a) ++ "}{\\left(" ++ axpb ++ "\\right)^2}"
+    , fx <| "\\frac{" ++ String.fromInt (a*a) ++ "}{" ++ axpb ++ "}" ++ String.fromInt ( b + 30 )
+    , fx <| "\\frac{" ++ String.fromInt (0 - a*a) ++ "}{\\left(" ++ axpb ++ "\\right)^2}"
+    , fx <| "\\frac{" ++ String.fromInt (0 - a*a) ++ "}{" ++ axpb ++ "}" ++ String.fromInt ( b + 30 )
+    , fx <| "\\frac{" ++ String.fromInt (0 - a*a) ++ "}{" ++ axpb ++ "}" ++ String.fromInt ( a - 20)
+    , fx <| "\\frac{" ++ poly [a*a, a*b+a*a] ++ "}{\\left(" ++ axpb ++ "\\right)^2}"
+    , fx <| "\\frac{" ++ poly [a*a, a*b-a*a] ++ "}{\\left(" ++ axpb ++ "\\right)^2}"
+    {--
+    , p [] [ text ("----") ]
+    --}
+    , p [] [ text ("==== Primitives, Logarithme, primitLn02") ]
+    ]
+
+primitPoly02 a_k =
+  case a_k of
+    [] -> div [] []
+    a :: [] -> div [] []
+    a :: b :: [] -> div [] []
+    a :: b :: c :: [] -> div [] []
+    a :: b :: c :: d :: e -> primitPoly02Bis a b c d
+
+primitPoly02Bis a b c d =
+  let
+    pol = [a,b,c,d,0]
+    polD = polyD pol
+    polDD = polyD polD
+    f a_k = mathTeX ( fonction ( poly a_k ) )
+    vr a_k = p [] [ text ( "+" ++ ( f a_k ) ) ]
+    fx a_k = p [] [ text ( "-" ++ ( f a_k ) ) ]
+  in
+  div []
+    [ p [] [ text <| "Parmi les fonctions ci-dessous, lesquelles sont des primitives de la fonction " ++ ( f polD ) ++ " ?" ]
+    , vr <| List.map2 (+) pol [0,0,0,0,5]
+    , vr <| List.map2 (+) pol [0,0,0,0,-8]
+    , vr <| List.map2 (+) pol [0,0,0,0,8]
+    , fx <| List.map2 (+) polD [0,0,0,8]
+    , fx <| List.map2 (+) polD [0,0,0,-5]
+    , fx <| List.map2 (+) polD [0,0,0,-8]
+    , fx <| List.map2 (+) polDD [0,0,8]
+    , fx <| List.map2 (+) polDD [0,0,-5]
+    , fx <| List.map2 (+) polDD [0,0,-8]
+    {--
+    , p [] [ text ("----") ]
+    --}
+    , p [] [ text ("==== Primitives, Polynômes, primitPoly02") ]
+    ]
+
+
+
+
