1631 lines
67 KiB
Plaintext
1631 lines
67 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Elements of $C_L$ as meaningful circuits"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": 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\n",
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|
||
"$\\displaystyle \\left[ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\\\\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2}}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}1 & 0\\\\0 & i\\end{matrix}\\right], \\ \\left[\\begin{matrix}1 & 0\\\\0 & 1\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\\\\\frac{\\sqrt{2} i}{2} & - \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2} i}{2}\\\\\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}1 & 0\\\\0 & -1\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2} i}{2}\\\\\\frac{\\sqrt{2} i}{2} & \\frac{\\sqrt{2}}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2}}{2}\\\\\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}1 & 0\\\\0 & - i\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2}}{2}\\\\\\frac{\\sqrt{2} i}{2} & \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2} i}{2}\\\\\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2} i}{2}\\\\\\frac{\\sqrt{2} i}{2} & - \\frac{\\sqrt{2}}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{1}{2} + \\frac{i}{2} & \\frac{1}{2} - \\frac{i}{2}\\\\\\frac{1}{2} - \\frac{i}{2} & \\frac{1}{2} + \\frac{i}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\\\- \\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}0 & 1\\\\1 & 0\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\\\- \\frac{\\sqrt{2} i}{2} & \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}0 & 1\\\\i & 0\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{1}{2} - \\frac{i}{2} & \\frac{1}{2} + \\frac{i}{2}\\\\- \\frac{1}{2} + \\frac{i}{2} & \\frac{1}{2} + \\frac{i}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}0 & i\\\\1 & 0\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2} i}{2}\\\\- \\frac{\\sqrt{2} i}{2} & - \\frac{\\sqrt{2}}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{1}{2} - \\frac{i}{2} & - \\frac{1}{2} + \\frac{i}{2}\\\\- \\frac{1}{2} + \\frac{i}{2} & - \\frac{1}{2} + \\frac{i}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}0 & -1\\\\1 & 0\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2}}{2}\\\\- \\frac{\\sqrt{2} i}{2} & - \\frac{\\sqrt{2} i}{2}\\end{matrix}\\right], \\ \\left[\\begin{matrix}\\frac{1}{2} - \\frac{i}{2} & \\frac{i \\left(-1 + i\\right)}{2}\\\\- \\frac{1}{2} + \\frac{i}{2} & \\frac{i \\left(-1 + i\\right)}{2}\\end{matrix}\\right]\\right]$"
|
||
],
|
||
"text/plain": [
|
||
"⎡⎡√2 √2 ⎤ ⎡ √2 √2 ⎤ ⎡√2 √2⋅ⅈ ⎤ ⎡ √2 √2⋅\n",
|
||
"⎢⎢── ── ⎥ ⎢ ── ── ⎥ ⎢── ──── ⎥ ⎢ ── ───\n",
|
||
"⎢⎢2 2 ⎥ ⎡1 0⎤ ⎡1 0⎤ ⎢ 2 2 ⎥ ⎢2 2 ⎥ ⎡1 0 ⎤ ⎢ 2 2 \n",
|
||
"⎢⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ \n",
|
||
"⎢⎢√2 -√2 ⎥ ⎣0 ⅈ⎦ ⎣0 1⎦ ⎢√2⋅ⅈ -√2⋅ⅈ ⎥ ⎢√2 -√2⋅ⅈ ⎥ ⎣0 -1⎦ ⎢√2⋅ⅈ √2\n",
|
||
"⎢⎢── ────⎥ ⎢──── ──────⎥ ⎢── ──────⎥ ⎢──── ──\n",
|
||
"⎣⎣2 2 ⎦ ⎣ 2 2 ⎦ ⎣2 2 ⎦ ⎣ 2 2 \n",
|
||
"\n",
|
||
"ⅈ⎤ ⎡√2 -√2 ⎤ ⎡ √2 -√2 ⎤ ⎡√2 -√2⋅ⅈ ⎤ ⎡ √2 -√2⋅ⅈ ⎤ ⎡1 ⅈ 1\n",
|
||
"─⎥ ⎢── ────⎥ ⎢ ── ────⎥ ⎢── ──────⎥ ⎢ ── ──────⎥ ⎢─ + ─ ─\n",
|
||
" ⎥ ⎢2 2 ⎥ ⎡1 0 ⎤ ⎢ 2 2 ⎥ ⎢2 2 ⎥ ⎢ 2 2 ⎥ ⎢2 2 2\n",
|
||
" ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ \n",
|
||
" ⎥ ⎢√2 √2 ⎥ ⎣0 -ⅈ⎦ ⎢√2⋅ⅈ √2⋅ⅈ⎥ ⎢√2 √2⋅ⅈ ⎥ ⎢√2⋅ⅈ -√2 ⎥ ⎢1 ⅈ 1\n",
|
||
" ⎥ ⎢── ── ⎥ ⎢──── ────⎥ ⎢── ──── ⎥ ⎢──── ──── ⎥ ⎢─ - ─ ─\n",
|
||
" ⎦ ⎣2 2 ⎦ ⎣ 2 2 ⎦ ⎣2 2 ⎦ ⎣ 2 2 ⎦ ⎣2 2 2\n",
|
||
"\n",
|
||
" ⅈ⎤ ⎡ √2 √2⎤ ⎡ √2 √2 ⎤ ⎡ 1 ⅈ 1 ⅈ⎤ ⎡\n",
|
||
" - ─⎥ ⎢ ── ──⎥ ⎢ ── ── ⎥ ⎢ ─ - ─ ─ + ─⎥ ⎢\n",
|
||
" 2⎥ ⎢ 2 2 ⎥ ⎡0 1⎤ ⎢ 2 2 ⎥ ⎡0 1⎤ ⎢ 2 2 2 2⎥ ⎡0 ⅈ⎤ ⎢\n",
|
||
" ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢\n",
|
||
" ⅈ⎥ ⎢-√2 √2⎥ ⎣1 0⎦ ⎢-√2⋅ⅈ √2⋅ⅈ⎥ ⎣ⅈ 0⎦ ⎢ 1 ⅈ 1 ⅈ⎥ ⎣1 0⎦ ⎢\n",
|
||
" + ─⎥ ⎢──── ──⎥ ⎢────── ────⎥ ⎢- ─ + ─ ─ + ─⎥ ⎢\n",
|
||
" 2⎦ ⎣ 2 2 ⎦ ⎣ 2 2 ⎦ ⎣ 2 2 2 2⎦ ⎣\n",
|
||
"\n",
|
||
" √2 √2⋅ⅈ⎤ ⎡ 1 ⅈ 1 ⅈ⎤ ⎡ √2 -√2 ⎤ ⎡ 1 ⅈ ⅈ⋅(-1 \n",
|
||
" ── ────⎥ ⎢ ─ - ─ - ─ + ─⎥ ⎢ ── ──── ⎥ ⎢ ─ - ─ ──────\n",
|
||
" 2 2 ⎥ ⎢ 2 2 2 2⎥ ⎡0 -1⎤ ⎢ 2 2 ⎥ ⎢ 2 2 2 \n",
|
||
" ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ \n",
|
||
"-√2⋅ⅈ -√2 ⎥ ⎢ 1 ⅈ 1 ⅈ⎥ ⎣1 0 ⎦ ⎢-√2⋅ⅈ -√2⋅ⅈ ⎥ ⎢ 1 ⅈ ⅈ⋅(-1 \n",
|
||
"────── ────⎥ ⎢- ─ + ─ - ─ + ─⎥ ⎢────── ──────⎥ ⎢- ─ + ─ ──────\n",
|
||
" 2 2 ⎦ ⎣ 2 2 2 2⎦ ⎣ 2 2 ⎦ ⎣ 2 2 2 \n",
|
||
"\n",
|
||
"+ ⅈ)⎤⎤\n",
|
||
"────⎥⎥\n",
|
||
" ⎥⎥\n",
|
||
" ⎥⎥\n",
|
||
"+ ⅈ)⎥⎥\n",
|
||
"────⎥⎥\n",
|
||
" ⎦⎦"
|
||
]
|
||
},
|
||
"execution_count": 1,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"import sympy\n",
|
||
"\n",
|
||
"M = sympy.Matrix\n",
|
||
"simplify = sympy.simplify\n",
|
||
"sqrt = sympy.sqrt\n",
|
||
"i = sympy.I\n",
|
||
"\n",
|
||
"from sympy.physics.quantum import Dagger\n",
|
||
"\n",
|
||
"sympy.init_printing()\n",
|
||
"H = simplify(M([[1, 1], [1, -1]]) / sqrt(2))\n",
|
||
"S = M([[1, 0], [0, i]])\n",
|
||
"C_L = [H, S]\n",
|
||
"basis_vectors = [M([1, 0]), M([0, 1])]\n",
|
||
"\n",
|
||
"def getitem(m, i, j):\n",
|
||
" # Note that sympy uses an extremely weird way to store the matrices,\n",
|
||
" # in particular the internal representation is vastly different from what\n",
|
||
" # is printed. For instance the H matrix is stored as a Mul object\n",
|
||
" # (even after using simplify) instead of a matrix. \n",
|
||
" # Therefore m[i][j] will NOT work. This is a workaround.\n",
|
||
" return (Dagger(basis_vectors[i]) * m * basis_vectors[j])[0]\n",
|
||
"\n",
|
||
"def is_known(C_L, a):\n",
|
||
" for c in C_L:\n",
|
||
" test = c * Dagger(a)\n",
|
||
" if(simplify(getitem(test, 0, 1)) != 0):\n",
|
||
" continue\n",
|
||
" if(simplify(getitem(test, 0, 0) / getitem(test, 1, 1)) == 1):\n",
|
||
" return True\n",
|
||
" return False\n",
|
||
"for i in range(5):\n",
|
||
" for m in (H, S):\n",
|
||
" for c in C_L:\n",
|
||
" c = simplify(c*m)\n",
|
||
" if(is_known(C_L, c)):\n",
|
||
" continue\n",
|
||
" C_L.append(c)\n",
|
||
"C_L"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 2,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"X = M([[0, 1], [1, 0]])\n",
|
||
"Z = M([[1, 0], [0, -1]])\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 3,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"s2m = {\"H\": H, \"S\": S, \"X\": X, \"Z\": Z}\n",
|
||
"def eval_str(s):\n",
|
||
" result = M([[1, 0], [0, 1]])\n",
|
||
" for c in s:\n",
|
||
" result *= s2m[c]\n",
|
||
" return result"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 4,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"def get_product_index(a):\n",
|
||
" for i,c in enumerate(C_L):\n",
|
||
" test = c * Dagger(a)\n",
|
||
" if(simplify(getitem(test, 0, 1)) != 0):\n",
|
||
" continue\n",
|
||
" if(simplify(getitem(test, 0, 0) / getitem(test, 1, 1)) == 1):\n",
|
||
" return i\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 5,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"from itertools import product\n",
|
||
"from collections import defaultdict\n",
|
||
"\n",
|
||
"results = defaultdict(set)\n",
|
||
"\n",
|
||
"def recursive_xs_products(length):\n",
|
||
" if(length == 1):\n",
|
||
" yield \"H\"\n",
|
||
" yield \"S\"\n",
|
||
" yield \"X\"\n",
|
||
" yield \"Z\"\n",
|
||
" else:\n",
|
||
" for p in recursive_xs_products(length - 1):\n",
|
||
" yield p\n",
|
||
" yield p + \"H\"\n",
|
||
" yield p + \"S\"\n",
|
||
" yield p + \"X\"\n",
|
||
" yield p + \"Z\"\n",
|
||
" \n",
|
||
" \n",
|
||
"for p in recursive_xs_products(5):\n",
|
||
" results[get_product_index(eval_str(p))] |= {p}\n",
|
||
" "
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 6,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"defaultdict(set,\n",
|
||
" {0: {'H',\n",
|
||
" 'HHH',\n",
|
||
" 'HHHHH',\n",
|
||
" 'HHHXX',\n",
|
||
" 'HHHZZ',\n",
|
||
" 'HHXHZ',\n",
|
||
" 'HHXXH',\n",
|
||
" 'HHZHX',\n",
|
||
" 'HHZZH',\n",
|
||
" 'HSSSS',\n",
|
||
" 'HSSZ',\n",
|
||
" 'HSXSX',\n",
|
||
" 'HSZS',\n",
|
||
" 'HXHHX',\n",
|
||
" 'HXHZH',\n",
|
||
" 'HXSXS',\n",
|
||
" 'HXX',\n",
|
||
" 'HXXHH',\n",
|
||
" 'HXXXX',\n",
|
||
" 'HXXZZ',\n",
|
||
" 'HXZXZ',\n",
|
||
" 'HXZZX',\n",
|
||
" 'HZHHZ',\n",
|
||
" 'HZHXH',\n",
|
||
" 'HZSS',\n",
|
||
" 'HZXXZ',\n",
|
||
" 'HZXZX',\n",
|
||
" 'HZZ',\n",
|
||
" 'HZZHH',\n",
|
||
" 'HZZXX',\n",
|
||
" 'HZZZZ',\n",
|
||
" 'SHSHS',\n",
|
||
" 'SSHX',\n",
|
||
" 'SSSSH',\n",
|
||
" 'SSZH',\n",
|
||
" 'SXSHZ',\n",
|
||
" 'SXSXH',\n",
|
||
" 'SZSH',\n",
|
||
" 'XHHHZ',\n",
|
||
" 'XHHXH',\n",
|
||
" 'XHSS',\n",
|
||
" 'XHXXZ',\n",
|
||
" 'XHXZX',\n",
|
||
" 'XHZ',\n",
|
||
" 'XHZHH',\n",
|
||
" 'XHZXX',\n",
|
||
" 'XHZZZ',\n",
|
||
" 'XSXSH',\n",
|
||
" 'XXH',\n",
|
||
" 'XXHHH',\n",
|
||
" 'XXHXX',\n",
|
||
" 'XXHZZ',\n",
|
||
" 'XXXHZ',\n",
|
||
" 'XXXXH',\n",
|
||
" 'XXZHX',\n",
|
||
" 'XXZZH',\n",
|
||
" 'XZHXZ',\n",
|
||
" 'XZHZX',\n",
|
||
" 'XZXHX',\n",
|
||
" 'XZXZH',\n",
|
||
" 'XZZHZ',\n",
|
||
" 'XZZXH',\n",
|
||
" 'ZHHHX',\n",
|
||
" 'ZHHZH',\n",
|
||
" 'ZHSXS',\n",
|
||
" 'ZHX',\n",
|
||
" 'ZHXHH',\n",
|
||
" 'ZHXXX',\n",
|
||
" 'ZHXZZ',\n",
|
||
" 'ZHZXZ',\n",
|
||
" 'ZHZZX',\n",
|
||
" 'ZSSH',\n",
|
||
" 'ZXHXZ',\n",
|
||
" 'ZXHZX',\n",
|
||
" 'ZXXHX',\n",
|
||
" 'ZXXZH',\n",
|
||
" 'ZXZHZ',\n",
|
||
" 'ZXZXH',\n",
|
||
" 'ZZH',\n",
|
||
" 'ZZHHH',\n",
|
||
" 'ZZHXX',\n",
|
||
" 'ZZHZZ',\n",
|
||
" 'ZZXHZ',\n",
|
||
" 'ZZXXH',\n",
|
||
" 'ZZZHX',\n",
|
||
" 'ZZZZH'},\n",
|
||
" 2: {'HH',\n",
|
||
" 'HHHH',\n",
|
||
" 'HHSSZ',\n",
|
||
" 'HHSZS',\n",
|
||
" 'HHXX',\n",
|
||
" 'HHZSS',\n",
|
||
" 'HHZZ',\n",
|
||
" 'HSSHX',\n",
|
||
" 'HSSZH',\n",
|
||
" 'HSZSH',\n",
|
||
" 'HXHSS',\n",
|
||
" 'HXHZ',\n",
|
||
" 'HXXH',\n",
|
||
" 'HZHX',\n",
|
||
" 'HZSSH',\n",
|
||
" 'HZZH',\n",
|
||
" 'SHHSZ',\n",
|
||
" 'SHHZS',\n",
|
||
" 'SHXHS',\n",
|
||
" 'SSHHZ',\n",
|
||
" 'SSHXH',\n",
|
||
" 'SSSS',\n",
|
||
" 'SSXXZ',\n",
|
||
" 'SSXZX',\n",
|
||
" 'SSZ',\n",
|
||
" 'SSZHH',\n",
|
||
" 'SSZXX',\n",
|
||
" 'SSZZZ',\n",
|
||
" 'SXSX',\n",
|
||
" 'SXXSZ',\n",
|
||
" 'SXXZS',\n",
|
||
" 'SXZXS',\n",
|
||
" 'SZHHS',\n",
|
||
" 'SZS',\n",
|
||
" 'SZSHH',\n",
|
||
" 'SZSXX',\n",
|
||
" 'SZSZZ',\n",
|
||
" 'SZXXS',\n",
|
||
" 'SZZSZ',\n",
|
||
" 'SZZZS',\n",
|
||
" 'XHHX',\n",
|
||
" 'XHSSH',\n",
|
||
" 'XHZH',\n",
|
||
" 'XSSXZ',\n",
|
||
" 'XSSZX',\n",
|
||
" 'XSXS',\n",
|
||
" 'XSZSX',\n",
|
||
" 'XX',\n",
|
||
" 'XXHH',\n",
|
||
" 'XXSSZ',\n",
|
||
" 'XXSZS',\n",
|
||
" 'XXXX',\n",
|
||
" 'XXZSS',\n",
|
||
" 'XXZZ',\n",
|
||
" 'XZSSX',\n",
|
||
" 'XZXSS',\n",
|
||
" 'XZXZ',\n",
|
||
" 'XZZX',\n",
|
||
" 'ZHHSS',\n",
|
||
" 'ZHHZ',\n",
|
||
" 'ZHXH',\n",
|
||
" 'ZSHHS',\n",
|
||
" 'ZSS',\n",
|
||
" 'ZSSHH',\n",
|
||
" 'ZSSXX',\n",
|
||
" 'ZSSZZ',\n",
|
||
" 'ZSXXS',\n",
|
||
" 'ZSZSZ',\n",
|
||
" 'ZSZZS',\n",
|
||
" 'ZXSSX',\n",
|
||
" 'ZXXSS',\n",
|
||
" 'ZXXZ',\n",
|
||
" 'ZXZX',\n",
|
||
" 'ZZ',\n",
|
||
" 'ZZHH',\n",
|
||
" 'ZZSSZ',\n",
|
||
" 'ZZSZS',\n",
|
||
" 'ZZXX',\n",
|
||
" 'ZZZSS',\n",
|
||
" 'ZZZZ'},\n",
|
||
" 4: {'HHHS',\n",
|
||
" 'HS',\n",
|
||
" 'HSHH',\n",
|
||
" 'HSSSZ',\n",
|
||
" 'HSSZS',\n",
|
||
" 'HSXX',\n",
|
||
" 'HSZSS',\n",
|
||
" 'HSZZ',\n",
|
||
" 'HXSXZ',\n",
|
||
" 'HXSZX',\n",
|
||
" 'HXXS',\n",
|
||
" 'HXZSX',\n",
|
||
" 'HZSSS',\n",
|
||
" 'HZSZ',\n",
|
||
" 'HZXSX',\n",
|
||
" 'HZZS',\n",
|
||
" 'SHSHZ',\n",
|
||
" 'SHSXH',\n",
|
||
" 'SSHXS',\n",
|
||
" 'SSZHS',\n",
|
||
" 'SZSHS',\n",
|
||
" 'XHSSS',\n",
|
||
" 'XHSZ',\n",
|
||
" 'XHXSX',\n",
|
||
" 'XHZS',\n",
|
||
" 'XSHSH',\n",
|
||
" 'XXHS',\n",
|
||
" 'XZHSX',\n",
|
||
" 'ZHSXZ',\n",
|
||
" 'ZHSZX',\n",
|
||
" 'ZHXS',\n",
|
||
" 'ZHZSX',\n",
|
||
" 'ZSSHS',\n",
|
||
" 'ZXHSX',\n",
|
||
" 'ZZHS'},\n",
|
||
" 13: {'HHHX',\n",
|
||
" 'HHSSH',\n",
|
||
" 'HHZH',\n",
|
||
" 'HSSXZ',\n",
|
||
" 'HSSZX',\n",
|
||
" 'HSXS',\n",
|
||
" 'HSZSX',\n",
|
||
" 'HX',\n",
|
||
" 'HXHH',\n",
|
||
" 'HXSSZ',\n",
|
||
" 'HXSZS',\n",
|
||
" 'HXXX',\n",
|
||
" 'HXZSS',\n",
|
||
" 'HXZZ',\n",
|
||
" 'HZSSX',\n",
|
||
" 'HZXSS',\n",
|
||
" 'HZXZ',\n",
|
||
" 'HZZX',\n",
|
||
" 'SHHSH',\n",
|
||
" 'SSH',\n",
|
||
" 'SSHHH',\n",
|
||
" 'SSHXX',\n",
|
||
" 'SSHZZ',\n",
|
||
" 'SSXHZ',\n",
|
||
" 'SSXXH',\n",
|
||
" 'SSZHX',\n",
|
||
" 'SSZZH',\n",
|
||
" 'SXXSH',\n",
|
||
" 'SZSHX',\n",
|
||
" 'SZSZH',\n",
|
||
" 'SZZSH',\n",
|
||
" 'XHSSX',\n",
|
||
" 'XHXSS',\n",
|
||
" 'XHXZ',\n",
|
||
" 'XHZX',\n",
|
||
" 'XSSHZ',\n",
|
||
" 'XSSXH',\n",
|
||
" 'XXHX',\n",
|
||
" 'XXSSH',\n",
|
||
" 'XXZH',\n",
|
||
" 'XZHSS',\n",
|
||
" 'XZHZ',\n",
|
||
" 'XZXH',\n",
|
||
" 'ZH',\n",
|
||
" 'ZHHH',\n",
|
||
" 'ZHSSZ',\n",
|
||
" 'ZHSZS',\n",
|
||
" 'ZHXX',\n",
|
||
" 'ZHZSS',\n",
|
||
" 'ZHZZ',\n",
|
||
" 'ZSSHX',\n",
|
||
" 'ZSSZH',\n",
|
||
" 'ZSZSH',\n",
|
||
" 'ZXHSS',\n",
|
||
" 'ZXHZ',\n",
|
||
" 'ZXXH',\n",
|
||
" 'ZZHX',\n",
|
||
" 'ZZSSH',\n",
|
||
" 'ZZZH'},\n",
|
||
" 7: {'HHHSS',\n",
|
||
" 'HHHZ',\n",
|
||
" 'HHXH',\n",
|
||
" 'HSHHS',\n",
|
||
" 'HSS',\n",
|
||
" 'HSSHH',\n",
|
||
" 'HSSXX',\n",
|
||
" 'HSSZZ',\n",
|
||
" 'HSXXS',\n",
|
||
" 'HSZSZ',\n",
|
||
" 'HSZZS',\n",
|
||
" 'HXSSX',\n",
|
||
" 'HXXSS',\n",
|
||
" 'HXXZ',\n",
|
||
" 'HXZX',\n",
|
||
" 'HZ',\n",
|
||
" 'HZHH',\n",
|
||
" 'HZSSZ',\n",
|
||
" 'HZSZS',\n",
|
||
" 'HZXX',\n",
|
||
" 'HZZSS',\n",
|
||
" 'HZZZ',\n",
|
||
" 'SSHXZ',\n",
|
||
" 'SSHZX',\n",
|
||
" 'SSXHX',\n",
|
||
" 'SSXZH',\n",
|
||
" 'SSZHZ',\n",
|
||
" 'SSZXH',\n",
|
||
" 'SXSH',\n",
|
||
" 'SZSHZ',\n",
|
||
" 'SZSXH',\n",
|
||
" 'XH',\n",
|
||
" 'XHHH',\n",
|
||
" 'XHSSZ',\n",
|
||
" 'XHSZS',\n",
|
||
" 'XHXX',\n",
|
||
" 'XHZSS',\n",
|
||
" 'XHZZ',\n",
|
||
" 'XSSHX',\n",
|
||
" 'XSSZH',\n",
|
||
" 'XSZSH',\n",
|
||
" 'XXHSS',\n",
|
||
" 'XXHZ',\n",
|
||
" 'XXXH',\n",
|
||
" 'XZHX',\n",
|
||
" 'XZSSH',\n",
|
||
" 'XZZH',\n",
|
||
" 'ZHSSX',\n",
|
||
" 'ZHXSS',\n",
|
||
" 'ZHXZ',\n",
|
||
" 'ZHZX',\n",
|
||
" 'ZSSHZ',\n",
|
||
" 'ZSSXH',\n",
|
||
" 'ZXHX',\n",
|
||
" 'ZXSSH',\n",
|
||
" 'ZXZH',\n",
|
||
" 'ZZHSS',\n",
|
||
" 'ZZHZ',\n",
|
||
" 'ZZXH'},\n",
|
||
" 1: {'HHHHS',\n",
|
||
" 'HHS',\n",
|
||
" 'HHSHH',\n",
|
||
" 'HHSXX',\n",
|
||
" 'HHSZZ',\n",
|
||
" 'HHXXS',\n",
|
||
" 'HHZSZ',\n",
|
||
" 'HHZZS',\n",
|
||
" 'HXHSZ',\n",
|
||
" 'HXHZS',\n",
|
||
" 'HXXHS',\n",
|
||
" 'HZHXS',\n",
|
||
" 'HZZHS',\n",
|
||
" 'S',\n",
|
||
" 'SHH',\n",
|
||
" 'SHHHH',\n",
|
||
" 'SHHXX',\n",
|
||
" 'SHHZZ',\n",
|
||
" 'SHXHZ',\n",
|
||
" 'SHXXH',\n",
|
||
" 'SHZHX',\n",
|
||
" 'SHZZH',\n",
|
||
" 'SSSSS',\n",
|
||
" 'SSSZ',\n",
|
||
" 'SSXSX',\n",
|
||
" 'SSZS',\n",
|
||
" 'SXHHX',\n",
|
||
" 'SXHZH',\n",
|
||
" 'SXSXS',\n",
|
||
" 'SXX',\n",
|
||
" 'SXXHH',\n",
|
||
" 'SXXXX',\n",
|
||
" 'SXXZZ',\n",
|
||
" 'SXZXZ',\n",
|
||
" 'SXZZX',\n",
|
||
" 'SZHHZ',\n",
|
||
" 'SZHXH',\n",
|
||
" 'SZSS',\n",
|
||
" 'SZXXZ',\n",
|
||
" 'SZXZX',\n",
|
||
" 'SZZ',\n",
|
||
" 'SZZHH',\n",
|
||
" 'SZZXX',\n",
|
||
" 'SZZZZ',\n",
|
||
" 'XHHXS',\n",
|
||
" 'XHZHS',\n",
|
||
" 'XSSSX',\n",
|
||
" 'XSXSS',\n",
|
||
" 'XSXZ',\n",
|
||
" 'XSZX',\n",
|
||
" 'XXHHS',\n",
|
||
" 'XXS',\n",
|
||
" 'XXSHH',\n",
|
||
" 'XXSXX',\n",
|
||
" 'XXSZZ',\n",
|
||
" 'XXXXS',\n",
|
||
" 'XXZSZ',\n",
|
||
" 'XXZZS',\n",
|
||
" 'XZSX',\n",
|
||
" 'XZXSZ',\n",
|
||
" 'XZXZS',\n",
|
||
" 'XZZXS',\n",
|
||
" 'ZHHSZ',\n",
|
||
" 'ZHHZS',\n",
|
||
" 'ZHXHS',\n",
|
||
" 'ZSHHZ',\n",
|
||
" 'ZSHXH',\n",
|
||
" 'ZSSS',\n",
|
||
" 'ZSXXZ',\n",
|
||
" 'ZSXZX',\n",
|
||
" 'ZSZ',\n",
|
||
" 'ZSZHH',\n",
|
||
" 'ZSZXX',\n",
|
||
" 'ZSZZZ',\n",
|
||
" 'ZXSX',\n",
|
||
" 'ZXXSZ',\n",
|
||
" 'ZXXZS',\n",
|
||
" 'ZXZXS',\n",
|
||
" 'ZZHHS',\n",
|
||
" 'ZZS',\n",
|
||
" 'ZZSHH',\n",
|
||
" 'ZZSXX',\n",
|
||
" 'ZZSZZ',\n",
|
||
" 'ZZXXS',\n",
|
||
" 'ZZZSZ',\n",
|
||
" 'ZZZZS'},\n",
|
||
" 14: {'HHHHX',\n",
|
||
" 'HHHZH',\n",
|
||
" 'HHSXS',\n",
|
||
" 'HHX',\n",
|
||
" 'HHXHH',\n",
|
||
" 'HHXXX',\n",
|
||
" 'HHXZZ',\n",
|
||
" 'HHZXZ',\n",
|
||
" 'HHZZX',\n",
|
||
" 'HSSH',\n",
|
||
" 'HXHXZ',\n",
|
||
" 'HXHZX',\n",
|
||
" 'HXXHX',\n",
|
||
" 'HXXZH',\n",
|
||
" 'HXZHZ',\n",
|
||
" 'HXZXH',\n",
|
||
" 'HZH',\n",
|
||
" 'HZHHH',\n",
|
||
" 'HZHXX',\n",
|
||
" 'HZHZZ',\n",
|
||
" 'HZXHZ',\n",
|
||
" 'HZXXH',\n",
|
||
" 'HZZHX',\n",
|
||
" 'HZZZH',\n",
|
||
" 'SHHXS',\n",
|
||
" 'SHZHS',\n",
|
||
" 'SSSSX',\n",
|
||
" 'SSXSS',\n",
|
||
" 'SSXZ',\n",
|
||
" 'SSZX',\n",
|
||
" 'SXHHS',\n",
|
||
" 'SXS',\n",
|
||
" 'SXSHH',\n",
|
||
" 'SXSXX',\n",
|
||
" 'SXSZZ',\n",
|
||
" 'SXXXS',\n",
|
||
" 'SXZSZ',\n",
|
||
" 'SXZZS',\n",
|
||
" 'SZSX',\n",
|
||
" 'SZXSZ',\n",
|
||
" 'SZXZS',\n",
|
||
" 'SZZXS',\n",
|
||
" 'X',\n",
|
||
" 'XHH',\n",
|
||
" 'XHHHH',\n",
|
||
" 'XHHXX',\n",
|
||
" 'XHHZZ',\n",
|
||
" 'XHXHZ',\n",
|
||
" 'XHXXH',\n",
|
||
" 'XHZHX',\n",
|
||
" 'XHZZH',\n",
|
||
" 'XSSSS',\n",
|
||
" 'XSSZ',\n",
|
||
" 'XSXSX',\n",
|
||
" 'XSZS',\n",
|
||
" 'XXHHX',\n",
|
||
" 'XXHZH',\n",
|
||
" 'XXSXS',\n",
|
||
" 'XXX',\n",
|
||
" 'XXXHH',\n",
|
||
" 'XXXXX',\n",
|
||
" 'XXXZZ',\n",
|
||
" 'XXZXZ',\n",
|
||
" 'XXZZX',\n",
|
||
" 'XZHHZ',\n",
|
||
" 'XZHXH',\n",
|
||
" 'XZSS',\n",
|
||
" 'XZXXZ',\n",
|
||
" 'XZXZX',\n",
|
||
" 'XZZ',\n",
|
||
" 'XZZHH',\n",
|
||
" 'XZZXX',\n",
|
||
" 'XZZZZ',\n",
|
||
" 'ZHHXZ',\n",
|
||
" 'ZHHZX',\n",
|
||
" 'ZHXHX',\n",
|
||
" 'ZHXZH',\n",
|
||
" 'ZHZHZ',\n",
|
||
" 'ZHZXH',\n",
|
||
" 'ZSSX',\n",
|
||
" 'ZSXSZ',\n",
|
||
" 'ZSXZS',\n",
|
||
" 'ZSZXS',\n",
|
||
" 'ZXHHZ',\n",
|
||
" 'ZXHXH',\n",
|
||
" 'ZXSS',\n",
|
||
" 'ZXXXZ',\n",
|
||
" 'ZXXZX',\n",
|
||
" 'ZXZ',\n",
|
||
" 'ZXZHH',\n",
|
||
" 'ZXZXX',\n",
|
||
" 'ZXZZZ',\n",
|
||
" 'ZZHHX',\n",
|
||
" 'ZZHZH',\n",
|
||
" 'ZZSXS',\n",
|
||
" 'ZZX',\n",
|
||
" 'ZZXHH',\n",
|
||
" 'ZZXXX',\n",
|
||
" 'ZZXZZ',\n",
|
||
" 'ZZZXZ',\n",
|
||
" 'ZZZZX'},\n",
|
||
" 5: {'HHHHZ',\n",
|
||
" 'HHHXH',\n",
|
||
" 'HHSS',\n",
|
||
" 'HHXXZ',\n",
|
||
" 'HHXZX',\n",
|
||
" 'HHZ',\n",
|
||
" 'HHZHH',\n",
|
||
" 'HHZXX',\n",
|
||
" 'HHZZZ',\n",
|
||
" 'HSXSH',\n",
|
||
" 'HXH',\n",
|
||
" 'HXHHH',\n",
|
||
" 'HXHXX',\n",
|
||
" 'HXHZZ',\n",
|
||
" 'HXXHZ',\n",
|
||
" 'HXXXH',\n",
|
||
" 'HXZHX',\n",
|
||
" 'HXZZH',\n",
|
||
" 'HZHXZ',\n",
|
||
" 'HZHZX',\n",
|
||
" 'HZXHX',\n",
|
||
" 'HZXZH',\n",
|
||
" 'HZZHZ',\n",
|
||
" 'HZZXH',\n",
|
||
" 'SHHS',\n",
|
||
" 'SS',\n",
|
||
" 'SSHH',\n",
|
||
" 'SSSSZ',\n",
|
||
" 'SSSZS',\n",
|
||
" 'SSXX',\n",
|
||
" 'SSZSS',\n",
|
||
" 'SSZZ',\n",
|
||
" 'SXSXZ',\n",
|
||
" 'SXSZX',\n",
|
||
" 'SXXS',\n",
|
||
" 'SXZSX',\n",
|
||
" 'SZSSS',\n",
|
||
" 'SZSZ',\n",
|
||
" 'SZXSX',\n",
|
||
" 'SZZS',\n",
|
||
" 'XHHXZ',\n",
|
||
" 'XHHZX',\n",
|
||
" 'XHXHX',\n",
|
||
" 'XHXZH',\n",
|
||
" 'XHZHZ',\n",
|
||
" 'XHZXH',\n",
|
||
" 'XSSX',\n",
|
||
" 'XSXSZ',\n",
|
||
" 'XSXZS',\n",
|
||
" 'XSZXS',\n",
|
||
" 'XXHHZ',\n",
|
||
" 'XXHXH',\n",
|
||
" 'XXSS',\n",
|
||
" 'XXXXZ',\n",
|
||
" 'XXXZX',\n",
|
||
" 'XXZ',\n",
|
||
" 'XXZHH',\n",
|
||
" 'XXZXX',\n",
|
||
" 'XXZZZ',\n",
|
||
" 'XZHHX',\n",
|
||
" 'XZHZH',\n",
|
||
" 'XZSXS',\n",
|
||
" 'XZX',\n",
|
||
" 'XZXHH',\n",
|
||
" 'XZXXX',\n",
|
||
" 'XZXZZ',\n",
|
||
" 'XZZXZ',\n",
|
||
" 'XZZZX',\n",
|
||
" 'Z',\n",
|
||
" 'ZHH',\n",
|
||
" 'ZHHHH',\n",
|
||
" 'ZHHXX',\n",
|
||
" 'ZHHZZ',\n",
|
||
" 'ZHXHZ',\n",
|
||
" 'ZHXXH',\n",
|
||
" 'ZHZHX',\n",
|
||
" 'ZHZZH',\n",
|
||
" 'ZSSSS',\n",
|
||
" 'ZSSZ',\n",
|
||
" 'ZSXSX',\n",
|
||
" 'ZSZS',\n",
|
||
" 'ZXHHX',\n",
|
||
" 'ZXHZH',\n",
|
||
" 'ZXSXS',\n",
|
||
" 'ZXX',\n",
|
||
" 'ZXXHH',\n",
|
||
" 'ZXXXX',\n",
|
||
" 'ZXXZZ',\n",
|
||
" 'ZXZXZ',\n",
|
||
" 'ZXZZX',\n",
|
||
" 'ZZHHZ',\n",
|
||
" 'ZZHXH',\n",
|
||
" 'ZZSS',\n",
|
||
" 'ZZXXZ',\n",
|
||
" 'ZZXZX',\n",
|
||
" 'ZZZ',\n",
|
||
" 'ZZZHH',\n",
|
||
" 'ZZZXX',\n",
|
||
" 'ZZZZZ'},\n",
|
||
" 12: {'HHHSH',\n",
|
||
" 'HSH',\n",
|
||
" 'HSHHH',\n",
|
||
" 'HSHXX',\n",
|
||
" 'HSHZZ',\n",
|
||
" 'HSXHZ',\n",
|
||
" 'HSXXH',\n",
|
||
" 'HSZHX',\n",
|
||
" 'HSZZH',\n",
|
||
" 'HXXSH',\n",
|
||
" 'HZSHX',\n",
|
||
" 'HZSZH',\n",
|
||
" 'HZZSH',\n",
|
||
" 'SHSX',\n",
|
||
" 'SHXSZ',\n",
|
||
" 'SHXZS',\n",
|
||
" 'SHZXS',\n",
|
||
" 'SXHXS',\n",
|
||
" 'SXZHS',\n",
|
||
" 'SZHSZ',\n",
|
||
" 'SZHZS',\n",
|
||
" 'SZXHS',\n",
|
||
" 'XHSHX',\n",
|
||
" 'XHSZH',\n",
|
||
" 'XHZSH',\n",
|
||
" 'XSHS',\n",
|
||
" 'XXHSH',\n",
|
||
" 'ZHXSH',\n",
|
||
" 'ZSHSZ',\n",
|
||
" 'ZSHZS',\n",
|
||
" 'ZSXHS',\n",
|
||
" 'ZZHSH'},\n",
|
||
" 23: {'HHHSX',\n",
|
||
" 'HSHHX',\n",
|
||
" 'HSHZH',\n",
|
||
" 'HSSXS',\n",
|
||
" 'HSX',\n",
|
||
" 'HSXHH',\n",
|
||
" 'HSXXX',\n",
|
||
" 'HSXZZ',\n",
|
||
" 'HSZXZ',\n",
|
||
" 'HSZZX',\n",
|
||
" 'HXSSS',\n",
|
||
" 'HXSZ',\n",
|
||
" 'HXXSX',\n",
|
||
" 'HXZS',\n",
|
||
" 'HZSXZ',\n",
|
||
" 'HZSZX',\n",
|
||
" 'HZXS',\n",
|
||
" 'HZZSX',\n",
|
||
" 'SHXSH',\n",
|
||
" 'SSHSZ',\n",
|
||
" 'SSHZS',\n",
|
||
" 'SSXHS',\n",
|
||
" 'SZHSH',\n",
|
||
" 'XHSXZ',\n",
|
||
" 'XHSZX',\n",
|
||
" 'XHXS',\n",
|
||
" 'XHZSX',\n",
|
||
" 'XSSHS',\n",
|
||
" 'XXHSX',\n",
|
||
" 'XZHS',\n",
|
||
" 'ZHSSS',\n",
|
||
" 'ZHSZ',\n",
|
||
" 'ZHXSX',\n",
|
||
" 'ZHZS',\n",
|
||
" 'ZSHSH',\n",
|
||
" 'ZXHS',\n",
|
||
" 'ZZHSX'},\n",
|
||
" 10: {'HHHSZ',\n",
|
||
" 'HHHZS',\n",
|
||
" 'HHXHS',\n",
|
||
" 'HSHHZ',\n",
|
||
" 'HSHXH',\n",
|
||
" 'HSSS',\n",
|
||
" 'HSXXZ',\n",
|
||
" 'HSXZX',\n",
|
||
" 'HSZ',\n",
|
||
" 'HSZHH',\n",
|
||
" 'HSZXX',\n",
|
||
" 'HSZZZ',\n",
|
||
" 'HXSX',\n",
|
||
" 'HXXSZ',\n",
|
||
" 'HXXZS',\n",
|
||
" 'HXZXS',\n",
|
||
" 'HZHHS',\n",
|
||
" 'HZS',\n",
|
||
" 'HZSHH',\n",
|
||
" 'HZSXX',\n",
|
||
" 'HZSZZ',\n",
|
||
" 'HZXXS',\n",
|
||
" 'HZZSZ',\n",
|
||
" 'HZZZS',\n",
|
||
" 'SHSH',\n",
|
||
" 'SSHSX',\n",
|
||
" 'SXSHS',\n",
|
||
" 'XHHHS',\n",
|
||
" 'XHS',\n",
|
||
" 'XHSHH',\n",
|
||
" 'XHSXX',\n",
|
||
" 'XHSZZ',\n",
|
||
" 'XHXXS',\n",
|
||
" 'XHZSZ',\n",
|
||
" 'XHZZS',\n",
|
||
" 'XXHSZ',\n",
|
||
" 'XXHZS',\n",
|
||
" 'XXXHS',\n",
|
||
" 'XZHXS',\n",
|
||
" 'XZZHS',\n",
|
||
" 'ZHSX',\n",
|
||
" 'ZHXSZ',\n",
|
||
" 'ZHXZS',\n",
|
||
" 'ZHZXS',\n",
|
||
" 'ZXHXS',\n",
|
||
" 'ZXZHS',\n",
|
||
" 'ZZHSZ',\n",
|
||
" 'ZZHZS',\n",
|
||
" 'ZZXHS'},\n",
|
||
" 17: {'HHHXS',\n",
|
||
" 'HHZHS',\n",
|
||
" 'HSSSX',\n",
|
||
" 'HSXSS',\n",
|
||
" 'HSXZ',\n",
|
||
" 'HSZX',\n",
|
||
" 'HXHHS',\n",
|
||
" 'HXS',\n",
|
||
" 'HXSHH',\n",
|
||
" 'HXSXX',\n",
|
||
" 'HXSZZ',\n",
|
||
" 'HXXXS',\n",
|
||
" 'HXZSZ',\n",
|
||
" 'HXZZS',\n",
|
||
" 'HZSX',\n",
|
||
" 'HZXSZ',\n",
|
||
" 'HZXZS',\n",
|
||
" 'HZZXS',\n",
|
||
" 'SHSHX',\n",
|
||
" 'SHSZH',\n",
|
||
" 'SHZSH',\n",
|
||
" 'SSHS',\n",
|
||
" 'SXHSH',\n",
|
||
" 'XHSX',\n",
|
||
" 'XHXSZ',\n",
|
||
" 'XHXZS',\n",
|
||
" 'XHZXS',\n",
|
||
" 'XXHXS',\n",
|
||
" 'XXZHS',\n",
|
||
" 'XZHSZ',\n",
|
||
" 'XZHZS',\n",
|
||
" 'XZXHS',\n",
|
||
" 'ZHHHS',\n",
|
||
" 'ZHS',\n",
|
||
" 'ZHSHH',\n",
|
||
" 'ZHSXX',\n",
|
||
" 'ZHSZZ',\n",
|
||
" 'ZHXXS',\n",
|
||
" 'ZHZSZ',\n",
|
||
" 'ZHZZS',\n",
|
||
" 'ZXHSZ',\n",
|
||
" 'ZXHZS',\n",
|
||
" 'ZXXHS',\n",
|
||
" 'ZZHXS',\n",
|
||
" 'ZZZHS'},\n",
|
||
" 20: {'HHHXZ',\n",
|
||
" 'HHHZX',\n",
|
||
" 'HHXHX',\n",
|
||
" 'HHXZH',\n",
|
||
" 'HHZHZ',\n",
|
||
" 'HHZXH',\n",
|
||
" 'HSSX',\n",
|
||
" 'HSXSZ',\n",
|
||
" 'HSXZS',\n",
|
||
" 'HSZXS',\n",
|
||
" 'HXHHZ',\n",
|
||
" 'HXHXH',\n",
|
||
" 'HXSS',\n",
|
||
" 'HXXXZ',\n",
|
||
" 'HXXZX',\n",
|
||
" 'HXZ',\n",
|
||
" 'HXZHH',\n",
|
||
" 'HXZXX',\n",
|
||
" 'HXZZZ',\n",
|
||
" 'HZHHX',\n",
|
||
" 'HZHZH',\n",
|
||
" 'HZSXS',\n",
|
||
" 'HZX',\n",
|
||
" 'HZXHH',\n",
|
||
" 'HZXXX',\n",
|
||
" 'HZXZZ',\n",
|
||
" 'HZZXZ',\n",
|
||
" 'HZZZX',\n",
|
||
" 'SSHSS',\n",
|
||
" 'SSHZ',\n",
|
||
" 'SSXH',\n",
|
||
" 'SXSHX',\n",
|
||
" 'SXSZH',\n",
|
||
" 'SXZSH',\n",
|
||
" 'SZXSH',\n",
|
||
" 'XHHHX',\n",
|
||
" 'XHHZH',\n",
|
||
" 'XHSXS',\n",
|
||
" 'XHX',\n",
|
||
" 'XHXHH',\n",
|
||
" 'XHXXX',\n",
|
||
" 'XHXZZ',\n",
|
||
" 'XHZXZ',\n",
|
||
" 'XHZZX',\n",
|
||
" 'XSSH',\n",
|
||
" 'XXHXZ',\n",
|
||
" 'XXHZX',\n",
|
||
" 'XXXHX',\n",
|
||
" 'XXXZH',\n",
|
||
" 'XXZHZ',\n",
|
||
" 'XXZXH',\n",
|
||
" 'XZH',\n",
|
||
" 'XZHHH',\n",
|
||
" 'XZHXX',\n",
|
||
" 'XZHZZ',\n",
|
||
" 'XZXHZ',\n",
|
||
" 'XZXXH',\n",
|
||
" 'XZZHX',\n",
|
||
" 'XZZZH',\n",
|
||
" 'ZHHHZ',\n",
|
||
" 'ZHHXH',\n",
|
||
" 'ZHSS',\n",
|
||
" 'ZHXXZ',\n",
|
||
" 'ZHXZX',\n",
|
||
" 'ZHZ',\n",
|
||
" 'ZHZHH',\n",
|
||
" 'ZHZXX',\n",
|
||
" 'ZHZZZ',\n",
|
||
" 'ZSXSH',\n",
|
||
" 'ZXH',\n",
|
||
" 'ZXHHH',\n",
|
||
" 'ZXHXX',\n",
|
||
" 'ZXHZZ',\n",
|
||
" 'ZXXHZ',\n",
|
||
" 'ZXXXH',\n",
|
||
" 'ZXZHX',\n",
|
||
" 'ZXZZH',\n",
|
||
" 'ZZHXZ',\n",
|
||
" 'ZZHZX',\n",
|
||
" 'ZZXHX',\n",
|
||
" 'ZZXZH',\n",
|
||
" 'ZZZHZ',\n",
|
||
" 'ZZZXH'},\n",
|
||
" 3: {'HHSH',\n",
|
||
" 'HSHSX',\n",
|
||
" 'HXSHS',\n",
|
||
" 'SH',\n",
|
||
" 'SHHH',\n",
|
||
" 'SHSSZ',\n",
|
||
" 'SHSZS',\n",
|
||
" 'SHXX',\n",
|
||
" 'SHZSS',\n",
|
||
" 'SHZZ',\n",
|
||
" 'SSSHX',\n",
|
||
" 'SSSZH',\n",
|
||
" 'SSZSH',\n",
|
||
" 'SXHSS',\n",
|
||
" 'SXHZ',\n",
|
||
" 'SXXH',\n",
|
||
" 'SZHX',\n",
|
||
" 'SZSSH',\n",
|
||
" 'SZZH',\n",
|
||
" 'XSHXZ',\n",
|
||
" 'XSHZX',\n",
|
||
" 'XSXHX',\n",
|
||
" 'XSXZH',\n",
|
||
" 'XSZHZ',\n",
|
||
" 'XSZXH',\n",
|
||
" 'XXSH',\n",
|
||
" 'XZSHZ',\n",
|
||
" 'XZSXH',\n",
|
||
" 'ZHSHS',\n",
|
||
" 'ZSHX',\n",
|
||
" 'ZSSSH',\n",
|
||
" 'ZSZH',\n",
|
||
" 'ZXSHZ',\n",
|
||
" 'ZXSXH',\n",
|
||
" 'ZZSH'},\n",
|
||
" 16: {'HHSX',\n",
|
||
" 'HHXSZ',\n",
|
||
" 'HHXZS',\n",
|
||
" 'HHZXS',\n",
|
||
" 'HXHXS',\n",
|
||
" 'HXZHS',\n",
|
||
" 'HZHSZ',\n",
|
||
" 'HZHZS',\n",
|
||
" 'HZXHS',\n",
|
||
" 'SHHX',\n",
|
||
" 'SHSSH',\n",
|
||
" 'SHZH',\n",
|
||
" 'SSSXZ',\n",
|
||
" 'SSSZX',\n",
|
||
" 'SSXS',\n",
|
||
" 'SSZSX',\n",
|
||
" 'SX',\n",
|
||
" 'SXHH',\n",
|
||
" 'SXSSZ',\n",
|
||
" 'SXSZS',\n",
|
||
" 'SXXX',\n",
|
||
" 'SXZSS',\n",
|
||
" 'SXZZ',\n",
|
||
" 'SZSSX',\n",
|
||
" 'SZXSS',\n",
|
||
" 'SZXZ',\n",
|
||
" 'SZZX',\n",
|
||
" 'XHHSZ',\n",
|
||
" 'XHHZS',\n",
|
||
" 'XHXHS',\n",
|
||
" 'XSHHZ',\n",
|
||
" 'XSHXH',\n",
|
||
" 'XSSS',\n",
|
||
" 'XSXXZ',\n",
|
||
" 'XSXZX',\n",
|
||
" 'XSZ',\n",
|
||
" 'XSZHH',\n",
|
||
" 'XSZXX',\n",
|
||
" 'XSZZZ',\n",
|
||
" 'XXSX',\n",
|
||
" 'XXXSZ',\n",
|
||
" 'XXXZS',\n",
|
||
" 'XXZXS',\n",
|
||
" 'XZHHS',\n",
|
||
" 'XZS',\n",
|
||
" 'XZSHH',\n",
|
||
" 'XZSXX',\n",
|
||
" 'XZSZZ',\n",
|
||
" 'XZXXS',\n",
|
||
" 'XZZSZ',\n",
|
||
" 'XZZZS',\n",
|
||
" 'ZHHXS',\n",
|
||
" 'ZHZHS',\n",
|
||
" 'ZSSSX',\n",
|
||
" 'ZSXSS',\n",
|
||
" 'ZSXZ',\n",
|
||
" 'ZSZX',\n",
|
||
" 'ZXHHS',\n",
|
||
" 'ZXS',\n",
|
||
" 'ZXSHH',\n",
|
||
" 'ZXSXX',\n",
|
||
" 'ZXSZZ',\n",
|
||
" 'ZXXXS',\n",
|
||
" 'ZXZSZ',\n",
|
||
" 'ZXZZS',\n",
|
||
" 'ZZSX',\n",
|
||
" 'ZZXSZ',\n",
|
||
" 'ZZXZS',\n",
|
||
" 'ZZZXS'},\n",
|
||
" 8: {'HHSSS',\n",
|
||
" 'HHSZ',\n",
|
||
" 'HHXSX',\n",
|
||
" 'HHZS',\n",
|
||
" 'HSHSH',\n",
|
||
" 'HXHS',\n",
|
||
" 'HZHSX',\n",
|
||
" 'SHHSS',\n",
|
||
" 'SHHZ',\n",
|
||
" 'SHXH',\n",
|
||
" 'SSHHS',\n",
|
||
" 'SSS',\n",
|
||
" 'SSSHH',\n",
|
||
" 'SSSXX',\n",
|
||
" 'SSSZZ',\n",
|
||
" 'SSXXS',\n",
|
||
" 'SSZSZ',\n",
|
||
" 'SSZZS',\n",
|
||
" 'SXSSX',\n",
|
||
" 'SXXSS',\n",
|
||
" 'SXXZ',\n",
|
||
" 'SXZX',\n",
|
||
" 'SZ',\n",
|
||
" 'SZHH',\n",
|
||
" 'SZSSZ',\n",
|
||
" 'SZSZS',\n",
|
||
" 'SZXX',\n",
|
||
" 'SZZSS',\n",
|
||
" 'SZZZ',\n",
|
||
" 'XHHSX',\n",
|
||
" 'XSHHX',\n",
|
||
" 'XSHZH',\n",
|
||
" 'XSSXS',\n",
|
||
" 'XSX',\n",
|
||
" 'XSXHH',\n",
|
||
" 'XSXXX',\n",
|
||
" 'XSXZZ',\n",
|
||
" 'XSZXZ',\n",
|
||
" 'XSZZX',\n",
|
||
" 'XXSSS',\n",
|
||
" 'XXSZ',\n",
|
||
" 'XXXSX',\n",
|
||
" 'XXZS',\n",
|
||
" 'XZSXZ',\n",
|
||
" 'XZSZX',\n",
|
||
" 'XZXS',\n",
|
||
" 'XZZSX',\n",
|
||
" 'ZHHS',\n",
|
||
" 'ZS',\n",
|
||
" 'ZSHH',\n",
|
||
" 'ZSSSZ',\n",
|
||
" 'ZSSZS',\n",
|
||
" 'ZSXX',\n",
|
||
" 'ZSZSS',\n",
|
||
" 'ZSZZ',\n",
|
||
" 'ZXSXZ',\n",
|
||
" 'ZXSZX',\n",
|
||
" 'ZXXS',\n",
|
||
" 'ZXZSX',\n",
|
||
" 'ZZSSS',\n",
|
||
" 'ZZSZ',\n",
|
||
" 'ZZXSX',\n",
|
||
" 'ZZZS'},\n",
|
||
" 18: {'HHSXZ',\n",
|
||
" 'HHSZX',\n",
|
||
" 'HHXS',\n",
|
||
" 'HHZSX',\n",
|
||
" 'HSSHS',\n",
|
||
" 'HXHSX',\n",
|
||
" 'HZHS',\n",
|
||
" 'SHHXZ',\n",
|
||
" 'SHHZX',\n",
|
||
" 'SHXHX',\n",
|
||
" 'SHXZH',\n",
|
||
" 'SHZHZ',\n",
|
||
" 'SHZXH',\n",
|
||
" 'SSSX',\n",
|
||
" 'SSXSZ',\n",
|
||
" 'SSXZS',\n",
|
||
" 'SSZXS',\n",
|
||
" 'SXHHZ',\n",
|
||
" 'SXHXH',\n",
|
||
" 'SXSS',\n",
|
||
" 'SXXXZ',\n",
|
||
" 'SXXZX',\n",
|
||
" 'SXZ',\n",
|
||
" 'SXZHH',\n",
|
||
" 'SXZXX',\n",
|
||
" 'SXZZZ',\n",
|
||
" 'SZHHX',\n",
|
||
" 'SZHZH',\n",
|
||
" 'SZSXS',\n",
|
||
" 'SZX',\n",
|
||
" 'SZXHH',\n",
|
||
" 'SZXXX',\n",
|
||
" 'SZXZZ',\n",
|
||
" 'SZZXZ',\n",
|
||
" 'SZZZX',\n",
|
||
" 'XHHS',\n",
|
||
" 'XS',\n",
|
||
" 'XSHH',\n",
|
||
" 'XSSSZ',\n",
|
||
" 'XSSZS',\n",
|
||
" 'XSXX',\n",
|
||
" 'XSZSS',\n",
|
||
" 'XSZZ',\n",
|
||
" 'XXSXZ',\n",
|
||
" 'XXSZX',\n",
|
||
" 'XXXS',\n",
|
||
" 'XXZSX',\n",
|
||
" 'XZSSS',\n",
|
||
" 'XZSZ',\n",
|
||
" 'XZXSX',\n",
|
||
" 'XZZS',\n",
|
||
" 'ZHHSX',\n",
|
||
" 'ZSHHX',\n",
|
||
" 'ZSHZH',\n",
|
||
" 'ZSSXS',\n",
|
||
" 'ZSX',\n",
|
||
" 'ZSXHH',\n",
|
||
" 'ZSXXX',\n",
|
||
" 'ZSXZZ',\n",
|
||
" 'ZSZXZ',\n",
|
||
" 'ZSZZX',\n",
|
||
" 'ZXSSS',\n",
|
||
" 'ZXSZ',\n",
|
||
" 'ZXXSX',\n",
|
||
" 'ZXZS',\n",
|
||
" 'ZZSXZ',\n",
|
||
" 'ZZSZX',\n",
|
||
" 'ZZXS',\n",
|
||
" 'ZZZSX'},\n",
|
||
" 21: {'HHSSX',\n",
|
||
" 'HHXSS',\n",
|
||
" 'HHXZ',\n",
|
||
" 'HHZX',\n",
|
||
" 'HSSHZ',\n",
|
||
" 'HSSXH',\n",
|
||
" 'HXHX',\n",
|
||
" 'HXSSH',\n",
|
||
" 'HXZH',\n",
|
||
" 'HZHSS',\n",
|
||
" 'HZHZ',\n",
|
||
" 'HZXH',\n",
|
||
" 'SHHSX',\n",
|
||
" 'SSHHX',\n",
|
||
" 'SSHZH',\n",
|
||
" 'SSSXS',\n",
|
||
" 'SSX',\n",
|
||
" 'SSXHH',\n",
|
||
" 'SSXXX',\n",
|
||
" 'SSXZZ',\n",
|
||
" 'SSZXZ',\n",
|
||
" 'SSZZX',\n",
|
||
" 'SXSSS',\n",
|
||
" 'SXSZ',\n",
|
||
" 'SXXSX',\n",
|
||
" 'SXZS',\n",
|
||
" 'SZSXZ',\n",
|
||
" 'SZSZX',\n",
|
||
" 'SZXS',\n",
|
||
" 'SZZSX',\n",
|
||
" 'XHHSS',\n",
|
||
" 'XHHZ',\n",
|
||
" 'XHXH',\n",
|
||
" 'XSHHS',\n",
|
||
" 'XSS',\n",
|
||
" 'XSSHH',\n",
|
||
" 'XSSXX',\n",
|
||
" 'XSSZZ',\n",
|
||
" 'XSXXS',\n",
|
||
" 'XSZSZ',\n",
|
||
" 'XSZZS',\n",
|
||
" 'XXSSX',\n",
|
||
" 'XXXSS',\n",
|
||
" 'XXXZ',\n",
|
||
" 'XXZX',\n",
|
||
" 'XZ',\n",
|
||
" 'XZHH',\n",
|
||
" 'XZSSZ',\n",
|
||
" 'XZSZS',\n",
|
||
" 'XZXX',\n",
|
||
" 'XZZSS',\n",
|
||
" 'XZZZ',\n",
|
||
" 'ZHHX',\n",
|
||
" 'ZHSSH',\n",
|
||
" 'ZHZH',\n",
|
||
" 'ZSSXZ',\n",
|
||
" 'ZSSZX',\n",
|
||
" 'ZSXS',\n",
|
||
" 'ZSZSX',\n",
|
||
" 'ZX',\n",
|
||
" 'ZXHH',\n",
|
||
" 'ZXSSZ',\n",
|
||
" 'ZXSZS',\n",
|
||
" 'ZXXX',\n",
|
||
" 'ZXZSS',\n",
|
||
" 'ZXZZ',\n",
|
||
" 'ZZSSX',\n",
|
||
" 'ZZXSS',\n",
|
||
" 'ZZXZ',\n",
|
||
" 'ZZZX'},\n",
|
||
" 15: {'HHSHX',\n",
|
||
" 'HHSZH',\n",
|
||
" 'HHZSH',\n",
|
||
" 'HSHS',\n",
|
||
" 'HXHSH',\n",
|
||
" 'SHHHX',\n",
|
||
" 'SHHZH',\n",
|
||
" 'SHSXS',\n",
|
||
" 'SHX',\n",
|
||
" 'SHXHH',\n",
|
||
" 'SHXXX',\n",
|
||
" 'SHXZZ',\n",
|
||
" 'SHZXZ',\n",
|
||
" 'SHZZX',\n",
|
||
" 'SSSH',\n",
|
||
" 'SXHXZ',\n",
|
||
" 'SXHZX',\n",
|
||
" 'SXXHX',\n",
|
||
" 'SXXZH',\n",
|
||
" 'SXZHZ',\n",
|
||
" 'SXZXH',\n",
|
||
" 'SZH',\n",
|
||
" 'SZHHH',\n",
|
||
" 'SZHXX',\n",
|
||
" 'SZHZZ',\n",
|
||
" 'SZXHZ',\n",
|
||
" 'SZXXH',\n",
|
||
" 'SZZHX',\n",
|
||
" 'SZZZH',\n",
|
||
" 'XSHSS',\n",
|
||
" 'XSHZ',\n",
|
||
" 'XSXH',\n",
|
||
" 'XXSHX',\n",
|
||
" 'XXSZH',\n",
|
||
" 'XXZSH',\n",
|
||
" 'XZXSH',\n",
|
||
" 'ZHHSH',\n",
|
||
" 'ZSH',\n",
|
||
" 'ZSHHH',\n",
|
||
" 'ZSHXX',\n",
|
||
" 'ZSHZZ',\n",
|
||
" 'ZSXHZ',\n",
|
||
" 'ZSXXH',\n",
|
||
" 'ZSZHX',\n",
|
||
" 'ZSZZH',\n",
|
||
" 'ZXXSH',\n",
|
||
" 'ZZSHX',\n",
|
||
" 'ZZSZH',\n",
|
||
" 'ZZZSH'},\n",
|
||
" 6: {'HHSHS',\n",
|
||
" 'HSHX',\n",
|
||
" 'HSSSH',\n",
|
||
" 'HSZH',\n",
|
||
" 'HXSHZ',\n",
|
||
" 'HXSXH',\n",
|
||
" 'HZSH',\n",
|
||
" 'SHHHS',\n",
|
||
" 'SHS',\n",
|
||
" 'SHSHH',\n",
|
||
" 'SHSXX',\n",
|
||
" 'SHSZZ',\n",
|
||
" 'SHXXS',\n",
|
||
" 'SHZSZ',\n",
|
||
" 'SHZZS',\n",
|
||
" 'SXHSZ',\n",
|
||
" 'SXHZS',\n",
|
||
" 'SXXHS',\n",
|
||
" 'SZHXS',\n",
|
||
" 'SZZHS',\n",
|
||
" 'XHSH',\n",
|
||
" 'XSHSX',\n",
|
||
" 'XXSHS',\n",
|
||
" 'ZHSHZ',\n",
|
||
" 'ZHSXH',\n",
|
||
" 'ZSHXS',\n",
|
||
" 'ZSZHS',\n",
|
||
" 'ZZSHS'},\n",
|
||
" 19: {'HSHSS',\n",
|
||
" 'HSHZ',\n",
|
||
" 'HSXH',\n",
|
||
" 'HXSHX',\n",
|
||
" 'HXSZH',\n",
|
||
" 'HXZSH',\n",
|
||
" 'HZXSH',\n",
|
||
" 'SHSXZ',\n",
|
||
" 'SHSZX',\n",
|
||
" 'SHXS',\n",
|
||
" 'SHZSX',\n",
|
||
" 'SSSHS',\n",
|
||
" 'SXHSX',\n",
|
||
" 'SZHS',\n",
|
||
" 'XHXSH',\n",
|
||
" 'XSHSZ',\n",
|
||
" 'XSHZS',\n",
|
||
" 'XSXHS',\n",
|
||
" 'XZHSH',\n",
|
||
" 'ZHSHX',\n",
|
||
" 'ZHSZH',\n",
|
||
" 'ZHZSH',\n",
|
||
" 'ZSHS',\n",
|
||
" 'ZXHSH'},\n",
|
||
" 11: {'HSHXZ',\n",
|
||
" 'HSHZX',\n",
|
||
" 'HSXHX',\n",
|
||
" 'HSXZH',\n",
|
||
" 'HSZHZ',\n",
|
||
" 'HSZXH',\n",
|
||
" 'HXSH',\n",
|
||
" 'HZSHZ',\n",
|
||
" 'HZSXH',\n",
|
||
" 'SHSSS',\n",
|
||
" 'SHSZ',\n",
|
||
" 'SHXSX',\n",
|
||
" 'SHZS',\n",
|
||
" 'SSHSH',\n",
|
||
" 'SXHS',\n",
|
||
" 'SZHSX',\n",
|
||
" 'XHSHZ',\n",
|
||
" 'XHSXH',\n",
|
||
" 'XSHXS',\n",
|
||
" 'XSZHS',\n",
|
||
" 'XZSHS',\n",
|
||
" 'ZHSH',\n",
|
||
" 'ZSHSX',\n",
|
||
" 'ZXSHS'},\n",
|
||
" 9: {'HHSHZ',\n",
|
||
" 'HHSXH',\n",
|
||
" 'HSHXS',\n",
|
||
" 'HSZHS',\n",
|
||
" 'HZSHS',\n",
|
||
" 'SHHHZ',\n",
|
||
" 'SHHXH',\n",
|
||
" 'SHSS',\n",
|
||
" 'SHXXZ',\n",
|
||
" 'SHXZX',\n",
|
||
" 'SHZ',\n",
|
||
" 'SHZHH',\n",
|
||
" 'SHZXX',\n",
|
||
" 'SHZZZ',\n",
|
||
" 'SSXSH',\n",
|
||
" 'SXH',\n",
|
||
" 'SXHHH',\n",
|
||
" 'SXHXX',\n",
|
||
" 'SXHZZ',\n",
|
||
" 'SXXHZ',\n",
|
||
" 'SXXXH',\n",
|
||
" 'SXZHX',\n",
|
||
" 'SXZZH',\n",
|
||
" 'SZHXZ',\n",
|
||
" 'SZHZX',\n",
|
||
" 'SZXHX',\n",
|
||
" 'SZXZH',\n",
|
||
" 'SZZHZ',\n",
|
||
" 'SZZXH',\n",
|
||
" 'XHSHS',\n",
|
||
" 'XSHX',\n",
|
||
" 'XSSSH',\n",
|
||
" 'XSZH',\n",
|
||
" 'XXSHZ',\n",
|
||
" 'XXSXH',\n",
|
||
" 'XZSH',\n",
|
||
" 'ZSHXZ',\n",
|
||
" 'ZSHZX',\n",
|
||
" 'ZSXHX',\n",
|
||
" 'ZSXZH',\n",
|
||
" 'ZSZHZ',\n",
|
||
" 'ZSZXH',\n",
|
||
" 'ZXSH',\n",
|
||
" 'ZZSHZ',\n",
|
||
" 'ZZSXH'},\n",
|
||
" 22: {'HHXSH',\n",
|
||
" 'HSHSZ',\n",
|
||
" 'HSHZS',\n",
|
||
" 'HSXHS',\n",
|
||
" 'HZHSH',\n",
|
||
" 'SHSSX',\n",
|
||
" 'SHXSS',\n",
|
||
" 'SHXZ',\n",
|
||
" 'SHZX',\n",
|
||
" 'SSSHZ',\n",
|
||
" 'SSSXH',\n",
|
||
" 'SXHX',\n",
|
||
" 'SXSSH',\n",
|
||
" 'SXZH',\n",
|
||
" 'SZHSS',\n",
|
||
" 'SZHZ',\n",
|
||
" 'SZXH',\n",
|
||
" 'XHHSH',\n",
|
||
" 'XSH',\n",
|
||
" 'XSHHH',\n",
|
||
" 'XSHXX',\n",
|
||
" 'XSHZZ',\n",
|
||
" 'XSXHZ',\n",
|
||
" 'XSXXH',\n",
|
||
" 'XSZHX',\n",
|
||
" 'XSZZH',\n",
|
||
" 'XXXSH',\n",
|
||
" 'XZSHX',\n",
|
||
" 'XZSZH',\n",
|
||
" 'XZZSH',\n",
|
||
" 'ZSHSS',\n",
|
||
" 'ZSHZ',\n",
|
||
" 'ZSXH',\n",
|
||
" 'ZXSHX',\n",
|
||
" 'ZXSZH',\n",
|
||
" 'ZXZSH',\n",
|
||
" 'ZZXSH'}})"
|
||
]
|
||
},
|
||
"execution_count": 6,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"results"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 8,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"['H',\n",
|
||
" 'S',\n",
|
||
" 'ZZ',\n",
|
||
" 'SH',\n",
|
||
" 'HS',\n",
|
||
" 'Z',\n",
|
||
" 'SHS',\n",
|
||
" 'HZ',\n",
|
||
" 'ZS',\n",
|
||
" 'SXH',\n",
|
||
" 'HSZ',\n",
|
||
" 'HXSH',\n",
|
||
" 'HSH',\n",
|
||
" 'HX',\n",
|
||
" 'X',\n",
|
||
" 'ZSH',\n",
|
||
" 'SX',\n",
|
||
" 'HXS',\n",
|
||
" 'XS',\n",
|
||
" 'SZHS',\n",
|
||
" 'ZXH',\n",
|
||
" 'XZ',\n",
|
||
" 'XSH',\n",
|
||
" 'HSX']"
|
||
]
|
||
},
|
||
"execution_count": 8,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"lookup_table = [min(v, key=lambda x:len(x)) for k,v in sorted(results.items(), key=lambda x:x[0])]\n",
|
||
"lookup_table"
|
||
]
|
||
}
|
||
],
|
||
"metadata": {
|
||
"kernelspec": {
|
||
"display_name": "Python 3",
|
||
"language": "python",
|
||
"name": "python3"
|
||
},
|
||
"language_info": {
|
||
"codemirror_mode": {
|
||
"name": "ipython",
|
||
"version": 3
|
||
},
|
||
"file_extension": ".py",
|
||
"mimetype": "text/x-python",
|
||
"name": "python",
|
||
"nbconvert_exporter": "python",
|
||
"pygments_lexer": "ipython3",
|
||
"version": "3.7.3"
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 2
|
||
}
|