{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "person 1: my code is too slow\n",
    "\n",
    "person 2: make better algorithm\n",
    "\n",
    "person 1: I did and it is still slow\n",
    "\n",
    "person 2: let us try Cython\n",
    "\n",
    "References: Cython website (+ cysignals)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Cython extension is already loaded. To reload it, use:\n",
      "  %reload_ext Cython\n"
     ]
    }
   ],
   "source": [
    "%load_ext Cython\n",
    "# to activate the option -a of Cython\n",
    "# be careful: it might mess everything up!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "hello\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/lib/python2.7/site-packages/Cython/Compiler/Main.py:369: FutureWarning: Cython directive 'language_level' not set, using 2 for now (Py2). This will change in a later release! File: /home/vincent/.cache/ipython/cython/_cython_magic_8fa21c1b43de7954c881a3cf375d946e.pyx\n",
      "  tree = Parsing.p_module(s, pxd, full_module_name)\n"
     ]
    }
   ],
   "source": [
    "%%cython\n",
    "print(\"hello\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1.84 s, sys: 91 ms, total: 1.93 s\n",
      "Wall time: 1.78 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "s = 0\n",
    "for i in range(100):\n",
    "    for j in range(100):\n",
    "        for k in range(100):\n",
    "            s += i**2 + i*j*k + 2*k + i - j"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "124669875000"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<type 'int'>, <type 'int'>, <type 'int'>, <type 'int'>]"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "map(type, range(int(4)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/lib/python2.7/site-packages/Cython/Compiler/Main.py:369: FutureWarning: Cython directive 'language_level' not set, using 2 for now (Py2). This will change in a later release! File: /home/vincent/.cache/ipython/cython/_cython_magic_0f6407bef3789247c6025a198ff7b605.pyx\n",
      "  tree = Parsing.p_module(s, pxd, full_module_name)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<!DOCTYPE html>\n",
       "<!-- Generated by Cython 0.29.12 -->\n",
       "<html>\n",
       "<head>\n",
       "    <meta http-equiv=\"Content-Type\" content=\"text/html; charset=utf-8\" />\n",
       "    <title>Cython: _cython_magic_0f6407bef3789247c6025a198ff7b605.pyx</title>\n",
       "    <style type=\"text/css\">\n",
       "    \n",
       "body.cython { font-family: courier; font-size: 12; }\n",
       "\n",
       ".cython.tag  {  }\n",
       ".cython.line { margin: 0em }\n",
       ".cython.code { font-size: 9; color: #444444; display: none; margin: 0px 0px 0px 8px; border-left: 8px none; }\n",
       "\n",
       ".cython.line .run { background-color: #B0FFB0; }\n",
       ".cython.line .mis { background-color: #FFB0B0; }\n",
       ".cython.code.run  { border-left: 8px solid #B0FFB0; }\n",
       ".cython.code.mis  { border-left: 8px solid #FFB0B0; }\n",
       "\n",
       ".cython.code .py_c_api  { color: red; }\n",
       ".cython.code .py_macro_api  { color: #FF7000; }\n",
       ".cython.code .pyx_c_api  { color: #FF3000; }\n",
       ".cython.code .pyx_macro_api  { color: #FF7000; }\n",
       ".cython.code .refnanny  { color: #FFA000; }\n",
       ".cython.code .trace  { color: #FFA000; }\n",
       ".cython.code .error_goto  { color: #FFA000; }\n",
       "\n",
       ".cython.code .coerce  { color: #008000; border: 1px dotted #008000 }\n",
       ".cython.code .py_attr { color: #FF0000; font-weight: bold; }\n",
       ".cython.code .c_attr  { color: #0000FF; }\n",
       ".cython.code .py_call { color: #FF0000; font-weight: bold; }\n",
       ".cython.code .c_call  { color: #0000FF; }\n",
       "\n",
       ".cython.score-0 {background-color: #FFFFff;}\n",
       ".cython.score-1 {background-color: #FFFFe7;}\n",
       ".cython.score-2 {background-color: #FFFFd4;}\n",
       ".cython.score-3 {background-color: #FFFFc4;}\n",
       ".cython.score-4 {background-color: #FFFFb6;}\n",
       ".cython.score-5 {background-color: #FFFFaa;}\n",
       ".cython.score-6 {background-color: #FFFF9f;}\n",
       ".cython.score-7 {background-color: #FFFF96;}\n",
       ".cython.score-8 {background-color: #FFFF8d;}\n",
       ".cython.score-9 {background-color: #FFFF86;}\n",
       ".cython.score-10 {background-color: #FFFF7f;}\n",
       ".cython.score-11 {background-color: #FFFF79;}\n",
       ".cython.score-12 {background-color: #FFFF73;}\n",
       ".cython.score-13 {background-color: #FFFF6e;}\n",
       ".cython.score-14 {background-color: #FFFF6a;}\n",
       ".cython.score-15 {background-color: #FFFF66;}\n",
       ".cython.score-16 {background-color: #FFFF62;}\n",
       ".cython.score-17 {background-color: #FFFF5e;}\n",
       ".cython.score-18 {background-color: #FFFF5b;}\n",
       ".cython.score-19 {background-color: #FFFF57;}\n",
       ".cython.score-20 {background-color: #FFFF55;}\n",
       ".cython.score-21 {background-color: #FFFF52;}\n",
       ".cython.score-22 {background-color: #FFFF4f;}\n",
       ".cython.score-23 {background-color: #FFFF4d;}\n",
       ".cython.score-24 {background-color: #FFFF4b;}\n",
       ".cython.score-25 {background-color: #FFFF48;}\n",
       ".cython.score-26 {background-color: #FFFF46;}\n",
       ".cython.score-27 {background-color: #FFFF44;}\n",
       ".cython.score-28 {background-color: #FFFF43;}\n",
       ".cython.score-29 {background-color: #FFFF41;}\n",
       ".cython.score-30 {background-color: #FFFF3f;}\n",
       ".cython.score-31 {background-color: #FFFF3e;}\n",
       ".cython.score-32 {background-color: #FFFF3c;}\n",
       ".cython.score-33 {background-color: #FFFF3b;}\n",
       ".cython.score-34 {background-color: #FFFF39;}\n",
       ".cython.score-35 {background-color: #FFFF38;}\n",
       ".cython.score-36 {background-color: #FFFF37;}\n",
       ".cython.score-37 {background-color: #FFFF36;}\n",
       ".cython.score-38 {background-color: #FFFF35;}\n",
       ".cython.score-39 {background-color: #FFFF34;}\n",
       ".cython.score-40 {background-color: #FFFF33;}\n",
       ".cython.score-41 {background-color: #FFFF32;}\n",
       ".cython.score-42 {background-color: #FFFF31;}\n",
       ".cython.score-43 {background-color: #FFFF30;}\n",
       ".cython.score-44 {background-color: #FFFF2f;}\n",
       ".cython.score-45 {background-color: #FFFF2e;}\n",
       ".cython.score-46 {background-color: #FFFF2d;}\n",
       ".cython.score-47 {background-color: #FFFF2c;}\n",
       ".cython.score-48 {background-color: #FFFF2b;}\n",
       ".cython.score-49 {background-color: #FFFF2b;}\n",
       ".cython.score-50 {background-color: #FFFF2a;}\n",
       ".cython.score-51 {background-color: #FFFF29;}\n",
       ".cython.score-52 {background-color: #FFFF29;}\n",
       ".cython.score-53 {background-color: #FFFF28;}\n",
       ".cython.score-54 {background-color: #FFFF27;}\n",
       ".cython.score-55 {background-color: #FFFF27;}\n",
       ".cython.score-56 {background-color: #FFFF26;}\n",
       ".cython.score-57 {background-color: #FFFF26;}\n",
       ".cython.score-58 {background-color: #FFFF25;}\n",
       ".cython.score-59 {background-color: #FFFF24;}\n",
       ".cython.score-60 {background-color: #FFFF24;}\n",
       ".cython.score-61 {background-color: #FFFF23;}\n",
       ".cython.score-62 {background-color: #FFFF23;}\n",
       ".cython.score-63 {background-color: #FFFF22;}\n",
       ".cython.score-64 {background-color: #FFFF22;}\n",
       ".cython.score-65 {background-color: #FFFF22;}\n",
       ".cython.score-66 {background-color: #FFFF21;}\n",
       ".cython.score-67 {background-color: #FFFF21;}\n",
       ".cython.score-68 {background-color: #FFFF20;}\n",
       ".cython.score-69 {background-color: #FFFF20;}\n",
       ".cython.score-70 {background-color: #FFFF1f;}\n",
       ".cython.score-71 {background-color: #FFFF1f;}\n",
       ".cython.score-72 {background-color: #FFFF1f;}\n",
       ".cython.score-73 {background-color: #FFFF1e;}\n",
       ".cython.score-74 {background-color: #FFFF1e;}\n",
       ".cython.score-75 {background-color: #FFFF1e;}\n",
       ".cython.score-76 {background-color: #FFFF1d;}\n",
       ".cython.score-77 {background-color: #FFFF1d;}\n",
       ".cython.score-78 {background-color: #FFFF1c;}\n",
       ".cython.score-79 {background-color: #FFFF1c;}\n",
       ".cython.score-80 {background-color: #FFFF1c;}\n",
       ".cython.score-81 {background-color: #FFFF1c;}\n",
       ".cython.score-82 {background-color: #FFFF1b;}\n",
       ".cython.score-83 {background-color: #FFFF1b;}\n",
       ".cython.score-84 {background-color: #FFFF1b;}\n",
       ".cython.score-85 {background-color: #FFFF1a;}\n",
       ".cython.score-86 {background-color: #FFFF1a;}\n",
       ".cython.score-87 {background-color: #FFFF1a;}\n",
       ".cython.score-88 {background-color: #FFFF1a;}\n",
       ".cython.score-89 {background-color: #FFFF19;}\n",
       ".cython.score-90 {background-color: #FFFF19;}\n",
       ".cython.score-91 {background-color: #FFFF19;}\n",
       ".cython.score-92 {background-color: #FFFF19;}\n",
       ".cython.score-93 {background-color: #FFFF18;}\n",
       ".cython.score-94 {background-color: #FFFF18;}\n",
       ".cython.score-95 {background-color: #FFFF18;}\n",
       ".cython.score-96 {background-color: #FFFF18;}\n",
       ".cython.score-97 {background-color: #FFFF17;}\n",
       ".cython.score-98 {background-color: #FFFF17;}\n",
       ".cython.score-99 {background-color: #FFFF17;}\n",
       ".cython.score-100 {background-color: #FFFF17;}\n",
       ".cython.score-101 {background-color: #FFFF16;}\n",
       ".cython.score-102 {background-color: #FFFF16;}\n",
       ".cython.score-103 {background-color: #FFFF16;}\n",
       ".cython.score-104 {background-color: #FFFF16;}\n",
       ".cython.score-105 {background-color: #FFFF16;}\n",
       ".cython.score-106 {background-color: #FFFF15;}\n",
       ".cython.score-107 {background-color: #FFFF15;}\n",
       ".cython.score-108 {background-color: #FFFF15;}\n",
       ".cython.score-109 {background-color: #FFFF15;}\n",
       ".cython.score-110 {background-color: #FFFF15;}\n",
       ".cython.score-111 {background-color: #FFFF15;}\n",
       ".cython.score-112 {background-color: #FFFF14;}\n",
       ".cython.score-113 {background-color: #FFFF14;}\n",
       ".cython.score-114 {background-color: #FFFF14;}\n",
       ".cython.score-115 {background-color: #FFFF14;}\n",
       ".cython.score-116 {background-color: #FFFF14;}\n",
       ".cython.score-117 {background-color: #FFFF14;}\n",
       ".cython.score-118 {background-color: #FFFF13;}\n",
       ".cython.score-119 {background-color: #FFFF13;}\n",
       ".cython.score-120 {background-color: #FFFF13;}\n",
       ".cython.score-121 {background-color: #FFFF13;}\n",
       ".cython.score-122 {background-color: #FFFF13;}\n",
       ".cython.score-123 {background-color: #FFFF13;}\n",
       ".cython.score-124 {background-color: #FFFF13;}\n",
       ".cython.score-125 {background-color: #FFFF12;}\n",
       ".cython.score-126 {background-color: #FFFF12;}\n",
       ".cython.score-127 {background-color: #FFFF12;}\n",
       ".cython.score-128 {background-color: #FFFF12;}\n",
       ".cython.score-129 {background-color: #FFFF12;}\n",
       ".cython.score-130 {background-color: #FFFF12;}\n",
       ".cython.score-131 {background-color: #FFFF12;}\n",
       ".cython.score-132 {background-color: #FFFF11;}\n",
       ".cython.score-133 {background-color: #FFFF11;}\n",
       ".cython.score-134 {background-color: #FFFF11;}\n",
       ".cython.score-135 {background-color: #FFFF11;}\n",
       ".cython.score-136 {background-color: #FFFF11;}\n",
       ".cython.score-137 {background-color: #FFFF11;}\n",
       ".cython.score-138 {background-color: #FFFF11;}\n",
       ".cython.score-139 {background-color: #FFFF11;}\n",
       ".cython.score-140 {background-color: #FFFF11;}\n",
       ".cython.score-141 {background-color: #FFFF10;}\n",
       ".cython.score-142 {background-color: #FFFF10;}\n",
       ".cython.score-143 {background-color: #FFFF10;}\n",
       ".cython.score-144 {background-color: #FFFF10;}\n",
       ".cython.score-145 {background-color: #FFFF10;}\n",
       ".cython.score-146 {background-color: #FFFF10;}\n",
       ".cython.score-147 {background-color: #FFFF10;}\n",
       ".cython.score-148 {background-color: #FFFF10;}\n",
       ".cython.score-149 {background-color: #FFFF10;}\n",
       ".cython.score-150 {background-color: #FFFF0f;}\n",
       ".cython.score-151 {background-color: #FFFF0f;}\n",
       ".cython.score-152 {background-color: #FFFF0f;}\n",
       ".cython.score-153 {background-color: #FFFF0f;}\n",
       ".cython.score-154 {background-color: #FFFF0f;}\n",
       ".cython.score-155 {background-color: #FFFF0f;}\n",
       ".cython.score-156 {background-color: #FFFF0f;}\n",
       ".cython.score-157 {background-color: #FFFF0f;}\n",
       ".cython.score-158 {background-color: #FFFF0f;}\n",
       ".cython.score-159 {background-color: #FFFF0f;}\n",
       ".cython.score-160 {background-color: #FFFF0f;}\n",
       ".cython.score-161 {background-color: #FFFF0e;}\n",
       ".cython.score-162 {background-color: #FFFF0e;}\n",
       ".cython.score-163 {background-color: #FFFF0e;}\n",
       ".cython.score-164 {background-color: #FFFF0e;}\n",
       ".cython.score-165 {background-color: #FFFF0e;}\n",
       ".cython.score-166 {background-color: #FFFF0e;}\n",
       ".cython.score-167 {background-color: #FFFF0e;}\n",
       ".cython.score-168 {background-color: #FFFF0e;}\n",
       ".cython.score-169 {background-color: #FFFF0e;}\n",
       ".cython.score-170 {background-color: #FFFF0e;}\n",
       ".cython.score-171 {background-color: #FFFF0e;}\n",
       ".cython.score-172 {background-color: #FFFF0e;}\n",
       ".cython.score-173 {background-color: #FFFF0d;}\n",
       ".cython.score-174 {background-color: #FFFF0d;}\n",
       ".cython.score-175 {background-color: #FFFF0d;}\n",
       ".cython.score-176 {background-color: #FFFF0d;}\n",
       ".cython.score-177 {background-color: #FFFF0d;}\n",
       ".cython.score-178 {background-color: #FFFF0d;}\n",
       ".cython.score-179 {background-color: #FFFF0d;}\n",
       ".cython.score-180 {background-color: #FFFF0d;}\n",
       ".cython.score-181 {background-color: #FFFF0d;}\n",
       ".cython.score-182 {background-color: #FFFF0d;}\n",
       ".cython.score-183 {background-color: #FFFF0d;}\n",
       ".cython.score-184 {background-color: #FFFF0d;}\n",
       ".cython.score-185 {background-color: #FFFF0d;}\n",
       ".cython.score-186 {background-color: #FFFF0d;}\n",
       ".cython.score-187 {background-color: #FFFF0c;}\n",
       ".cython.score-188 {background-color: #FFFF0c;}\n",
       ".cython.score-189 {background-color: #FFFF0c;}\n",
       ".cython.score-190 {background-color: #FFFF0c;}\n",
       ".cython.score-191 {background-color: #FFFF0c;}\n",
       ".cython.score-192 {background-color: #FFFF0c;}\n",
       ".cython.score-193 {background-color: #FFFF0c;}\n",
       ".cython.score-194 {background-color: #FFFF0c;}\n",
       ".cython.score-195 {background-color: #FFFF0c;}\n",
       ".cython.score-196 {background-color: #FFFF0c;}\n",
       ".cython.score-197 {background-color: #FFFF0c;}\n",
       ".cython.score-198 {background-color: #FFFF0c;}\n",
       ".cython.score-199 {background-color: #FFFF0c;}\n",
       ".cython.score-200 {background-color: #FFFF0c;}\n",
       ".cython.score-201 {background-color: #FFFF0c;}\n",
       ".cython.score-202 {background-color: #FFFF0c;}\n",
       ".cython.score-203 {background-color: #FFFF0b;}\n",
       ".cython.score-204 {background-color: #FFFF0b;}\n",
       ".cython.score-205 {background-color: #FFFF0b;}\n",
       ".cython.score-206 {background-color: #FFFF0b;}\n",
       ".cython.score-207 {background-color: #FFFF0b;}\n",
       ".cython.score-208 {background-color: #FFFF0b;}\n",
       ".cython.score-209 {background-color: #FFFF0b;}\n",
       ".cython.score-210 {background-color: #FFFF0b;}\n",
       ".cython.score-211 {background-color: #FFFF0b;}\n",
       ".cython.score-212 {background-color: #FFFF0b;}\n",
       ".cython.score-213 {background-color: #FFFF0b;}\n",
       ".cython.score-214 {background-color: #FFFF0b;}\n",
       ".cython.score-215 {background-color: #FFFF0b;}\n",
       ".cython.score-216 {background-color: #FFFF0b;}\n",
       ".cython.score-217 {background-color: #FFFF0b;}\n",
       ".cython.score-218 {background-color: #FFFF0b;}\n",
       ".cython.score-219 {background-color: #FFFF0b;}\n",
       ".cython.score-220 {background-color: #FFFF0b;}\n",
       ".cython.score-221 {background-color: #FFFF0b;}\n",
       ".cython.score-222 {background-color: #FFFF0a;}\n",
       ".cython.score-223 {background-color: #FFFF0a;}\n",
       ".cython.score-224 {background-color: #FFFF0a;}\n",
       ".cython.score-225 {background-color: #FFFF0a;}\n",
       ".cython.score-226 {background-color: #FFFF0a;}\n",
       ".cython.score-227 {background-color: #FFFF0a;}\n",
       ".cython.score-228 {background-color: #FFFF0a;}\n",
       ".cython.score-229 {background-color: #FFFF0a;}\n",
       ".cython.score-230 {background-color: #FFFF0a;}\n",
       ".cython.score-231 {background-color: #FFFF0a;}\n",
       ".cython.score-232 {background-color: #FFFF0a;}\n",
       ".cython.score-233 {background-color: #FFFF0a;}\n",
       ".cython.score-234 {background-color: #FFFF0a;}\n",
       ".cython.score-235 {background-color: #FFFF0a;}\n",
       ".cython.score-236 {background-color: #FFFF0a;}\n",
       ".cython.score-237 {background-color: #FFFF0a;}\n",
       ".cython.score-238 {background-color: #FFFF0a;}\n",
       ".cython.score-239 {background-color: #FFFF0a;}\n",
       ".cython.score-240 {background-color: #FFFF0a;}\n",
       ".cython.score-241 {background-color: #FFFF0a;}\n",
       ".cython.score-242 {background-color: #FFFF0a;}\n",
       ".cython.score-243 {background-color: #FFFF0a;}\n",
       ".cython.score-244 {background-color: #FFFF0a;}\n",
       ".cython.score-245 {background-color: #FFFF0a;}\n",
       ".cython.score-246 {background-color: #FFFF09;}\n",
       ".cython.score-247 {background-color: #FFFF09;}\n",
       ".cython.score-248 {background-color: #FFFF09;}\n",
       ".cython.score-249 {background-color: #FFFF09;}\n",
       ".cython.score-250 {background-color: #FFFF09;}\n",
       ".cython.score-251 {background-color: #FFFF09;}\n",
       ".cython.score-252 {background-color: #FFFF09;}\n",
       ".cython.score-253 {background-color: #FFFF09;}\n",
       ".cython.score-254 {background-color: #FFFF09;}\n",
       ".cython .hll { background-color: #ffffcc }\n",
       ".cython  { background: #f8f8f8; }\n",
       ".cython .c { color: #408080; font-style: italic } /* Comment */\n",
       ".cython .err { border: 1px solid #FF0000 } /* Error */\n",
       ".cython .k { color: #008000; font-weight: bold } /* Keyword */\n",
       ".cython .o { color: #666666 } /* Operator */\n",
       ".cython .ch { color: #408080; font-style: italic } /* Comment.Hashbang */\n",
       ".cython .cm { color: #408080; font-style: italic } /* Comment.Multiline */\n",
       ".cython .cp { color: #BC7A00 } /* Comment.Preproc */\n",
       ".cython .cpf { color: #408080; font-style: italic } /* Comment.PreprocFile */\n",
       ".cython .c1 { color: #408080; font-style: italic } /* Comment.Single */\n",
       ".cython .cs { color: #408080; font-style: italic } /* Comment.Special */\n",
       ".cython .gd { color: #A00000 } /* Generic.Deleted */\n",
       ".cython .ge { font-style: italic } /* Generic.Emph */\n",
       ".cython .gr { color: #FF0000 } /* Generic.Error */\n",
       ".cython .gh { color: #000080; font-weight: bold } /* Generic.Heading */\n",
       ".cython .gi { color: #00A000 } /* Generic.Inserted */\n",
       ".cython .go { color: #888888 } /* Generic.Output */\n",
       ".cython .gp { color: #000080; font-weight: bold } /* Generic.Prompt */\n",
       ".cython .gs { font-weight: bold } /* Generic.Strong */\n",
       ".cython .gu { color: #800080; font-weight: bold } /* Generic.Subheading */\n",
       ".cython .gt { color: #0044DD } /* Generic.Traceback */\n",
       ".cython .kc { color: #008000; font-weight: bold } /* Keyword.Constant */\n",
       ".cython .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */\n",
       ".cython .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */\n",
       ".cython .kp { color: #008000 } /* Keyword.Pseudo */\n",
       ".cython .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */\n",
       ".cython .kt { color: #B00040 } /* Keyword.Type */\n",
       ".cython .m { color: #666666 } /* Literal.Number */\n",
       ".cython .s { color: #BA2121 } /* Literal.String */\n",
       ".cython .na { color: #7D9029 } /* Name.Attribute */\n",
       ".cython .nb { color: #008000 } /* Name.Builtin */\n",
       ".cython .nc { color: #0000FF; font-weight: bold } /* Name.Class */\n",
       ".cython .no { color: #880000 } /* Name.Constant */\n",
       ".cython .nd { color: #AA22FF } /* Name.Decorator */\n",
       ".cython .ni { color: #999999; font-weight: bold } /* Name.Entity */\n",
       ".cython .ne { color: #D2413A; font-weight: bold } /* Name.Exception */\n",
       ".cython .nf { color: #0000FF } /* Name.Function */\n",
       ".cython .nl { color: #A0A000 } /* Name.Label */\n",
       ".cython .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */\n",
       ".cython .nt { color: #008000; font-weight: bold } /* Name.Tag */\n",
       ".cython .nv { color: #19177C } /* Name.Variable */\n",
       ".cython .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */\n",
       ".cython .w { color: #bbbbbb } /* Text.Whitespace */\n",
       ".cython .mb { color: #666666 } /* Literal.Number.Bin */\n",
       ".cython .mf { color: #666666 } /* Literal.Number.Float */\n",
       ".cython .mh { color: #666666 } /* Literal.Number.Hex */\n",
       ".cython .mi { color: #666666 } /* Literal.Number.Integer */\n",
       ".cython .mo { color: #666666 } /* Literal.Number.Oct */\n",
       ".cython .sa { color: #BA2121 } /* Literal.String.Affix */\n",
       ".cython .sb { color: #BA2121 } /* Literal.String.Backtick */\n",
       ".cython .sc { color: #BA2121 } /* Literal.String.Char */\n",
       ".cython .dl { color: #BA2121 } /* Literal.String.Delimiter */\n",
       ".cython .sd { color: #BA2121; font-style: italic } /* Literal.String.Doc */\n",
       ".cython .s2 { color: #BA2121 } /* Literal.String.Double */\n",
       ".cython .se { color: #BB6622; font-weight: bold } /* Literal.String.Escape */\n",
       ".cython .sh { color: #BA2121 } /* Literal.String.Heredoc */\n",
       ".cython .si { color: #BB6688; font-weight: bold } /* Literal.String.Interpol */\n",
       ".cython .sx { color: #008000 } /* Literal.String.Other */\n",
       ".cython .sr { color: #BB6688 } /* Literal.String.Regex */\n",
       ".cython .s1 { color: #BA2121 } /* Literal.String.Single */\n",
       ".cython .ss { color: #19177C } /* Literal.String.Symbol */\n",
       ".cython .bp { color: #008000 } /* Name.Builtin.Pseudo */\n",
       ".cython .fm { color: #0000FF } /* Name.Function.Magic */\n",
       ".cython .vc { color: #19177C } /* Name.Variable.Class */\n",
       ".cython .vg { color: #19177C } /* Name.Variable.Global */\n",
       ".cython .vi { color: #19177C } /* Name.Variable.Instance */\n",
       ".cython .vm { color: #19177C } /* Name.Variable.Magic */\n",
       ".cython .il { color: #666666 } /* Literal.Number.Integer.Long */\n",
       "    </style>\n",
       "</head>\n",
       "<body class=\"cython\">\n",
       "<p><span style=\"border-bottom: solid 1px grey;\">Generated by Cython 0.29.12</span></p>\n",
       "<p>\n",
       "    <span style=\"background-color: #FFFF00\">Yellow lines</span> hint at Python interaction.<br />\n",
       "    Click on a line that starts with a \"<code>+</code>\" to see the C code that Cython generated for it.\n",
       "</p>\n",
       "<div class=\"cython\"><pre class=\"cython line score-8\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">01</span>: <span class=\"c\"># distutils: language = c++</span></pre>\n",
       "<pre class='cython code score-8 '>  __pyx_t_1 = <span class='pyx_c_api'>__Pyx_PyDict_NewPresized</span>(0);<span class='error_goto'> if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 1, __pyx_L1_error)</span>\n",
       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_1);\n",
       "  if (<span class='py_c_api'>PyDict_SetItem</span>(__pyx_d, __pyx_n_s_test, __pyx_t_1) &lt; 0) <span class='error_goto'>__PYX_ERR(0, 1, __pyx_L1_error)</span>\n",
       "  <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_1); __pyx_t_1 = 0;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">02</span>: </pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">03</span>: <span class=\"c\"># importing types that are defined in other Cython files</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">04</span>: <span class=\"k\">from</span> <span class=\"nn\">sage.rings.integer</span> <span class=\"k\">cimport</span> <span class=\"n\">Integer</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">05</span>: </pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">06</span>: <span class=\"c\"># importing C++</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">07</span>: <span class=\"k\">from</span> <span class=\"nn\">libcpp.vector</span> <span class=\"k\">cimport</span> <span class=\"n\">vector</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">08</span>: </pre>\n",
       "<pre class=\"cython line score-67\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">09</span>: <span class=\"k\">def</span> <span class=\"nf\">f1</span><span class=\"p\">(</span><span class=\"nb\">long</span> <span class=\"n\">N1</span><span class=\"p\">,</span> <span class=\"nb\">long</span> <span class=\"n\">N2</span><span class=\"p\">,</span> <span class=\"nb\">long</span> <span class=\"n\">N3</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-67 '>/* Python wrapper */\n",
       "static PyObject *__pyx_pw_46_cython_magic_0f6407bef3789247c6025a198ff7b605_1f1(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/\n",
       "static PyMethodDef __pyx_mdef_46_cython_magic_0f6407bef3789247c6025a198ff7b605_1f1 = {\"f1\", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_46_cython_magic_0f6407bef3789247c6025a198ff7b605_1f1, METH_VARARGS|METH_KEYWORDS, 0};\n",
       "static PyObject *__pyx_pw_46_cython_magic_0f6407bef3789247c6025a198ff7b605_1f1(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds) {\n",
       "  long __pyx_v_N1;\n",
       "  long __pyx_v_N2;\n",
       "  long __pyx_v_N3;\n",
       "  PyObject *__pyx_r = 0;\n",
       "  <span class='refnanny'>__Pyx_RefNannyDeclarations</span>\n",
       "  <span class='refnanny'>__Pyx_RefNannySetupContext</span>(\"f1 (wrapper)\", 0);\n",
       "  {\n",
       "    static PyObject **__pyx_pyargnames[] = {&amp;__pyx_n_s_N1,&amp;__pyx_n_s_N2,&amp;__pyx_n_s_N3,0};\n",
       "    PyObject* values[3] = {0,0,0};\n",
       "    if (unlikely(__pyx_kwds)) {\n",
       "      Py_ssize_t kw_args;\n",
       "      const Py_ssize_t pos_args = <span class='py_macro_api'>PyTuple_GET_SIZE</span>(__pyx_args);\n",
       "      switch (pos_args) {\n",
       "        case  3: values[2] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 2);\n",
       "        CYTHON_FALLTHROUGH;\n",
       "        case  2: values[1] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 1);\n",
       "        CYTHON_FALLTHROUGH;\n",
       "        case  1: values[0] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 0);\n",
       "        CYTHON_FALLTHROUGH;\n",
       "        case  0: break;\n",
       "        default: goto __pyx_L5_argtuple_error;\n",
       "      }\n",
       "      kw_args = <span class='py_c_api'>PyDict_Size</span>(__pyx_kwds);\n",
       "      switch (pos_args) {\n",
       "        case  0:\n",
       "        if (likely((values[0] = <span class='pyx_c_api'>__Pyx_PyDict_GetItemStr</span>(__pyx_kwds, __pyx_n_s_N1)) != 0)) kw_args--;\n",
       "        else goto __pyx_L5_argtuple_error;\n",
       "        CYTHON_FALLTHROUGH;\n",
       "        case  1:\n",
       "        if (likely((values[1] = <span class='pyx_c_api'>__Pyx_PyDict_GetItemStr</span>(__pyx_kwds, __pyx_n_s_N2)) != 0)) kw_args--;\n",
       "        else {\n",
       "          <span class='pyx_c_api'>__Pyx_RaiseArgtupleInvalid</span>(\"f1\", 1, 3, 3, 1); <span class='error_goto'>__PYX_ERR(0, 9, __pyx_L3_error)</span>\n",
       "        }\n",
       "        CYTHON_FALLTHROUGH;\n",
       "        case  2:\n",
       "        if (likely((values[2] = <span class='pyx_c_api'>__Pyx_PyDict_GetItemStr</span>(__pyx_kwds, __pyx_n_s_N3)) != 0)) kw_args--;\n",
       "        else {\n",
       "          <span class='pyx_c_api'>__Pyx_RaiseArgtupleInvalid</span>(\"f1\", 1, 3, 3, 2); <span class='error_goto'>__PYX_ERR(0, 9, __pyx_L3_error)</span>\n",
       "        }\n",
       "      }\n",
       "      if (unlikely(kw_args &gt; 0)) {\n",
       "        if (unlikely(<span class='pyx_c_api'>__Pyx_ParseOptionalKeywords</span>(__pyx_kwds, __pyx_pyargnames, 0, values, pos_args, \"f1\") &lt; 0)) <span class='error_goto'>__PYX_ERR(0, 9, __pyx_L3_error)</span>\n",
       "      }\n",
       "    } else if (<span class='py_macro_api'>PyTuple_GET_SIZE</span>(__pyx_args) != 3) {\n",
       "      goto __pyx_L5_argtuple_error;\n",
       "    } else {\n",
       "      values[0] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 0);\n",
       "      values[1] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 1);\n",
       "      values[2] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 2);\n",
       "    }\n",
       "    __pyx_v_N1 = <span class='pyx_c_api'>__Pyx_PyInt_As_long</span>(values[0]); if (unlikely((__pyx_v_N1 == (long)-1) &amp;&amp; <span class='py_c_api'>PyErr_Occurred</span>())) <span class='error_goto'>__PYX_ERR(0, 9, __pyx_L3_error)</span>\n",
       "    __pyx_v_N2 = <span class='pyx_c_api'>__Pyx_PyInt_As_long</span>(values[1]); if (unlikely((__pyx_v_N2 == (long)-1) &amp;&amp; <span class='py_c_api'>PyErr_Occurred</span>())) <span class='error_goto'>__PYX_ERR(0, 9, __pyx_L3_error)</span>\n",
       "    __pyx_v_N3 = <span class='pyx_c_api'>__Pyx_PyInt_As_long</span>(values[2]); if (unlikely((__pyx_v_N3 == (long)-1) &amp;&amp; <span class='py_c_api'>PyErr_Occurred</span>())) <span class='error_goto'>__PYX_ERR(0, 9, __pyx_L3_error)</span>\n",
       "  }\n",
       "  goto __pyx_L4_argument_unpacking_done;\n",
       "  __pyx_L5_argtuple_error:;\n",
       "  <span class='pyx_c_api'>__Pyx_RaiseArgtupleInvalid</span>(\"f1\", 1, 3, 3, <span class='py_macro_api'>PyTuple_GET_SIZE</span>(__pyx_args)); <span class='error_goto'>__PYX_ERR(0, 9, __pyx_L3_error)</span>\n",
       "  __pyx_L3_error:;\n",
       "  <span class='pyx_c_api'>__Pyx_AddTraceback</span>(\"_cython_magic_0f6407bef3789247c6025a198ff7b605.f1\", __pyx_clineno, __pyx_lineno, __pyx_filename);\n",
       "  <span class='refnanny'>__Pyx_RefNannyFinishContext</span>();\n",
       "  return NULL;\n",
       "  __pyx_L4_argument_unpacking_done:;\n",
       "  __pyx_r = __pyx_pf_46_cython_magic_0f6407bef3789247c6025a198ff7b605_f1(__pyx_self, __pyx_v_N1, __pyx_v_N2, __pyx_v_N3);\n",
       "\n",
       "  /* function exit code */\n",
       "  <span class='refnanny'>__Pyx_RefNannyFinishContext</span>();\n",
       "  return __pyx_r;\n",
       "}\n",
       "\n",
       "static PyObject *__pyx_pf_46_cython_magic_0f6407bef3789247c6025a198ff7b605_f1(CYTHON_UNUSED PyObject *__pyx_self, long __pyx_v_N1, long __pyx_v_N2, long __pyx_v_N3) {\n",
       "  long __pyx_v_s2;\n",
       "  long __pyx_v_i;\n",
       "  long __pyx_v_j;\n",
       "  long __pyx_v_k;\n",
       "  PyObject *__pyx_r = NULL;\n",
       "  <span class='refnanny'>__Pyx_RefNannyDeclarations</span>\n",
       "  <span class='refnanny'>__Pyx_RefNannySetupContext</span>(\"f1\", 0);\n",
       "/* … */\n",
       "  /* function exit code */\n",
       "  __pyx_L1_error:;\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_10);\n",
       "  <span class='pyx_c_api'>__Pyx_AddTraceback</span>(\"_cython_magic_0f6407bef3789247c6025a198ff7b605.f1\", __pyx_clineno, __pyx_lineno, __pyx_filename);\n",
       "  __pyx_r = NULL;\n",
       "  __pyx_L0:;\n",
       "  <span class='refnanny'>__Pyx_XGIVEREF</span>(__pyx_r);\n",
       "  <span class='refnanny'>__Pyx_RefNannyFinishContext</span>();\n",
       "  return __pyx_r;\n",
       "}\n",
       "/* … */\n",
       "  __pyx_tuple__2 = <span class='py_c_api'>PyTuple_Pack</span>(7, __pyx_n_s_N1, __pyx_n_s_N2, __pyx_n_s_N3, __pyx_n_s_s2, __pyx_n_s_i, __pyx_n_s_j, __pyx_n_s_k);<span class='error_goto'> if (unlikely(!__pyx_tuple__2)) __PYX_ERR(0, 9, __pyx_L1_error)</span>\n",
       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_tuple__2);\n",
       "  <span class='refnanny'>__Pyx_GIVEREF</span>(__pyx_tuple__2);\n",
       "/* … */\n",
       "  __pyx_t_1 = PyCFunction_NewEx(&amp;__pyx_mdef_46_cython_magic_0f6407bef3789247c6025a198ff7b605_1f1, NULL, __pyx_n_s_cython_magic_0f6407bef3789247c6);<span class='error_goto'> if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 9, __pyx_L1_error)</span>\n",
       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_1);\n",
       "  if (<span class='py_c_api'>PyDict_SetItem</span>(__pyx_d, __pyx_n_s_f1, __pyx_t_1) &lt; 0) <span class='error_goto'>__PYX_ERR(0, 9, __pyx_L1_error)</span>\n",
       "  <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_1); __pyx_t_1 = 0;\n",
       "  __pyx_codeobj__3 = (PyObject*)<span class='pyx_c_api'>__Pyx_PyCode_New</span>(3, 0, 7, 0, CO_OPTIMIZED|CO_NEWLOCALS, __pyx_empty_bytes, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_tuple__2, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_kp_s_cache_ipython_cython__cython_ma, __pyx_n_s_f1, 9, __pyx_empty_bytes);<span class='error_goto'> if (unlikely(!__pyx_codeobj__3)) __PYX_ERR(0, 9, __pyx_L1_error)</span>\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">10</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">long</span> <span class=\"nf\">s2</span> <span class=\"o\">=</span> <span class=\"mf\">0</span>   <span class=\"c\"># this declares s as a C int</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_v_s2 = 0;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">11</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">long</span> <span class=\"nf\">i</span><span class=\"p\">,</span><span class=\"nf\">j</span><span class=\"p\">,</span><span class=\"nf\">k</span></pre>\n",
       "<pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">12</span>:     <span class=\"k\">for</span> <span class=\"n\">i</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">N1</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_t_1 = __pyx_v_N1;\n",
       "  __pyx_t_2 = __pyx_t_1;\n",
       "  for (__pyx_t_3 = 0; __pyx_t_3 &lt; __pyx_t_2; __pyx_t_3+=1) {\n",
       "    __pyx_v_i = __pyx_t_3;\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">13</span>:         <span class=\"k\">for</span> <span class=\"n\">j</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">N2</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-0 '>    __pyx_t_4 = __pyx_v_N2;\n",
       "    __pyx_t_5 = __pyx_t_4;\n",
       "    for (__pyx_t_6 = 0; __pyx_t_6 &lt; __pyx_t_5; __pyx_t_6+=1) {\n",
       "      __pyx_v_j = __pyx_t_6;\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">14</span>:             <span class=\"k\">for</span> <span class=\"n\">k</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">N3</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-0 '>      __pyx_t_7 = __pyx_v_N3;\n",
       "      __pyx_t_8 = __pyx_t_7;\n",
       "      for (__pyx_t_9 = 0; __pyx_t_9 &lt; __pyx_t_8; __pyx_t_9+=1) {\n",
       "        __pyx_v_k = __pyx_t_9;\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">15</span>:                 <span class=\"n\">s2</span> <span class=\"o\">+=</span> <span class=\"n\">i</span><span class=\"o\">**</span><span class=\"mf\">2</span> <span class=\"o\">+</span> <span class=\"n\">i</span><span class=\"o\">*</span><span class=\"n\">j</span><span class=\"o\">*</span><span class=\"n\">k</span> <span class=\"o\">+</span> <span class=\"mf\">2</span><span class=\"o\">*</span><span class=\"n\">k</span> <span class=\"o\">+</span> <span class=\"n\">i</span> <span class=\"o\">-</span> <span class=\"n\">j</span></pre>\n",
       "<pre class='cython code score-0 '>        __pyx_v_s2 = (__pyx_v_s2 + ((((__Pyx_pow_long(__pyx_v_i, 2) + ((__pyx_v_i * __pyx_v_j) * __pyx_v_k)) + (2 * __pyx_v_k)) + __pyx_v_i) - __pyx_v_j));\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "</pre><pre class=\"cython line score-3\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">16</span>:     <span class=\"k\">return</span> <span class=\"n\">s2</span></pre>\n",
       "<pre class='cython code score-3 '>  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_r);\n",
       "  __pyx_t_10 = <span class='pyx_c_api'>__Pyx_PyInt_From_long</span>(__pyx_v_s2);<span class='error_goto'> if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 16, __pyx_L1_error)</span>\n",
       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_10);\n",
       "  __pyx_r = __pyx_t_10;\n",
       "  __pyx_t_10 = 0;\n",
       "  goto __pyx_L0;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">17</span>: </pre>\n",
       "<pre class=\"cython line score-55\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">18</span>: <span class=\"k\">def</span> <span class=\"nf\">f2</span><span class=\"p\">(</span><span class=\"n\">N1</span><span class=\"p\">,</span> <span class=\"n\">N2</span><span class=\"p\">,</span> <span class=\"n\">N3</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-55 '>/* Python wrapper */\n",
       "static PyObject *__pyx_pw_46_cython_magic_0f6407bef3789247c6025a198ff7b605_3f2(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/\n",
       "static PyMethodDef __pyx_mdef_46_cython_magic_0f6407bef3789247c6025a198ff7b605_3f2 = {\"f2\", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_46_cython_magic_0f6407bef3789247c6025a198ff7b605_3f2, METH_VARARGS|METH_KEYWORDS, 0};\n",
       "static PyObject *__pyx_pw_46_cython_magic_0f6407bef3789247c6025a198ff7b605_3f2(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds) {\n",
       "  PyObject *__pyx_v_N1 = 0;\n",
       "  PyObject *__pyx_v_N2 = 0;\n",
       "  PyObject *__pyx_v_N3 = 0;\n",
       "  PyObject *__pyx_r = 0;\n",
       "  <span class='refnanny'>__Pyx_RefNannyDeclarations</span>\n",
       "  <span class='refnanny'>__Pyx_RefNannySetupContext</span>(\"f2 (wrapper)\", 0);\n",
       "  {\n",
       "    static PyObject **__pyx_pyargnames[] = {&amp;__pyx_n_s_N1,&amp;__pyx_n_s_N2,&amp;__pyx_n_s_N3,0};\n",
       "    PyObject* values[3] = {0,0,0};\n",
       "    if (unlikely(__pyx_kwds)) {\n",
       "      Py_ssize_t kw_args;\n",
       "      const Py_ssize_t pos_args = <span class='py_macro_api'>PyTuple_GET_SIZE</span>(__pyx_args);\n",
       "      switch (pos_args) {\n",
       "        case  3: values[2] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 2);\n",
       "        CYTHON_FALLTHROUGH;\n",
       "        case  2: values[1] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 1);\n",
       "        CYTHON_FALLTHROUGH;\n",
       "        case  1: values[0] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 0);\n",
       "        CYTHON_FALLTHROUGH;\n",
       "        case  0: break;\n",
       "        default: goto __pyx_L5_argtuple_error;\n",
       "      }\n",
       "      kw_args = <span class='py_c_api'>PyDict_Size</span>(__pyx_kwds);\n",
       "      switch (pos_args) {\n",
       "        case  0:\n",
       "        if (likely((values[0] = <span class='pyx_c_api'>__Pyx_PyDict_GetItemStr</span>(__pyx_kwds, __pyx_n_s_N1)) != 0)) kw_args--;\n",
       "        else goto __pyx_L5_argtuple_error;\n",
       "        CYTHON_FALLTHROUGH;\n",
       "        case  1:\n",
       "        if (likely((values[1] = <span class='pyx_c_api'>__Pyx_PyDict_GetItemStr</span>(__pyx_kwds, __pyx_n_s_N2)) != 0)) kw_args--;\n",
       "        else {\n",
       "          <span class='pyx_c_api'>__Pyx_RaiseArgtupleInvalid</span>(\"f2\", 1, 3, 3, 1); <span class='error_goto'>__PYX_ERR(0, 18, __pyx_L3_error)</span>\n",
       "        }\n",
       "        CYTHON_FALLTHROUGH;\n",
       "        case  2:\n",
       "        if (likely((values[2] = <span class='pyx_c_api'>__Pyx_PyDict_GetItemStr</span>(__pyx_kwds, __pyx_n_s_N3)) != 0)) kw_args--;\n",
       "        else {\n",
       "          <span class='pyx_c_api'>__Pyx_RaiseArgtupleInvalid</span>(\"f2\", 1, 3, 3, 2); <span class='error_goto'>__PYX_ERR(0, 18, __pyx_L3_error)</span>\n",
       "        }\n",
       "      }\n",
       "      if (unlikely(kw_args &gt; 0)) {\n",
       "        if (unlikely(<span class='pyx_c_api'>__Pyx_ParseOptionalKeywords</span>(__pyx_kwds, __pyx_pyargnames, 0, values, pos_args, \"f2\") &lt; 0)) <span class='error_goto'>__PYX_ERR(0, 18, __pyx_L3_error)</span>\n",
       "      }\n",
       "    } else if (<span class='py_macro_api'>PyTuple_GET_SIZE</span>(__pyx_args) != 3) {\n",
       "      goto __pyx_L5_argtuple_error;\n",
       "    } else {\n",
       "      values[0] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 0);\n",
       "      values[1] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 1);\n",
       "      values[2] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 2);\n",
       "    }\n",
       "    __pyx_v_N1 = values[0];\n",
       "    __pyx_v_N2 = values[1];\n",
       "    __pyx_v_N3 = values[2];\n",
       "  }\n",
       "  goto __pyx_L4_argument_unpacking_done;\n",
       "  __pyx_L5_argtuple_error:;\n",
       "  <span class='pyx_c_api'>__Pyx_RaiseArgtupleInvalid</span>(\"f2\", 1, 3, 3, <span class='py_macro_api'>PyTuple_GET_SIZE</span>(__pyx_args)); <span class='error_goto'>__PYX_ERR(0, 18, __pyx_L3_error)</span>\n",
       "  __pyx_L3_error:;\n",
       "  <span class='pyx_c_api'>__Pyx_AddTraceback</span>(\"_cython_magic_0f6407bef3789247c6025a198ff7b605.f2\", __pyx_clineno, __pyx_lineno, __pyx_filename);\n",
       "  <span class='refnanny'>__Pyx_RefNannyFinishContext</span>();\n",
       "  return NULL;\n",
       "  __pyx_L4_argument_unpacking_done:;\n",
       "  __pyx_r = __pyx_pf_46_cython_magic_0f6407bef3789247c6025a198ff7b605_2f2(__pyx_self, __pyx_v_N1, __pyx_v_N2, __pyx_v_N3);\n",
       "\n",
       "  /* function exit code */\n",
       "  <span class='refnanny'>__Pyx_RefNannyFinishContext</span>();\n",
       "  return __pyx_r;\n",
       "}\n",
       "\n",
       "static PyObject *__pyx_pf_46_cython_magic_0f6407bef3789247c6025a198ff7b605_2f2(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_N1, PyObject *__pyx_v_N2, PyObject *__pyx_v_N3) {\n",
       "  PyObject *__pyx_v_s2 = NULL;\n",
       "  PyObject *__pyx_v_i = NULL;\n",
       "  PyObject *__pyx_v_j = NULL;\n",
       "  PyObject *__pyx_v_k = NULL;\n",
       "  PyObject *__pyx_r = NULL;\n",
       "  <span class='refnanny'>__Pyx_RefNannyDeclarations</span>\n",
       "  <span class='refnanny'>__Pyx_RefNannySetupContext</span>(\"f2\", 0);\n",
       "/* … */\n",
       "  /* function exit code */\n",
       "  __pyx_L1_error:;\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_1);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_2);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_5);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_8);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_11);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_12);\n",
       "  <span class='pyx_c_api'>__Pyx_AddTraceback</span>(\"_cython_magic_0f6407bef3789247c6025a198ff7b605.f2\", __pyx_clineno, __pyx_lineno, __pyx_filename);\n",
       "  __pyx_r = NULL;\n",
       "  __pyx_L0:;\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_v_s2);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_v_i);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_v_j);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_v_k);\n",
       "  <span class='refnanny'>__Pyx_XGIVEREF</span>(__pyx_r);\n",
       "  <span class='refnanny'>__Pyx_RefNannyFinishContext</span>();\n",
       "  return __pyx_r;\n",
       "}\n",
       "/* … */\n",
       "  __pyx_tuple__4 = <span class='py_c_api'>PyTuple_Pack</span>(7, __pyx_n_s_N1, __pyx_n_s_N2, __pyx_n_s_N3, __pyx_n_s_s2, __pyx_n_s_i, __pyx_n_s_j, __pyx_n_s_k);<span class='error_goto'> if (unlikely(!__pyx_tuple__4)) __PYX_ERR(0, 18, __pyx_L1_error)</span>\n",
       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_tuple__4);\n",
       "  <span class='refnanny'>__Pyx_GIVEREF</span>(__pyx_tuple__4);\n",
       "/* … */\n",
       "  __pyx_t_1 = PyCFunction_NewEx(&amp;__pyx_mdef_46_cython_magic_0f6407bef3789247c6025a198ff7b605_3f2, NULL, __pyx_n_s_cython_magic_0f6407bef3789247c6);<span class='error_goto'> if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 18, __pyx_L1_error)</span>\n",
       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_1);\n",
       "  if (<span class='py_c_api'>PyDict_SetItem</span>(__pyx_d, __pyx_n_s_f2, __pyx_t_1) &lt; 0) <span class='error_goto'>__PYX_ERR(0, 18, __pyx_L1_error)</span>\n",
       "  <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_1); __pyx_t_1 = 0;\n",
       "  __pyx_codeobj__5 = (PyObject*)<span class='pyx_c_api'>__Pyx_PyCode_New</span>(3, 0, 7, 0, CO_OPTIMIZED|CO_NEWLOCALS, __pyx_empty_bytes, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_tuple__4, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_kp_s_cache_ipython_cython__cython_ma, __pyx_n_s_f2, 18, __pyx_empty_bytes);<span class='error_goto'> if (unlikely(!__pyx_codeobj__5)) __PYX_ERR(0, 18, __pyx_L1_error)</span>\n",
       "</pre><pre class=\"cython line score-1\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">19</span>:     <span class=\"n\">s2</span> <span class=\"o\">=</span> <span class=\"mf\">0</span>   <span class=\"c\"># this declares s as a C int</span></pre>\n",
       "<pre class='cython code score-1 '>  <span class='pyx_macro_api'>__Pyx_INCREF</span>(__pyx_int_0);\n",
       "  __pyx_v_s2 = __pyx_int_0;\n",
       "</pre><pre class=\"cython line score-46\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">20</span>:     <span class=\"k\">for</span> <span class=\"n\">i</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">N1</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-46 '>  __pyx_t_1 = <span class='pyx_c_api'>__Pyx_PyObject_CallOneArg</span>(__pyx_builtin_range, __pyx_v_N1);<span class='error_goto'> if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 20, __pyx_L1_error)</span>\n",
       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_1);\n",
       "  if (likely(<span class='py_c_api'>PyList_CheckExact</span>(__pyx_t_1)) || <span class='py_c_api'>PyTuple_CheckExact</span>(__pyx_t_1)) {\n",
       "    __pyx_t_2 = __pyx_t_1; <span class='pyx_macro_api'>__Pyx_INCREF</span>(__pyx_t_2); __pyx_t_3 = 0;\n",
       "    __pyx_t_4 = NULL;\n",
       "  } else {\n",
       "    __pyx_t_3 = -1; __pyx_t_2 = <span class='py_c_api'>PyObject_GetIter</span>(__pyx_t_1);<span class='error_goto'> if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 20, __pyx_L1_error)</span>\n",
       "    <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_2);\n",
       "    __pyx_t_4 = Py_TYPE(__pyx_t_2)-&gt;tp_iternext;<span class='error_goto'> if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 20, __pyx_L1_error)</span>\n",
       "  }\n",
       "  <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_1); __pyx_t_1 = 0;\n",
       "  for (;;) {\n",
       "    if (likely(!__pyx_t_4)) {\n",
       "      if (likely(<span class='py_c_api'>PyList_CheckExact</span>(__pyx_t_2))) {\n",
       "        if (__pyx_t_3 &gt;= <span class='py_macro_api'>PyList_GET_SIZE</span>(__pyx_t_2)) break;\n",
       "        #if CYTHON_ASSUME_SAFE_MACROS &amp;&amp; !CYTHON_AVOID_BORROWED_REFS\n",
       "        __pyx_t_1 = <span class='py_macro_api'>PyList_GET_ITEM</span>(__pyx_t_2, __pyx_t_3); <span class='pyx_macro_api'>__Pyx_INCREF</span>(__pyx_t_1); __pyx_t_3++; if (unlikely(0 &lt; 0)) <span class='error_goto'>__PYX_ERR(0, 20, __pyx_L1_error)</span>\n",
       "        #else\n",
       "        __pyx_t_1 = <span class='py_macro_api'>PySequence_ITEM</span>(__pyx_t_2, __pyx_t_3); __pyx_t_3++;<span class='error_goto'> if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 20, __pyx_L1_error)</span>\n",
       "        <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_1);\n",
       "        #endif\n",
       "      } else {\n",
       "        if (__pyx_t_3 &gt;= <span class='py_macro_api'>PyTuple_GET_SIZE</span>(__pyx_t_2)) break;\n",
       "        #if CYTHON_ASSUME_SAFE_MACROS &amp;&amp; !CYTHON_AVOID_BORROWED_REFS\n",
       "        __pyx_t_1 = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_t_2, __pyx_t_3); <span class='pyx_macro_api'>__Pyx_INCREF</span>(__pyx_t_1); __pyx_t_3++; if (unlikely(0 &lt; 0)) <span class='error_goto'>__PYX_ERR(0, 20, __pyx_L1_error)</span>\n",
       "        #else\n",
       "        __pyx_t_1 = <span class='py_macro_api'>PySequence_ITEM</span>(__pyx_t_2, __pyx_t_3); __pyx_t_3++;<span class='error_goto'> if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 20, __pyx_L1_error)</span>\n",
       "        <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_1);\n",
       "        #endif\n",
       "      }\n",
       "    } else {\n",
       "      __pyx_t_1 = __pyx_t_4(__pyx_t_2);\n",
       "      if (unlikely(!__pyx_t_1)) {\n",
       "        PyObject* exc_type = <span class='py_c_api'>PyErr_Occurred</span>();\n",
       "        if (exc_type) {\n",
       "          if (likely(<span class='pyx_c_api'>__Pyx_PyErr_GivenExceptionMatches</span>(exc_type, PyExc_StopIteration))) <span class='py_c_api'>PyErr_Clear</span>();\n",
       "          else <span class='error_goto'>__PYX_ERR(0, 20, __pyx_L1_error)</span>\n",
       "        }\n",
       "        break;\n",
       "      }\n",
       "      <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_1);\n",
       "    }\n",
       "    <span class='pyx_macro_api'>__Pyx_XDECREF_SET</span>(__pyx_v_i, __pyx_t_1);\n",
       "    __pyx_t_1 = 0;\n",
       "/* … */\n",
       "  }\n",
       "  <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_2); __pyx_t_2 = 0;\n",
       "</pre><pre class=\"cython line score-46\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">21</span>:         <span class=\"k\">for</span> <span class=\"n\">j</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">N2</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-46 '>    __pyx_t_1 = <span class='pyx_c_api'>__Pyx_PyObject_CallOneArg</span>(__pyx_builtin_range, __pyx_v_N2);<span class='error_goto'> if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 21, __pyx_L1_error)</span>\n",
       "    <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_1);\n",
       "    if (likely(<span class='py_c_api'>PyList_CheckExact</span>(__pyx_t_1)) || <span class='py_c_api'>PyTuple_CheckExact</span>(__pyx_t_1)) {\n",
       "      __pyx_t_5 = __pyx_t_1; <span class='pyx_macro_api'>__Pyx_INCREF</span>(__pyx_t_5); __pyx_t_6 = 0;\n",
       "      __pyx_t_7 = NULL;\n",
       "    } else {\n",
       "      __pyx_t_6 = -1; __pyx_t_5 = <span class='py_c_api'>PyObject_GetIter</span>(__pyx_t_1);<span class='error_goto'> if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 21, __pyx_L1_error)</span>\n",
       "      <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_5);\n",
       "      __pyx_t_7 = Py_TYPE(__pyx_t_5)-&gt;tp_iternext;<span class='error_goto'> if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 21, __pyx_L1_error)</span>\n",
       "    }\n",
       "    <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_1); __pyx_t_1 = 0;\n",
       "    for (;;) {\n",
       "      if (likely(!__pyx_t_7)) {\n",
       "        if (likely(<span class='py_c_api'>PyList_CheckExact</span>(__pyx_t_5))) {\n",
       "          if (__pyx_t_6 &gt;= <span class='py_macro_api'>PyList_GET_SIZE</span>(__pyx_t_5)) break;\n",
       "          #if CYTHON_ASSUME_SAFE_MACROS &amp;&amp; !CYTHON_AVOID_BORROWED_REFS\n",
       "          __pyx_t_1 = <span class='py_macro_api'>PyList_GET_ITEM</span>(__pyx_t_5, __pyx_t_6); <span class='pyx_macro_api'>__Pyx_INCREF</span>(__pyx_t_1); __pyx_t_6++; if (unlikely(0 &lt; 0)) <span class='error_goto'>__PYX_ERR(0, 21, __pyx_L1_error)</span>\n",
       "          #else\n",
       "          __pyx_t_1 = <span class='py_macro_api'>PySequence_ITEM</span>(__pyx_t_5, __pyx_t_6); __pyx_t_6++;<span class='error_goto'> if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 21, __pyx_L1_error)</span>\n",
       "          <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_1);\n",
       "          #endif\n",
       "        } else {\n",
       "          if (__pyx_t_6 &gt;= <span class='py_macro_api'>PyTuple_GET_SIZE</span>(__pyx_t_5)) break;\n",
       "          #if CYTHON_ASSUME_SAFE_MACROS &amp;&amp; !CYTHON_AVOID_BORROWED_REFS\n",
       "          __pyx_t_1 = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_t_5, __pyx_t_6); <span class='pyx_macro_api'>__Pyx_INCREF</span>(__pyx_t_1); __pyx_t_6++; if (unlikely(0 &lt; 0)) <span class='error_goto'>__PYX_ERR(0, 21, __pyx_L1_error)</span>\n",
       "          #else\n",
       "          __pyx_t_1 = <span class='py_macro_api'>PySequence_ITEM</span>(__pyx_t_5, __pyx_t_6); __pyx_t_6++;<span class='error_goto'> if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 21, __pyx_L1_error)</span>\n",
       "          <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_1);\n",
       "          #endif\n",
       "        }\n",
       "      } else {\n",
       "        __pyx_t_1 = __pyx_t_7(__pyx_t_5);\n",
       "        if (unlikely(!__pyx_t_1)) {\n",
       "          PyObject* exc_type = <span class='py_c_api'>PyErr_Occurred</span>();\n",
       "          if (exc_type) {\n",
       "            if (likely(<span class='pyx_c_api'>__Pyx_PyErr_GivenExceptionMatches</span>(exc_type, PyExc_StopIteration))) <span class='py_c_api'>PyErr_Clear</span>();\n",
       "            else <span class='error_goto'>__PYX_ERR(0, 21, __pyx_L1_error)</span>\n",
       "          }\n",
       "          break;\n",
       "        }\n",
       "        <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_1);\n",
       "      }\n",
       "      <span class='pyx_macro_api'>__Pyx_XDECREF_SET</span>(__pyx_v_j, __pyx_t_1);\n",
       "      __pyx_t_1 = 0;\n",
       "/* … */\n",
       "    }\n",
       "    <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_5); __pyx_t_5 = 0;\n",
       "</pre><pre class=\"cython line score-46\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">22</span>:             <span class=\"k\">for</span> <span class=\"n\">k</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">N3</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-46 '>      __pyx_t_1 = <span class='pyx_c_api'>__Pyx_PyObject_CallOneArg</span>(__pyx_builtin_range, __pyx_v_N3);<span class='error_goto'> if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 22, __pyx_L1_error)</span>\n",
       "      <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_1);\n",
       "      if (likely(<span class='py_c_api'>PyList_CheckExact</span>(__pyx_t_1)) || <span class='py_c_api'>PyTuple_CheckExact</span>(__pyx_t_1)) {\n",
       "        __pyx_t_8 = __pyx_t_1; <span class='pyx_macro_api'>__Pyx_INCREF</span>(__pyx_t_8); __pyx_t_9 = 0;\n",
       "        __pyx_t_10 = NULL;\n",
       "      } else {\n",
       "        __pyx_t_9 = -1; __pyx_t_8 = <span class='py_c_api'>PyObject_GetIter</span>(__pyx_t_1);<span class='error_goto'> if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 22, __pyx_L1_error)</span>\n",
       "        <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_8);\n",
       "        __pyx_t_10 = Py_TYPE(__pyx_t_8)-&gt;tp_iternext;<span class='error_goto'> if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 22, __pyx_L1_error)</span>\n",
       "      }\n",
       "      <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_1); __pyx_t_1 = 0;\n",
       "      for (;;) {\n",
       "        if (likely(!__pyx_t_10)) {\n",
       "          if (likely(<span class='py_c_api'>PyList_CheckExact</span>(__pyx_t_8))) {\n",
       "            if (__pyx_t_9 &gt;= <span class='py_macro_api'>PyList_GET_SIZE</span>(__pyx_t_8)) break;\n",
       "            #if CYTHON_ASSUME_SAFE_MACROS &amp;&amp; !CYTHON_AVOID_BORROWED_REFS\n",
       "            __pyx_t_1 = <span class='py_macro_api'>PyList_GET_ITEM</span>(__pyx_t_8, __pyx_t_9); <span class='pyx_macro_api'>__Pyx_INCREF</span>(__pyx_t_1); __pyx_t_9++; if (unlikely(0 &lt; 0)) <span class='error_goto'>__PYX_ERR(0, 22, __pyx_L1_error)</span>\n",
       "            #else\n",
       "            __pyx_t_1 = <span class='py_macro_api'>PySequence_ITEM</span>(__pyx_t_8, __pyx_t_9); __pyx_t_9++;<span class='error_goto'> if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 22, __pyx_L1_error)</span>\n",
       "            <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_1);\n",
       "            #endif\n",
       "          } else {\n",
       "            if (__pyx_t_9 &gt;= <span class='py_macro_api'>PyTuple_GET_SIZE</span>(__pyx_t_8)) break;\n",
       "            #if CYTHON_ASSUME_SAFE_MACROS &amp;&amp; !CYTHON_AVOID_BORROWED_REFS\n",
       "            __pyx_t_1 = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_t_8, __pyx_t_9); <span class='pyx_macro_api'>__Pyx_INCREF</span>(__pyx_t_1); __pyx_t_9++; if (unlikely(0 &lt; 0)) <span class='error_goto'>__PYX_ERR(0, 22, __pyx_L1_error)</span>\n",
       "            #else\n",
       "            __pyx_t_1 = <span class='py_macro_api'>PySequence_ITEM</span>(__pyx_t_8, __pyx_t_9); __pyx_t_9++;<span class='error_goto'> if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 22, __pyx_L1_error)</span>\n",
       "            <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_1);\n",
       "            #endif\n",
       "          }\n",
       "        } else {\n",
       "          __pyx_t_1 = __pyx_t_10(__pyx_t_8);\n",
       "          if (unlikely(!__pyx_t_1)) {\n",
       "            PyObject* exc_type = <span class='py_c_api'>PyErr_Occurred</span>();\n",
       "            if (exc_type) {\n",
       "              if (likely(<span class='pyx_c_api'>__Pyx_PyErr_GivenExceptionMatches</span>(exc_type, PyExc_StopIteration))) <span class='py_c_api'>PyErr_Clear</span>();\n",
       "              else <span class='error_goto'>__PYX_ERR(0, 22, __pyx_L1_error)</span>\n",
       "            }\n",
       "            break;\n",
       "          }\n",
       "          <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_1);\n",
       "        }\n",
       "        <span class='pyx_macro_api'>__Pyx_XDECREF_SET</span>(__pyx_v_k, __pyx_t_1);\n",
       "        __pyx_t_1 = 0;\n",
       "/* … */\n",
       "      }\n",
       "      <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_8); __pyx_t_8 = 0;\n",
       "</pre><pre class=\"cython line score-54\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">23</span>:                 <span class=\"n\">s2</span> <span class=\"o\">+=</span> <span class=\"n\">i</span><span class=\"o\">**</span><span class=\"mf\">2</span> <span class=\"o\">+</span> <span class=\"n\">i</span><span class=\"o\">*</span><span class=\"n\">j</span><span class=\"o\">*</span><span class=\"n\">k</span> <span class=\"o\">+</span> <span class=\"mf\">2</span><span class=\"o\">*</span><span class=\"n\">k</span> <span class=\"o\">+</span> <span class=\"n\">i</span> <span class=\"o\">-</span> <span class=\"n\">j</span></pre>\n",
       "<pre class='cython code score-54 '>        __pyx_t_1 = <span class='py_c_api'>PyNumber_Power</span>(__pyx_v_i, __pyx_int_2, Py_None);<span class='error_goto'> if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 23, __pyx_L1_error)</span>\n",
       "        <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_1);\n",
       "        __pyx_t_11 = <span class='py_c_api'>PyNumber_Multiply</span>(__pyx_v_i, __pyx_v_j);<span class='error_goto'> if (unlikely(!__pyx_t_11)) __PYX_ERR(0, 23, __pyx_L1_error)</span>\n",
       "        <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_11);\n",
       "        __pyx_t_12 = <span class='py_c_api'>PyNumber_Multiply</span>(__pyx_t_11, __pyx_v_k);<span class='error_goto'> if (unlikely(!__pyx_t_12)) __PYX_ERR(0, 23, __pyx_L1_error)</span>\n",
       "        <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_12);\n",
       "        <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_11); __pyx_t_11 = 0;\n",
       "        __pyx_t_11 = <span class='py_c_api'>PyNumber_Add</span>(__pyx_t_1, __pyx_t_12);<span class='error_goto'> if (unlikely(!__pyx_t_11)) __PYX_ERR(0, 23, __pyx_L1_error)</span>\n",
       "        <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_11);\n",
       "        <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_1); __pyx_t_1 = 0;\n",
       "        <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_12); __pyx_t_12 = 0;\n",
       "        __pyx_t_12 = <span class='py_c_api'>PyNumber_Multiply</span>(__pyx_int_2, __pyx_v_k);<span class='error_goto'> if (unlikely(!__pyx_t_12)) __PYX_ERR(0, 23, __pyx_L1_error)</span>\n",
       "        <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_12);\n",
       "        __pyx_t_1 = <span class='py_c_api'>PyNumber_Add</span>(__pyx_t_11, __pyx_t_12);<span class='error_goto'> if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 23, __pyx_L1_error)</span>\n",
       "        <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_1);\n",
       "        <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_11); __pyx_t_11 = 0;\n",
       "        <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_12); __pyx_t_12 = 0;\n",
       "        __pyx_t_12 = <span class='py_c_api'>PyNumber_Add</span>(__pyx_t_1, __pyx_v_i);<span class='error_goto'> if (unlikely(!__pyx_t_12)) __PYX_ERR(0, 23, __pyx_L1_error)</span>\n",
       "        <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_12);\n",
       "        <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_1); __pyx_t_1 = 0;\n",
       "        __pyx_t_1 = <span class='py_c_api'>PyNumber_Subtract</span>(__pyx_t_12, __pyx_v_j);<span class='error_goto'> if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 23, __pyx_L1_error)</span>\n",
       "        <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_1);\n",
       "        <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_12); __pyx_t_12 = 0;\n",
       "        __pyx_t_12 = <span class='py_c_api'>PyNumber_InPlaceAdd</span>(__pyx_v_s2, __pyx_t_1);<span class='error_goto'> if (unlikely(!__pyx_t_12)) __PYX_ERR(0, 23, __pyx_L1_error)</span>\n",
       "        <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_12);\n",
       "        <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_1); __pyx_t_1 = 0;\n",
       "        <span class='pyx_macro_api'>__Pyx_DECREF_SET</span>(__pyx_v_s2, __pyx_t_12);\n",
       "        __pyx_t_12 = 0;\n",
       "</pre><pre class=\"cython line score-2\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">24</span>:     <span class=\"k\">return</span> <span class=\"n\">s2</span></pre>\n",
       "<pre class='cython code score-2 '>  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_r);\n",
       "  <span class='pyx_macro_api'>__Pyx_INCREF</span>(__pyx_v_s2);\n",
       "  __pyx_r = __pyx_v_s2;\n",
       "  goto __pyx_L0;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">25</span>: </pre>\n",
       "<pre class=\"cython line score-54\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">26</span>: <span class=\"k\">def</span> <span class=\"nf\">f3</span><span class=\"p\">(</span><span class=\"n\">Integer</span> <span class=\"n\">N1</span><span class=\"p\">,</span> <span class=\"n\">Integer</span> <span class=\"n\">N2</span><span class=\"p\">,</span> <span class=\"n\">Integer</span> <span class=\"n\">N3</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-54 '>/* Python wrapper */\n",
       "static PyObject *__pyx_pw_46_cython_magic_0f6407bef3789247c6025a198ff7b605_5f3(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/\n",
       "static PyMethodDef __pyx_mdef_46_cython_magic_0f6407bef3789247c6025a198ff7b605_5f3 = {\"f3\", (PyCFunction)(void*)(PyCFunctionWithKeywords)__pyx_pw_46_cython_magic_0f6407bef3789247c6025a198ff7b605_5f3, METH_VARARGS|METH_KEYWORDS, 0};\n",
       "static PyObject *__pyx_pw_46_cython_magic_0f6407bef3789247c6025a198ff7b605_5f3(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds) {\n",
       "  struct __pyx_obj_4sage_5rings_7integer_Integer *__pyx_v_N1 = 0;\n",
       "  struct __pyx_obj_4sage_5rings_7integer_Integer *__pyx_v_N2 = 0;\n",
       "  struct __pyx_obj_4sage_5rings_7integer_Integer *__pyx_v_N3 = 0;\n",
       "  PyObject *__pyx_r = 0;\n",
       "  <span class='refnanny'>__Pyx_RefNannyDeclarations</span>\n",
       "  <span class='refnanny'>__Pyx_RefNannySetupContext</span>(\"f3 (wrapper)\", 0);\n",
       "  {\n",
       "    static PyObject **__pyx_pyargnames[] = {&amp;__pyx_n_s_N1,&amp;__pyx_n_s_N2,&amp;__pyx_n_s_N3,0};\n",
       "    PyObject* values[3] = {0,0,0};\n",
       "    if (unlikely(__pyx_kwds)) {\n",
       "      Py_ssize_t kw_args;\n",
       "      const Py_ssize_t pos_args = <span class='py_macro_api'>PyTuple_GET_SIZE</span>(__pyx_args);\n",
       "      switch (pos_args) {\n",
       "        case  3: values[2] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 2);\n",
       "        CYTHON_FALLTHROUGH;\n",
       "        case  2: values[1] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 1);\n",
       "        CYTHON_FALLTHROUGH;\n",
       "        case  1: values[0] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 0);\n",
       "        CYTHON_FALLTHROUGH;\n",
       "        case  0: break;\n",
       "        default: goto __pyx_L5_argtuple_error;\n",
       "      }\n",
       "      kw_args = <span class='py_c_api'>PyDict_Size</span>(__pyx_kwds);\n",
       "      switch (pos_args) {\n",
       "        case  0:\n",
       "        if (likely((values[0] = <span class='pyx_c_api'>__Pyx_PyDict_GetItemStr</span>(__pyx_kwds, __pyx_n_s_N1)) != 0)) kw_args--;\n",
       "        else goto __pyx_L5_argtuple_error;\n",
       "        CYTHON_FALLTHROUGH;\n",
       "        case  1:\n",
       "        if (likely((values[1] = <span class='pyx_c_api'>__Pyx_PyDict_GetItemStr</span>(__pyx_kwds, __pyx_n_s_N2)) != 0)) kw_args--;\n",
       "        else {\n",
       "          <span class='pyx_c_api'>__Pyx_RaiseArgtupleInvalid</span>(\"f3\", 1, 3, 3, 1); <span class='error_goto'>__PYX_ERR(0, 26, __pyx_L3_error)</span>\n",
       "        }\n",
       "        CYTHON_FALLTHROUGH;\n",
       "        case  2:\n",
       "        if (likely((values[2] = <span class='pyx_c_api'>__Pyx_PyDict_GetItemStr</span>(__pyx_kwds, __pyx_n_s_N3)) != 0)) kw_args--;\n",
       "        else {\n",
       "          <span class='pyx_c_api'>__Pyx_RaiseArgtupleInvalid</span>(\"f3\", 1, 3, 3, 2); <span class='error_goto'>__PYX_ERR(0, 26, __pyx_L3_error)</span>\n",
       "        }\n",
       "      }\n",
       "      if (unlikely(kw_args &gt; 0)) {\n",
       "        if (unlikely(<span class='pyx_c_api'>__Pyx_ParseOptionalKeywords</span>(__pyx_kwds, __pyx_pyargnames, 0, values, pos_args, \"f3\") &lt; 0)) <span class='error_goto'>__PYX_ERR(0, 26, __pyx_L3_error)</span>\n",
       "      }\n",
       "    } else if (<span class='py_macro_api'>PyTuple_GET_SIZE</span>(__pyx_args) != 3) {\n",
       "      goto __pyx_L5_argtuple_error;\n",
       "    } else {\n",
       "      values[0] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 0);\n",
       "      values[1] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 1);\n",
       "      values[2] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 2);\n",
       "    }\n",
       "    __pyx_v_N1 = ((struct __pyx_obj_4sage_5rings_7integer_Integer *)values[0]);\n",
       "    __pyx_v_N2 = ((struct __pyx_obj_4sage_5rings_7integer_Integer *)values[1]);\n",
       "    __pyx_v_N3 = ((struct __pyx_obj_4sage_5rings_7integer_Integer *)values[2]);\n",
       "  }\n",
       "  goto __pyx_L4_argument_unpacking_done;\n",
       "  __pyx_L5_argtuple_error:;\n",
       "  <span class='pyx_c_api'>__Pyx_RaiseArgtupleInvalid</span>(\"f3\", 1, 3, 3, <span class='py_macro_api'>PyTuple_GET_SIZE</span>(__pyx_args)); <span class='error_goto'>__PYX_ERR(0, 26, __pyx_L3_error)</span>\n",
       "  __pyx_L3_error:;\n",
       "  <span class='pyx_c_api'>__Pyx_AddTraceback</span>(\"_cython_magic_0f6407bef3789247c6025a198ff7b605.f3\", __pyx_clineno, __pyx_lineno, __pyx_filename);\n",
       "  <span class='refnanny'>__Pyx_RefNannyFinishContext</span>();\n",
       "  return NULL;\n",
       "  __pyx_L4_argument_unpacking_done:;\n",
       "  if (unlikely(!<span class='pyx_c_api'>__Pyx_ArgTypeTest</span>(((PyObject *)__pyx_v_N1), __pyx_ptype_4sage_5rings_7integer_Integer, 1, \"N1\", 0))) <span class='error_goto'>__PYX_ERR(0, 26, __pyx_L1_error)</span>\n",
       "  if (unlikely(!<span class='pyx_c_api'>__Pyx_ArgTypeTest</span>(((PyObject *)__pyx_v_N2), __pyx_ptype_4sage_5rings_7integer_Integer, 1, \"N2\", 0))) <span class='error_goto'>__PYX_ERR(0, 26, __pyx_L1_error)</span>\n",
       "  if (unlikely(!<span class='pyx_c_api'>__Pyx_ArgTypeTest</span>(((PyObject *)__pyx_v_N3), __pyx_ptype_4sage_5rings_7integer_Integer, 1, \"N3\", 0))) <span class='error_goto'>__PYX_ERR(0, 26, __pyx_L1_error)</span>\n",
       "  __pyx_r = __pyx_pf_46_cython_magic_0f6407bef3789247c6025a198ff7b605_4f3(__pyx_self, __pyx_v_N1, __pyx_v_N2, __pyx_v_N3);\n",
       "\n",
       "  /* function exit code */\n",
       "  goto __pyx_L0;\n",
       "  __pyx_L1_error:;\n",
       "  __pyx_r = NULL;\n",
       "  __pyx_L0:;\n",
       "  <span class='refnanny'>__Pyx_RefNannyFinishContext</span>();\n",
       "  return __pyx_r;\n",
       "}\n",
       "\n",
       "static PyObject *__pyx_pf_46_cython_magic_0f6407bef3789247c6025a198ff7b605_4f3(CYTHON_UNUSED PyObject *__pyx_self, struct __pyx_obj_4sage_5rings_7integer_Integer *__pyx_v_N1, struct __pyx_obj_4sage_5rings_7integer_Integer *__pyx_v_N2, struct __pyx_obj_4sage_5rings_7integer_Integer *__pyx_v_N3) {\n",
       "  struct __pyx_obj_4sage_5rings_7integer_Integer *__pyx_v_s2 = 0;\n",
       "  long __pyx_v_i;\n",
       "  long __pyx_v_j;\n",
       "  long __pyx_v_k;\n",
       "  PyObject *__pyx_r = NULL;\n",
       "  <span class='refnanny'>__Pyx_RefNannyDeclarations</span>\n",
       "  <span class='refnanny'>__Pyx_RefNannySetupContext</span>(\"f3\", 0);\n",
       "/* … */\n",
       "  /* function exit code */\n",
       "  __pyx_L1_error:;\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_1);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_11);\n",
       "  <span class='pyx_c_api'>__Pyx_AddTraceback</span>(\"_cython_magic_0f6407bef3789247c6025a198ff7b605.f3\", __pyx_clineno, __pyx_lineno, __pyx_filename);\n",
       "  __pyx_r = NULL;\n",
       "  __pyx_L0:;\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>((PyObject *)__pyx_v_s2);\n",
       "  <span class='refnanny'>__Pyx_XGIVEREF</span>(__pyx_r);\n",
       "  <span class='refnanny'>__Pyx_RefNannyFinishContext</span>();\n",
       "  return __pyx_r;\n",
       "}\n",
       "/* … */\n",
       "  __pyx_tuple__6 = <span class='py_c_api'>PyTuple_Pack</span>(7, __pyx_n_s_N1, __pyx_n_s_N2, __pyx_n_s_N3, __pyx_n_s_s2, __pyx_n_s_i, __pyx_n_s_j, __pyx_n_s_k);<span class='error_goto'> if (unlikely(!__pyx_tuple__6)) __PYX_ERR(0, 26, __pyx_L1_error)</span>\n",
       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_tuple__6);\n",
       "  <span class='refnanny'>__Pyx_GIVEREF</span>(__pyx_tuple__6);\n",
       "/* … */\n",
       "  __pyx_t_1 = PyCFunction_NewEx(&amp;__pyx_mdef_46_cython_magic_0f6407bef3789247c6025a198ff7b605_5f3, NULL, __pyx_n_s_cython_magic_0f6407bef3789247c6);<span class='error_goto'> if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 26, __pyx_L1_error)</span>\n",
       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_1);\n",
       "  if (<span class='py_c_api'>PyDict_SetItem</span>(__pyx_d, __pyx_n_s_f3, __pyx_t_1) &lt; 0) <span class='error_goto'>__PYX_ERR(0, 26, __pyx_L1_error)</span>\n",
       "  <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_1); __pyx_t_1 = 0;\n",
       "  __pyx_codeobj__7 = (PyObject*)<span class='pyx_c_api'>__Pyx_PyCode_New</span>(3, 0, 7, 0, CO_OPTIMIZED|CO_NEWLOCALS, __pyx_empty_bytes, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_tuple__6, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_kp_s_cache_ipython_cython__cython_ma, __pyx_n_s_f3, 26, __pyx_empty_bytes);<span class='error_goto'> if (unlikely(!__pyx_codeobj__7)) __PYX_ERR(0, 26, __pyx_L1_error)</span>\n",
       "</pre><pre class=\"cython line score-7\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">27</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">Integer</span> <span class=\"nf\">s2</span> <span class=\"o\">=</span> <span class=\"n\">Integer</span><span class=\"p\">(</span><span class=\"mf\">0</span><span class=\"p\">)</span></pre>\n",
       "<pre class='cython code score-7 '>  __pyx_t_1 = <span class='pyx_c_api'>__Pyx_PyObject_Call</span>(((PyObject *)__pyx_ptype_4sage_5rings_7integer_Integer), __pyx_tuple_, NULL);<span class='error_goto'> if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 27, __pyx_L1_error)</span>\n",
       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_1);\n",
       "  __pyx_v_s2 = ((struct __pyx_obj_4sage_5rings_7integer_Integer *)__pyx_t_1);\n",
       "  __pyx_t_1 = 0;\n",
       "/* … */\n",
       "  __pyx_tuple_ = <span class='py_c_api'>PyTuple_Pack</span>(1, __pyx_int_0);<span class='error_goto'> if (unlikely(!__pyx_tuple_)) __PYX_ERR(0, 27, __pyx_L1_error)</span>\n",
       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_tuple_);\n",
       "  <span class='refnanny'>__Pyx_GIVEREF</span>(__pyx_tuple_);\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">28</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">long</span> <span class=\"nf\">i</span><span class=\"p\">,</span><span class=\"nf\">j</span><span class=\"p\">,</span><span class=\"nf\">k</span></pre>\n",
       "<pre class=\"cython line score-7\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">29</span>:     <span class=\"k\">for</span> <span class=\"n\">i</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">N1</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-7 '>  __pyx_t_2 = <span class='pyx_c_api'>__Pyx_PyInt_As_long</span>(((PyObject *)__pyx_v_N1)); if (unlikely((__pyx_t_2 == (long)-1) &amp;&amp; <span class='py_c_api'>PyErr_Occurred</span>())) <span class='error_goto'>__PYX_ERR(0, 29, __pyx_L1_error)</span>\n",
       "  __pyx_t_3 = __pyx_t_2;\n",
       "  for (__pyx_t_4 = 0; __pyx_t_4 &lt; __pyx_t_3; __pyx_t_4+=1) {\n",
       "    __pyx_v_i = __pyx_t_4;\n",
       "</pre><pre class=\"cython line score-7\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">30</span>:         <span class=\"k\">for</span> <span class=\"n\">j</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">N2</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-7 '>    __pyx_t_5 = <span class='pyx_c_api'>__Pyx_PyInt_As_long</span>(((PyObject *)__pyx_v_N2)); if (unlikely((__pyx_t_5 == (long)-1) &amp;&amp; <span class='py_c_api'>PyErr_Occurred</span>())) <span class='error_goto'>__PYX_ERR(0, 30, __pyx_L1_error)</span>\n",
       "    __pyx_t_6 = __pyx_t_5;\n",
       "    for (__pyx_t_7 = 0; __pyx_t_7 &lt; __pyx_t_6; __pyx_t_7+=1) {\n",
       "      __pyx_v_j = __pyx_t_7;\n",
       "</pre><pre class=\"cython line score-7\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">31</span>:             <span class=\"k\">for</span> <span class=\"n\">k</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">N3</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-7 '>      __pyx_t_8 = <span class='pyx_c_api'>__Pyx_PyInt_As_long</span>(((PyObject *)__pyx_v_N3)); if (unlikely((__pyx_t_8 == (long)-1) &amp;&amp; <span class='py_c_api'>PyErr_Occurred</span>())) <span class='error_goto'>__PYX_ERR(0, 31, __pyx_L1_error)</span>\n",
       "      __pyx_t_9 = __pyx_t_8;\n",
       "      for (__pyx_t_10 = 0; __pyx_t_10 &lt; __pyx_t_9; __pyx_t_10+=1) {\n",
       "        __pyx_v_k = __pyx_t_10;\n",
       "</pre><pre class=\"cython line score-11\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">32</span>:                 <span class=\"n\">s2</span> <span class=\"o\">+=</span> <span class=\"n\">i</span><span class=\"o\">**</span><span class=\"mf\">2</span> <span class=\"o\">+</span> <span class=\"n\">i</span><span class=\"o\">*</span><span class=\"n\">j</span><span class=\"o\">*</span><span class=\"n\">k</span> <span class=\"o\">+</span> <span class=\"mf\">2</span><span class=\"o\">*</span><span class=\"n\">k</span> <span class=\"o\">+</span> <span class=\"n\">i</span> <span class=\"o\">-</span> <span class=\"n\">j</span></pre>\n",
       "<pre class='cython code score-11 '>        __pyx_t_1 = <span class='pyx_c_api'>__Pyx_PyInt_From_long</span>(((((__Pyx_pow_long(__pyx_v_i, 2) + ((__pyx_v_i * __pyx_v_j) * __pyx_v_k)) + (2 * __pyx_v_k)) + __pyx_v_i) - __pyx_v_j));<span class='error_goto'> if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 32, __pyx_L1_error)</span>\n",
       "        <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_1);\n",
       "        __pyx_t_11 = <span class='py_c_api'>PyNumber_InPlaceAdd</span>(((PyObject *)__pyx_v_s2), __pyx_t_1);<span class='error_goto'> if (unlikely(!__pyx_t_11)) __PYX_ERR(0, 32, __pyx_L1_error)</span>\n",
       "        <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_11);\n",
       "        <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_1); __pyx_t_1 = 0;\n",
       "        if (!(likely(((__pyx_t_11) == Py_None) || likely(<span class='pyx_c_api'>__Pyx_TypeTest</span>(__pyx_t_11, __pyx_ptype_4sage_5rings_7integer_Integer))))) <span class='error_goto'>__PYX_ERR(0, 32, __pyx_L1_error)</span>\n",
       "        <span class='pyx_macro_api'>__Pyx_DECREF_SET</span>(__pyx_v_s2, ((struct __pyx_obj_4sage_5rings_7integer_Integer *)__pyx_t_11));\n",
       "        __pyx_t_11 = 0;\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "</pre><pre class=\"cython line score-2\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">33</span>:     <span class=\"k\">return</span> <span class=\"n\">s2</span></pre>\n",
       "<pre class='cython code score-2 '>  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_r);\n",
       "  <span class='pyx_macro_api'>__Pyx_INCREF</span>(((PyObject *)__pyx_v_s2));\n",
       "  __pyx_r = ((PyObject *)__pyx_v_s2);\n",
       "  goto __pyx_L0;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">34</span>: </pre>\n",
       "<pre class=\"cython line score-15\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">35</span>: <span class=\"k\">def</span> <span class=\"nf\">g</span><span class=\"p\">():</span></pre>\n",
       "<pre class='cython code score-15 '>/* Python wrapper */\n",
       "static PyObject *__pyx_pw_46_cython_magic_0f6407bef3789247c6025a198ff7b605_7g(PyObject *__pyx_self, CYTHON_UNUSED PyObject *unused); /*proto*/\n",
       "static PyMethodDef __pyx_mdef_46_cython_magic_0f6407bef3789247c6025a198ff7b605_7g = {\"g\", (PyCFunction)__pyx_pw_46_cython_magic_0f6407bef3789247c6025a198ff7b605_7g, METH_NOARGS, 0};\n",
       "static PyObject *__pyx_pw_46_cython_magic_0f6407bef3789247c6025a198ff7b605_7g(PyObject *__pyx_self, CYTHON_UNUSED PyObject *unused) {\n",
       "  PyObject *__pyx_r = 0;\n",
       "  <span class='refnanny'>__Pyx_RefNannyDeclarations</span>\n",
       "  <span class='refnanny'>__Pyx_RefNannySetupContext</span>(\"g (wrapper)\", 0);\n",
       "  __pyx_r = __pyx_pf_46_cython_magic_0f6407bef3789247c6025a198ff7b605_6g(__pyx_self);\n",
       "\n",
       "  /* function exit code */\n",
       "  <span class='refnanny'>__Pyx_RefNannyFinishContext</span>();\n",
       "  return __pyx_r;\n",
       "}\n",
       "\n",
       "static PyObject *__pyx_pf_46_cython_magic_0f6407bef3789247c6025a198ff7b605_6g(CYTHON_UNUSED PyObject *__pyx_self) {\n",
       "  std::vector&lt;int&gt;  __pyx_v_a;\n",
       "  PyObject *__pyx_r = NULL;\n",
       "  <span class='refnanny'>__Pyx_RefNannyDeclarations</span>\n",
       "  <span class='refnanny'>__Pyx_RefNannySetupContext</span>(\"g\", 0);\n",
       "/* … */\n",
       "  /* function exit code */\n",
       "  __pyx_L1_error:;\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_1);\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_2);\n",
       "  <span class='pyx_c_api'>__Pyx_AddTraceback</span>(\"_cython_magic_0f6407bef3789247c6025a198ff7b605.g\", __pyx_clineno, __pyx_lineno, __pyx_filename);\n",
       "  __pyx_r = NULL;\n",
       "  __pyx_L0:;\n",
       "  <span class='refnanny'>__Pyx_XGIVEREF</span>(__pyx_r);\n",
       "  <span class='refnanny'>__Pyx_RefNannyFinishContext</span>();\n",
       "  return __pyx_r;\n",
       "}\n",
       "/* … */\n",
       "  __pyx_tuple__8 = <span class='py_c_api'>PyTuple_Pack</span>(1, __pyx_n_s_a);<span class='error_goto'> if (unlikely(!__pyx_tuple__8)) __PYX_ERR(0, 35, __pyx_L1_error)</span>\n",
       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_tuple__8);\n",
       "  <span class='refnanny'>__Pyx_GIVEREF</span>(__pyx_tuple__8);\n",
       "/* … */\n",
       "  __pyx_t_1 = PyCFunction_NewEx(&amp;__pyx_mdef_46_cython_magic_0f6407bef3789247c6025a198ff7b605_7g, NULL, __pyx_n_s_cython_magic_0f6407bef3789247c6);<span class='error_goto'> if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 35, __pyx_L1_error)</span>\n",
       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_1);\n",
       "  if (<span class='py_c_api'>PyDict_SetItem</span>(__pyx_d, __pyx_n_s_g, __pyx_t_1) &lt; 0) <span class='error_goto'>__PYX_ERR(0, 35, __pyx_L1_error)</span>\n",
       "  <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_1); __pyx_t_1 = 0;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">36</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">vector</span>[<span class=\"kt\">int</span>] <span class=\"nf\">a</span></pre>\n",
       "<pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">37</span>:     <span class=\"n\">a</span><span class=\"o\">.</span><span class=\"n\">push_back</span><span class=\"p\">(</span><span class=\"mf\">3</span><span class=\"p\">)</span></pre>\n",
       "<pre class='cython code score-0 '>  try {\n",
       "    __pyx_v_a.push_back(3);\n",
       "  } catch(...) {\n",
       "    __Pyx_CppExn2PyErr();\n",
       "    <span class='error_goto'>__PYX_ERR(0, 37, __pyx_L1_error)</span>\n",
       "  }\n",
       "</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">38</span>:     <span class=\"n\">a</span><span class=\"o\">.</span><span class=\"n\">push_back</span><span class=\"p\">(</span><span class=\"mf\">2</span><span class=\"p\">)</span></pre>\n",
       "<pre class='cython code score-0 '>  try {\n",
       "    __pyx_v_a.push_back(2);\n",
       "  } catch(...) {\n",
       "    __Pyx_CppExn2PyErr();\n",
       "    <span class='error_goto'>__PYX_ERR(0, 38, __pyx_L1_error)</span>\n",
       "  }\n",
       "</pre><pre class=\"cython line score-9\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">39</span>:     <span class=\"k\">return</span> <span class=\"nb\">list</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">)</span></pre>\n",
       "<pre class='cython code score-9 '>  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_r);\n",
       "  __pyx_t_1 = <span class='pyx_c_api'>__pyx_convert_vector_to_py_int</span>(__pyx_v_a);<span class='error_goto'> if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 39, __pyx_L1_error)</span>\n",
       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_1);\n",
       "  __pyx_t_2 = <span class='py_c_api'>PySequence_List</span>(__pyx_t_1);<span class='error_goto'> if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 39, __pyx_L1_error)</span>\n",
       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_2);\n",
       "  <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_1); __pyx_t_1 = 0;\n",
       "  __pyx_r = __pyx_t_2;\n",
       "  __pyx_t_2 = 0;\n",
       "  goto __pyx_L0;\n",
       "</pre></div></body></html>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%cython -a\n",
    "# distutils: language = c++\n",
    "\n",
    "# importing types that are defined in other Cython files\n",
    "from sage.rings.integer cimport Integer\n",
    "\n",
    "# importing C++\n",
    "from libcpp.vector cimport vector\n",
    "\n",
    "def f1(long N1, long N2, long N3):\n",
    "    cdef long s2 = 0   # this declares s as a C int\n",
    "    cdef long i,j,k\n",
    "    for i in range(N1):\n",
    "        for j in range(N2):\n",
    "            for k in range(N3):\n",
    "                s2 += i**2 + i*j*k + 2*k + i - j\n",
    "    return s2\n",
    "\n",
    "def f2(N1, N2, N3):\n",
    "    s2 = 0   # this declares s as a C int\n",
    "    for i in range(N1):\n",
    "        for j in range(N2):\n",
    "            for k in range(N3):\n",
    "                s2 += i**2 + i*j*k + 2*k + i - j\n",
    "    return s2\n",
    "\n",
    "def f3(Integer N1, Integer N2, Integer N3):\n",
    "    cdef Integer s2 = Integer(0)\n",
    "    cdef long i,j,k\n",
    "    for i in range(N1):\n",
    "        for j in range(N2):\n",
    "            for k in range(N3):\n",
    "                s2 += i**2 + i*j*k + 2*k + i - j\n",
    "    return s2\n",
    "\n",
    "def g():\n",
    "    cdef vector[int] a\n",
    "    a.push_back(3)\n",
    "    a.push_back(2)\n",
    "    return list(a)  # wow!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 626 µs, sys: 0 ns, total: 626 µs\n",
      "Wall time: 638 µs\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "124669875000"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "f1(100,100,100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 108 ms, sys: 0 ns, total: 108 ms\n",
      "Wall time: 108 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "124669875000"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "f2(100,100,100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 219 ms, sys: 0 ns, total: 219 ms\n",
      "Wall time: 219 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "124669875000"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "f3(100,100,100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "124554051584"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s - 115823416"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[3, 2]"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "SageMath 8.8",
   "language": "sage",
   "name": "sagemath"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.16"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
