src/data_test.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "6a0ceb51",
   "metadata": {},
   "outputs": [
    {
     "ename": "FileNotFoundError",
     "evalue": "[Errno 2] No such file or directory: '/home/tianqiu/tts_schedule/batch_infer/src/memory_bank/similarity_retrieval/results/test_data_level_200.jsonl'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mFileNotFoundError\u001b[0m                         Traceback (most recent call last)",
      "\u001b[1;32m~\\AppData\\Local\\Temp\\ipykernel_51928\\500567839.py\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[0mPredicted_correct_num\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      6\u001b[0m \u001b[0mCorrect_sum\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 7\u001b[1;33m \u001b[1;32mwith\u001b[0m \u001b[0mopen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0minput_path\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'r'\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0mf\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      8\u001b[0m     \u001b[1;32mfor\u001b[0m \u001b[0mline\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mf\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      9\u001b[0m         \u001b[0mdata\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mjson\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mloads\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mline\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mFileNotFoundError\u001b[0m: [Errno 2] No such file or directory: '/home/tianqiu/tts_schedule/batch_infer/src/memory_bank/similarity_retrieval/results/test_data_level_200.jsonl'"
     ]
    }
   ],
   "source": [
    "import json\n",
    "\n",
    "input_path = '/home/tianqiu/tts_schedule/batch_infer/src/memory_bank/similarity_retrieval/results/test_data_level_200.jsonl'\n",
    "\n",
    "Predicted_correct_num = []\n",
    "Correct_sum = []\n",
    "with open(input_path, 'r') as f:\n",
    "    for line in f:\n",
    "        data = json.loads(line)\n",
    "        if data[\"predicted_correct_num_3\"] != -999:\n",
    "            Predicted_correct_num.append(data[\"predicted_correct_num_3\"])\n",
    "            Correct_sum.append(data[\"correct_sum\"])\n",
    "        \n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 散点图 二维\n",
    "plt.scatter(Predicted_correct_num,Correct_sum)\n",
    "plt.xlabel(\"Predicted correct num\")\n",
    "plt.ylabel(\"Correct sum\")\n",
    "plt.title(\"Predicted correct num vs Correct sum\")\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n",
    "       \n",
    "       \n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b06411ce",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "41\n"
     ]
    }
   ],
   "source": [
    "print(len(Predicted_correct_num))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42eefb18",
   "metadata": {},
   "source": [
    "查看parallel与sequence vote 在同样query次数下 边际正确的差异"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "00b8bd5a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "16\n",
      "0\n"
     ]
    },
    {
     "ename": "ZeroDivisionError",
     "evalue": "division by zero",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mZeroDivisionError\u001b[0m                         Traceback (most recent call last)",
      "\u001b[1;32m~\\AppData\\Local\\Temp\\ipykernel_59624\\2329339900.py\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m     19\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     20\u001b[0m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mbudget_sum\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 21\u001b[1;33m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mbudget_sum\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdata_list\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     22\u001b[0m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdata_list\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     23\u001b[0m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlevel_count\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mZeroDivisionError\u001b[0m: division by zero"
     ]
    }
   ],
   "source": [
    "import json\n",
    "input_path=\"E:/copy/tts_schedule_730/batch_infer/src/memory_bank/similarity_retrieval/data/mathhard_train_level.jsonl\"\n",
    "data_list=[]\n",
    "budget_sum=0\n",
    "level_count={\n",
    "    \"definite_simple\":0,\n",
    "    \"definite_hard\":0,\n",
    "    \"normal\":0,\n",
    "    \"hard\":0,\n",
    "    \"extreme_hard\":0\n",
    "}\n",
    "with open(input_path, 'r') as f:\n",
    "    for line in f:\n",
    "        data = json.loads(line)\n",
    "        print(len(data[\"outputs\"]))\n",
    "        break\n",
    "        data_list.append(data)\n",
    "        # level_count[data['strategy']]+=1\n",
    "        \n",
    "print(budget_sum)\n",
    "print(budget_sum/len(data_list))\n",
    "print(len(data_list))\n",
    "print(level_count)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d9041ec0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intersection: 722\n",
      "Parallel not in Sequence vote: 89\n",
      "Sequence vote not in Parallel: 68\n",
      "Basic in intersection: 681\n",
      "Intersection not in basic: 41\n"
     ]
    },
    {
     "data": {
      "image/png": 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Dhw+v9Rzy6quvGknm8ccfr7WO6seu+gV+bGxsrZHagQMHmnbt2pnc3Fz3bStWrDB2u91cfPHF7tuO9Xu6bNkyI6nOIw+O5VilsXrdN954o/u2w0tjterR98MdXqwO19zvr9PpND169DATJkyo8TNaXFxsunbtak4++WT3bdXPF5dddlmNbZ199tkmISGhxm1RUVFHHV2sb99Wr15tJJkff/zRGOM6YiI6OtoUFRXVenwb81xw7bXX1hrlO3zbCQkJ5sCBA+7bP/nkEyPJfPbZZ+7bGvozNnnyZBMeHl7jeWft2rUmKCioRobqNwKO9fwLAE3lHScfICAdOnRIkmqcz3Y0X375pSTppptuqnH7zTffLEm1zn3s06ePhg0b5v78hBNOkCSNGzdOnTt3rnX71q1ba23z8EkibDabrrvuOpWXl+vbb7913x4REeH+/8GDB5Wfn6+RI0fq119/rbW+0aNHq0+fPsfYU9e5RosWLdLevXvr/PqSJUuUk5Oja665psb5eqeffrp69epV53mgV199dY3PR44cWec+H+7bb79VeXm5brjhhhrnKl155ZWKjY1t0vmmTfm+BwUF6frrr69x+8033yxjjL766qsatx/tMb7yyisVFBTk/vx///uf8vLydNFFF2n//v3uj6CgIJ1wwgmaO3euJNc5YD/88IMuu+yyGj87kpo9Yc2bb76p008/3f149OjRQ0OGDNGbb75Z5/JXXXVVjW2OHDlSVVVV2rFjh6TfzlP7/PPPVVFRUec6Ro4cKUn64YcfJEk//vijjjvuOJ188sn68ccfJUl5eXlavXq1e1ljjD744ANNmjRJxpgaj9eECROUn59f62f+kksuqfH7UZ1vzZo12rRpU4Mfo2qzZs2S3W7XOeec477toosu0ldffaWDBw+6b/vggw+UmJiov/zlL7XWceT365xzzlFSUpL788zMTC1fvlxTp05V27Zt3bf3799fJ598svt5qHpfjvZ7GhcXJ0n65ptvVFxc3Mi9PbrqmT8LCgpaZH0t8f1dvny5Nm3apD/84Q/Kzc1137+oqEjjx4/XDz/8UGvW17qel3Jzc93PE83Rt29f9e/fX2+//bYk6a233tJZZ52lyMjIWss29LmgIS644AK1adOmxj5Jv/2NaejPWFVVlb755htNnjy5xvNO7969NWHChBrbrP69/+STT/x2RmEA1qI0wjLVs/419EXPjh07ZLfba83M6XA4FB8f737RXO3IF/fVL+A6depU5+2Hv+iUJLvdrrS0tBq3paenS3JN617t888/1+9+9zuFh4erbdu2SkpK0n/+8x/l5+fX2oeuXbseazclSY888ohWr16tTp066fjjj9e0adNqFLzqfe3Zs2et+/bq1avWYxEeHl7jhbEktWnTptY+H6m+7YSGhiotLa3WdhqiKd/39u3b1yqZvXv3rpGx2tEe4yO/Vl1cxo0bp6SkpBofs2fPdk/uU/3YZ2RkNChzQ61bt07Lli3TiBEjtHnzZvfHmDFj9Pnnn9f5wvnIn+vqF6fV38vRo0frnHPO0b333qvExESdddZZmj59usrKytz3SU5OVo8ePdwF8ccff9TIkSM1atQo7d27V1u3btX8+fPldDrdL3j37dunvLw8vfjii7Ueq0svvVTSb5MhVavre3HfffcpLy9P6enp6tevn/72t79p5cqVDXq83njjDR1//PHKzc11P1aDBg1SeXm53nvvPfdyW7ZsUc+ePRs0I/GRGY/2u9W7d293CZKO/XvatWtX3XTTTXr55ZeVmJioCRMm6LnnnqvzuaGxCgsLJTX8zZdjaYnvb/Xv0yWXXFJrHS+//LLKyspq7fuxfp6b6w9/+IPee+89bd68WQsWLNAf/vCHOpdr6HNBQxxrnxr6M7Zv3z6VlJSoR48etZY78r4XXHCBRowYoSuuuELJycm68MIL9e6771IgAbQYZk+FZWJjY9W+fftGz5LZ0JGdw0eUGnK7MaZROSTXi+0zzzxTo0aN0vPPP6+UlBSFhIRo+vTpeuutt2otf+SoS33OP/98jRw5Uh999JFmz56tRx99VA8//LA+/PBDnXrqqY3OWd8+W6F79+4KDg7WqlWrPLL+oz3GR36t+gXVzJkz5XA4ai3v6cugvPHGG5Jc19K78cYba339gw8+cL9gr3asn1+bzab3339fP//8sz777DN98803uuyyy/TYY4/p559/do9QnXjiiZozZ45KSkq0dOlS3X333crIyFB8fLx+/PFHrVu3TtHR0Ro0aJCk3x6rP/7xj7rkkkvqzNC/f/8an9f1vRg1apS2bNmiTz75RLNnz9bLL7+sJ554Qi+88IKuuOKKeh+rTZs2afHixZJU54voN998U1dddVW9969PQ38n69KQ39PHHntMU6dOde/v9ddfrwcffFA///yzOnbs2ORtVz9vNuTyNg3REt/f6nU8+uijGjhwYJ3rOPLaiC35fFyXiy66yD3TbEJCgk455ZQ6l2vJ5wJP71NdIiIi9MMPP2ju3Ln64osv9PXXX+udd97RuHHjNHv2bK/6GwDAN1EaYakzzjhDL774ohYuXFjjUNK6dOnSRU6nU5s2bXKPMklSdna28vLy1KVLlxbN5nQ6tXXrVvfooiRt3LhRkpSamirJ9aI+PDxc33zzjcLCwtzLTZ8+vdnbT0lJ0TXXXKNrrrlGOTk5Gjx4sP71r3/p1FNPde/rhg0bNG7cuBr327BhQ4s9Fodv5/BR1/Lycm3btq1JlzqIjIzUuHHj9N1332nXrl21Rn7ryvDtt9+qoKCgxqjK+vXra2Rsim7dukmS2rVrd9R9qd73Y73B0ZhDVY0xeuuttzR27Fhdc801tb7+z3/+U2+++Wat0thQv/vd7/S73/1O//rXv/TWW29pypQpmjVrlruYjRw5UtOnT9esWbNUVVWl4cOHy26368QTT3SXxuHDh7tfbCYlJSkmJkZVVVXNvsRF27Ztdemll+rSSy9VYWGhRo0apWnTph21NL755psKCQnRzJkza70A/umnn/T0009r586d6ty5s7p166ZFixapoqJCISEhjcp2+M/8kdavX6/ExMQal2o52u9ptX79+qlfv3668847tWDBAo0YMUIvvPBCvRefb4iZM2fKZrPp5JNPbvI6DtcS39/q36fY2NgWvXZmcw4B79y5s0aMGKF58+bpz3/+c73lr6HPBc3NIzX8Zyw8PFwRERF1Hspd133tdrvGjx+v8ePH6/HHH9cDDzygO+64Q3PnzvXba5kCaD0cngpL/f3vf1dUVJSuuOIKZWdn1/r6li1b9NRTT0lyXXdLkp588skayzz++OOSXOfztbRnn33W/X9jjJ599lmFhIRo/PjxklzvKNtsNlVVVbmX2759uz7++OMmb7OqqqrWIVzt2rVT+/bt3YcYDh06VO3atdMLL7xQ47DDr776SuvWrWuxx+Kkk05SaGionn766Rrvkr/yyivKz89v8nbuueceGWP0pz/9yX2Y3eGWLl2qGTNmSHJ936uqqmp8LyTpiSeekM1ma9LIa7UJEyYoNjZWDzzwQJ3n/1Vfzy4pKUmjRo3Sq6++qp07d9ZY5vDHpbpM5OXlHXPb8+fP1/bt23XppZfq3HPPrfVxwQUXaO7cufWeL1efgwcP1hrRqB71Ofxnpfqw04cfflj9+/d3H6Y9cuRIzZkzR0uWLHEvI7l+1s855xx98MEHdZbn6sfqWHJzc2t8Hh0dre7du9fIVpc333xTI0eO1AUXXFDrsfrb3/4mSe5z18455xzt37+/1s+MdOzRnpSUFA0cOFAzZsyo8X1cvXq1Zs+e7X4easjv6aFDh1RZWVljmX79+slutx9zf4/moYce0uzZs3XBBRfUOeraFC3x/R0yZIi6deumf//733X+Xjf0Z+RIUVFRDfqdqs/999+ve+65p85zXKs19LmgOo/UsN/zujT0ZywoKEgTJkzQxx9/XON5Z926dfrmm29qrPPAgQO1tlPX7z0ANBUjjbBUt27d9NZbb+mCCy5Q7969dfHFFysjI0Pl5eVasGCB3nvvPU2dOlWSNGDAAF1yySV68cUXlZeXp9GjR+uXX37RjBkzNHnyZI0dO7ZFs4WHh+vrr7/WJZdcohNOOEFfffWVvvjiC91+++3u8wNPP/10Pf7445o4caL+8Ic/KCcnR88995y6d+/e4PO0jlRQUKCOHTvq3HPP1YABAxQdHa1vv/1Wixcv1mOPPSZJCgkJ0cMPP6xLL71Uo0eP1kUXXaTs7Gw99dRTSk1NrfNQx6ZISkrSbbfdpnvvvVcTJ07UmWeeqQ0bNuj555/XcccdV+vC4w01fPhwPffcc7rmmmvUq1cv/elPf1KPHj1UUFCgefPm6dNPP3WPwkyaNEljx47VHXfcoe3bt2vAgAGaPXu2PvnkE91www3uEYKmiI2N1X/+8x/96U9/0uDBg3XhhRcqKSlJO3fu1BdffKERI0a4i8fTTz+tE088UYMHD9ZVV12lrl27avv27friiy+0fPlySa4XzZJ0xx136MILL1RISIgmTZpUY2Sq2ptvvqmgoKB6i/eZZ56pO+64Q7Nmzao1+dPRzJgxQ88//7zOPvtsdevWTQUFBXrppZcUGxvrfjEquQ5rdDgc2rBhQ40X06NGjdKtt94qSTVKo+QqK3PnztUJJ5ygK6+8Un369NGBAwf066+/6ttvv63zheuR+vTpozFjxmjIkCFq27atlixZovfff7/GpFNHWrRokTZv3lzvMh06dNDgwYP15ptv6tZbb9XFF1+s119/XTfddJN++eUXjRw5UkVFRfr22291zTXX6KyzzjpqxkcffVSnnnqqhg0bpssvv1wlJSV65plnFBcXp2nTpklq2O/pd999p+uuu07nnXee0tPTVVlZ6R4pPXwyn/pUVla6D2EuLS3Vjh079Omnn2rlypUaO3asXnzxxWOuozGa+/212+16+eWXdeqpp6pv37669NJL1aFDB+3Zs0dz585VbGysPvvss0bnGjJkiL799ls9/vjjat++vbp27eqewKwhRo8erdGjRx91mcY8F1T/nl9//fWaMGGCgoKCdOGFFzZqnxryMyZJ9957r77++muNHDlS11xzjSorK/XMM8+ob9++Nf7G3Hffffrhhx90+umnq0uXLsrJydHzzz+vjh076sQTT2xUNgCoU+tP2ArUtnHjRnPllVea1NRUExoaamJiYsyIESPMM888Y0pLS93LVVRUmHvvvdd07drVhISEmE6dOpnbbrutxjLGuC65Ude0/mrg9PPV07Fv2bLFnHLKKSYyMtIkJyebe+65p8alJ4wx5pVXXnFfQLxXr15m+vTpdV54ua5tH/616ktulJWVmb/97W9mwIABJiYmxkRFRZkBAwbUeU3Fd955xwwaNMh9kfQpU6aY3bt311imvqn768pYn2effdb06tXLhISEmOTkZPPnP/+5xrUgD19fY6Z8X7p0qfnDH/5g2rdvb0JCQkybNm3M+PHjzYwZM2o8zgUFBebGG290L9ejRw/z6KOP1pjW35j6H+Pqy1XUdxmKuXPnmgkTJpi4uDgTHh5uunXrZqZOnWqWLFlSY7nVq1ebs88+28THx5vw8HDTs2fPWtft/Oc//2k6dOhg7HZ7vZffKC8vNwkJCWbkyJFHfXy6du1qBg0adNR9qL78QfUlY3799Vdz0UUXmc6dO5uwsDDTrl07c8YZZ9TaF2OMOe+884wk884779TIFhkZaUJDQ2tczqVadna2ufbaa02nTp1MSEiIcTgcZvz48ebFF1+slamuS03cf//95vjjjzfx8fEmIiLC9OrVy/zrX/+qcQ27I/3lL38xksyWLVvqXWbatGlGkvv6oMXFxeaOO+5wP1c4HA5z7rnnutdR32Unqn377bdmxIgRJiIiwsTGxppJkybVuPB6Q35Pt27dai677DLTrVs3Ex4ebtq2bWvGjh1rvv3223r3o9qRF5GPjIw0qamp5pxzzjHvv/9+rechY5p/yQ1jmv/9NcZ1OZDf//73JiEhwYSFhZkuXbqY888/38yZM8e9TH3PF9U/54f/3qxfv96MGjXKREREGElHvfzGsb6v1ep7XmzIc0FlZaX5y1/+YpKSkozNZnM/jx5t24c/x1c71s9Yte+//94MGTLEhIaGmrS0NPPCCy/Uev6eM2eOOeuss0z79u1NaGioad++vbnooovMxo0bj/o4AEBD2Yzx4JnZgI+aOnWq3n///ToPsQIAAAACCec0AgAAAADqRWkEAAAAANSL0ggAAAAAqBfnNAIAAAAA6sVIIwAAAACgXpRGAAAAAEC9KI0AAAAAgHpRGgEAAAAA9aI0AgAAAADqRWkEAAAAANSL0ggAAAAAqBelEQAAAABQL0ojAAAAAKBelEYAAAAAQL0ojQAAAACAelEaAQAAAAD1ojQCAAAAAOpFaQQAAAAA1IvSCAAAAACoF6URAAAAAFAvSiMAAAAAoF6URgAAAABAvSiNAAAAAIB6URoBAAAAAPWiNAIAAAAA6kVpBAAAAADUi9IIAAAAAKgXpREAAAAAUC9KIwAAAACgXpRGAAAAAEC9KI0AAAAAgHpRGgEAAAAA9aI0AgAAAADqRWkEAAAAANSL0ggAODZjrE4AAAAsEmx1AABACysrc32Ul9f+/5H/VlZKTqdUVeX6OPz/h39eXRpttt8+7Paan1d/BAVJwcFSSIjr3+r/h4b+9m/1R3i4FBHx20dQkLWPHQAAqMVmDG8fA4BPKC+XiouloqK6/63+qKqyOmnThYb+ViDDw6XISNe/UVFSdLQUE+P6oFwCANBqKI0A4E2Ki6X8fOnQodr/VlRYnc57REb+ViCjo6XY2Jr/2jn7AgCAlkJpBIDWVlUlHTwoHTgg5eXVLIeVlVan8312uxQXJ7VpU/MjLo4yCQBAE1AaAcCTioqk3FxXQaz+Ny+PiWWsUF0m4+NdJbJtWykpyTVaCQAA6kVpBICWUlAgZWdL+/ZJ+/e7CmJZmdWpcCzh4VJioqtAVn9ERVmdCgAAr0FpBICmqKx0lcPsbCknx/VRXGx1KrSUyEhXkWzXzlUik5Ndk/QAABCAKI0A0BAFBVJW1m8lMTeXQ0wDic3mOpw1JeW3j/Bwq1MBANAqKI0AUJeiImnv3t8+CgqsTgRv06aNqzw6HFL79q7RSQAA/BClEQAk1zUQ9+6Vdu+W9uxxzWQKNEZsrNShg9Spk+vfkBCrEwEA0CIojQACkzGuyWp27HAVxX37ONwULcdud41Adurk+mjb1upEAAA0GaURQOCorHSNIu7YIe3cycQ1aD1RUb8VyA4dmFQHAOBTKI0A/Ftxsasg7tjhKoyVlVYnQqCrHoXs2tX1wbmQAAAvR2kE4H/y86WtW6Xt212HnQLeymZzXc6jukBGR1udCACAWiiNAPxDYaG0ZYvrY/9+q9MATdOu3W8FMjbW6jQAAEiiNALwZcXFrhHFLVtc108E/EliopSWJnXvzggkAMBSlEYAvqWs7LeimJnJjKcIDCkpUo8erhLJJDoAgFZGaQTg/YxxTWKzfr1rQpuqKqsTAdYICpK6dJHS06WOHV2T6gAA4GGURgDeq6BA2rBB2rjRdc4igN9ERrpGH3v2lOLjrU4DAPBjlEYA3qWqyjXr6fr10t69HH4KNERystS7t9Stm2s0EgCAFkRpBOAdDhxwFcVNm1znLQJovPBw16Grffow+yoAoMVQGgFYxxjXqOLq1a5JbQC0DJvNdc5jnz5S586uzwEAaCJKI4DWV1bmGlVcu9Z13iIAz4mJkXr1cn1ERFidBgDggyiNAFrPwYOuUcVNm6TKSqvTAIHFbned89i/v5SQYHUaAIAPoTQC8CxjpJ07XWVxzx6r0wCQXIeuDhggdehgdRIAgA+gNALwDKfTNaK4YoWUl2d1GgB1SUx0jTympXHNRwBAvSiNAFpWZaXrfMWVK7m2IuArYmKkfv1c5z0GB1udBgDgZSiNAFpGeblrYptVq6SSEqvTAGiKsDDXjKv9+rku3wEAgCiNAJqrtNRVFNescRVHAL4vJETq29d16CrlEQACHqURQNMUF0vLl7sORWUmVMA/hYRIGRmu8hgWZnUaAIBFKI0AGqeszDW5zerVlEUgUISEuA5Z7deP8ggAAYjSCKBhKipch6GuXMlhqECgCg39rTyGhlqdBgDQSiiNAI6uqkpat05atowJbgC4hIW5Dlnt14/ZVgEgAFAaAdTN6ZQ2bpR+/ZVLZwCoW1SUNHSolJ4u2WxWpwEAeAilEUBt27ZJv/wi5edbnQSAL0hIkE44QerY0eokAAAPoDQC+E1urrRwobR3r9VJAPiiTp1c5bFtW6uTAABaEKURgOtcxcWLpQ0bJJ4SADSHzeY6XPW446TISKvTAABaAKURCGROp+vSGb/+yoyoAFpWcLA0YIDrg8lyAMCnURqBQLV9u7RoEectAvCsmBhp2DApNdXqJACAJqI0AoHmwAHXeYt79lidBEAg6dxZGj5cio21OgkAoJEojUCgqKyUliyRVq3ivEUA1ggKkgYNch2yGhRkdRoAQANRGoFAsGOHNH8+11sE4B1iY6URI1yzrQIAvB6lEfBnhYXSggWu8xcBwNukproOWY2OtjoJAOAoKI2APzJGWrPGdRmNigqr0wBA/YKDXZfnyMhwXa4DAOB1KI2AvzlwQPrhByknx+okANBwycnS6NFSfLzVSQAAR6A0Av6iqsp1vcUVK1zXXwQAXxMUJA0ZIvXvL9ntVqcBAPwfSiPgD3JzpblzXaOMAODrkpJco45t21qdBAAgSiPg25xOafly1wgjo4sA/IndLg0eLA0cyKgjAFiM0gj4qrw81+jivn1WJwEAz0lIcI06JiZanQQAAhalEfA1xkirVrlmRq2qsjoNAHiezSYNHeoadWSGVQBodZRGwJccOiR9/72UmWl1EgBofSkp0tixXNcRAFoZpRHwFevXSwsXct1FAIEtLEwaOVJKS7M6CQAEDEoj4O3Ky13XXdy61eokAOA90tOlESOkkBCrkwCA36M0At4sJ0eaM0cqKLA6CQB4n9hYadw4qV07q5MAgF+jNALeqHqym19+4VIaAHA0Nps0ZIg0aBCT5ACAh1AaAW9TWirNmyft3Gl1EgDwHSkp0vjxUmSk1UkAwO9QGgFvsnev69qLRUVWJwEA3xMR4SqO7dtbnQQA/AqlEfAGxki//ur64FcSAJqOazoCQIujNAJWKyuTvvtO2rXL6iQA4D86dXJNkhMWZnUSAPB5lEbASgcOSLNnS4cOWZ0EAPxPTIx08slSYqLVSQDAp1EaAats3eqa8Kay0uokAOC/goKkkSNd13UEADQJpRFobca4LqWxYoXVSQAgcPTpIw0fLtntVicBAJ9DaQRaU2mp6/zF3butTgIAgSclxXW4ani41UkAwKdQGoHWkpvrOn+xoMDqJAAQuGJjpQkTpDZtrE4CAD6D0gi0Bs5fBADvERrqup5jp05WJwEAn0BpBDxt+XLXOYwAAO9hs0m/+53Ur5/VSQDA61EaAU9xOqWffpLWr7c6CQCgPr17SyNGMEEOABwFpRHwhPJy6dtvmfAGAHxB+/bSSScxQQ4A1IPSCLS0wkLpq6+kgwetTgIAaKi4OGniRNe/AIAaKI1AS9q3T/rmG6m42OokAIDGCg93Fcd27axOAgBehdIItJTt213XYGSGVADwXcHBrms5MrMqALhRGoGWsGaNtGCBxK8TAPg+u10aPVrq0cPqJADgFSiNQHP9+qu0ZInVKQAALe2EE6QBA6xOAQCW84v5pV977TXFx8c3+f7Tpk3TwIEDWyxPoJg3b55sNpvy8vKsjmINY1yjixRGAPBPixZJCxdyFAmAgOfx0jh16lTZbDb3R0JCgiZOnKiVK1e22DYuuOACbdy4scn3v+WWWzRnzpxmZWhKcR0zZoxuuOGGZm23tdSVdfjw4crMzFRcIM4053RK338vrV5tdRIAgCetWiXNnet63geAANUqI40TJ05UZmamMjMzNWfOHAUHB+uMM85osfVHRESoXTNmOouOjlZCQkKL5Wlt5eXllmw3NDRUDodDNpvNku1bpqrKdQ3GZrxRAQDwIZs3S19/LVVUWJ0EACzRKqUxLCxMDodDDodDAwcO1D/+8Q/t2rVL+/btcy9z6623Kj09XZGRkUpLS9Ndd92lisOenFesWKGxY8cqJiZGsbGxGjJkiJb832GBdY3yffbZZzruuOMUHh6uxMREnX322fXmO/Lw1KlTp2ry5Mn697//rZSUFCUkJOjaa6+tkedYqtc5c+ZMpaamKi4uThdeeKEKCgrc2/j+++/11FNPuUdht2/fLklavXq1Tj31VEVHRys5OVl/+tOftH//fve6x4wZo+uuu0433HCDEhMTNWHCBBljNG3aNHXu3FlhYWFq3769rr/+evd9ysrKdMstt6hDhw6KiorSCSecoHnz5tXIPH/+fI0ZM0aRkZFq06aNJkyYoIMHD9abta7DUz/44AP17dtXYWFhSk1N1WOPPVZjG6mpqXrggQd02WWXKSYmRp07d9aLL77Y4MfVchUVrmsw/t/3CgAQIHbvdj3/W/RGLQBYqdXPaSwsLNQbb7yh7t271xjdi4mJ0Wuvvaa1a9fqqaee0ksvvaQnnnjC/fUpU6aoY8eOWrx4sZYuXap//OMfCgkJqXMbX3zxhc4++2yddtppWrZsmebMmaPjjz++UTnnzp2rLVu2aO7cuZoxY4Zee+01vfbaa41ax5YtW/Txxx/r888/1+eff67vv/9eDz30kCTpqaee0rBhw3TllVe6R2E7deqkvLw8jRs3ToMGDdKSJUv09ddfKzs7W+eff36Ndc+YMUOhoaGaP3++XnjhBX3wwQd64okn9N///lebNm3Sxx9/rH79+rmXv+6667Rw4ULNmjVLK1eu1HnnnaeJEydq06ZNkqTly5dr/Pjx6tOnjxYuXKiffvpJkyZNUlVVVb1Zj7R06VKdf/75uvDCC7Vq1SpNmzZNd911V63H7bHHHtPQoUO1bNkyXXPNNfrzn/+sDRs2NOqxtURpqfT559LevVYnAQBYIStL+vJLiiOAgBPcGhv5/PPPFR0dLUkqKipSSkqKPv/8c9ntv3XWO++80/3/1NRU3XLLLZo1a5b+/ve/S5J27typv/3tb+rVq5ckqcdRpsH+17/+pQsvvFD33nuv+7YBjZz9rE2bNnr22WcVFBSkXr166fTTT9ecOXN05ZVXNngdTqdTr732mmJiYiRJf/rTnzRnzhz961//UlxcnEJDQxUZGSmHw+G+z7PPPqtBgwbpgQcecN/26quvqlOnTtq4caPS09Mlufb/kUcecS/zxRdfyOFw6KSTTlJISIg6d+7sLso7d+7U9OnTtXPnTrVv316S6zzOr7/+WtOnT9cDDzygRx55REOHDtXzzz/vXmffvn3d/68r65Eef/xxjR8/XnfddZckKT09XWvXrtWjjz6qqVOnupc77bTTdM0110hyjTA/8cQTmjt3rnr27Nngx7bVFRdLX3whHTxodRIAgJVyclxvIJ52mhQebnUaAGgVrTLSOHbsWC1fvlzLly/XL7/8ogkTJujUU0/Vjh073Mu88847GjFihBwOh6Kjo3XnnXdq586d7q/fdNNNuuKKK3TSSSfpoYce0pYtW+rdXvWoWXP07dtXQUFB7s9TUlKUk5PTqHWkpqa6C2ND17FixQrNnTtX0dHR7o/qonz4Pg8ZMqTG/c477zyVlJQoLS1NV155pT766CNV/t9F5letWqWqqiqlp6fXWO/333/vXmdLPGbr1q3TiBEjatw2YsQIbdq0SVVVVe7b+vfv7/6/zWaTw+Fo9GPbqoqLpc8+ozACAFz273e9kVhSYnUSAGgVrVIao6Ki1L17d3Xv3l3HHXecXn75ZRUVFemll16SJC1cuFBTpkzRaaedps8//1zLli3THXfcUWOCl2nTpmnNmjU6/fTT9d1336lPnz766KOP6txeREREszMfeeirzWaTs5EzpzVlHYWFhZo0aZK7ZFd/bNq0SaNGjXIvFxUVVeN+nTp10oYNG/T8888rIiJC11xzjUaNGqWKigoVFhYqKChIS5curbHOdevW6amnnpLUMo9ZQ7XEY9tqqgtjfr7VSQAA3iQ31zXiWFxsdRIA8DhLrtNos9lkt9tV8n/v0C1YsEBdunTRHXfcoaFDh6pHjx41RiGrpaen68Ybb9Ts2bP1+9//XtOnT69z/f3792/2JTRaQ2hoaI0ROEkaPHiw1qxZo9TUVHfRrv44sigeKSIiQpMmTdLTTz+tefPmaeHChVq1apUGDRqkqqoq5eTk1Fpn9eGmx3rM6sp6pN69e2v+/Pk1bps/f77S09NrjNr6jOJi1wsCCiMAoC4HD7reWCwqsjoJAHhUq5TGsrIyZWVlKSsrS+vWrdNf/vIX94ia5Do/b+fOnZo1a5a2bNmip59+usYoYklJia677jrNmzdPO3bs0Pz587V48WL17t27zu3dc889evvtt3XPPfdo3bp1WrVqlR5++OHW2NVGSU1N1aJFi7R9+3bt379fTqdT1157rQ4cOKCLLrpIixcv1pYtW/TNN9/o0ksvPWppe+211/TKK69o9erV2rp1q9544w1FRESoS5cuSk9P15QpU3TxxRfrww8/1LZt2/TLL7/owQcf1BdffCFJuu2227R48WJdc801WrlypdavX6///Oc/7llb68p6pJtvvllz5szRP//5T23cuFEzZszQs88+q1tuucUzD6AnVRfGw2aGBQCglvx8V3EsLLQ6CQB4TKuUxq+//lopKSlKSUnRCSecoMWLF+u9997TmDFjJElnnnmmbrzxRl133XUaOHCgFixY4J5MRZKCgoKUm5uriy++WOnp6Tr//PN16qmn1pjo5nBjxozRe++9p08//VQDBw7UuHHj9Msvv7TGrjbKLbfcoqCgIPXp00dJSUnuiWrmz5+vqqoqnXLKKerXr59uuOEGxcfH15g46Ejx8fF66aWXNGLECPXv31/ffvutPvvsM/cMtdOnT9fFF1+sm2++WT179tTkyZO1ePFide7cWZJrFHf27NlasWKFjj/+eA0bNkyffPKJgoOD6816pMGDB+vdd9/VrFmzlJGRobvvvlv33XdfjUlwfAKFEQDQGIcOURwB+DWbMcZYHQLwGsySCgBoqrg46cwzpVacJwAAWoMl5zQCXqmkhMIIAGi6/HzXdRzLyqxOAgAtitIISK4/8BRGAEBz5eZKX30lHTYDPAD4OkojUFkpff21dOCA1UkAAP4gJ0f65hvX3xcA8AOURgQ2p1P63/+k7GyrkwAA/ElmpuvvyzEuVwUAvoDSiMBljDR3rrRrl9VJAAD+aNcuac4c1xuUAODDKI0IXPPnS1u2WJ0CAODPtm+Xvv/e9UYlAPgoSiMC05Il0tq1VqcAAASCTZukRYusTgEATUZpROBZtUr69VerUwAAAsnKldLq1VanAIAmoTQisGzaJC1caHUKAEAgWrhQ2rbN6hQA0GiURgSO3bulefOsTgEACFTGSN99J2VlWZ0EABqF0ojAcOCAa+pzJiIAAFipqsp1Dce8PKuTAECDURrh/4qLpa+/lioqrE4CAIBUViZ99ZVUUmJ1EgBoEEoj/FtFhaswFhZanQQAgN8UFPCGJgCfQWmE/6o+d2T/fquTAABQ27590pw5ktNpdRIAOCpKI/zXokXSjh1WpwAAoH47d3INRwBej9II/7R+veuaWAAAeLtVq6SNG61OAQD1ojTC/+zZI/30k9UpAABouB9/lLKzrU4BAHWiNMK/HDokffst54cAAHxLVZXr0lBFRVYnAYBaKI3wH5WVrj+4ZWVWJwEAoPGKi6XZs11/zwDAi1Aa4T9++EHKzbU6BQAATbdvn+vvGQB4EUoj/MPq1dLmzVanAACg+TZvllassDoFALhRGuH7MjOlhQutTgEAQMv55Rdp1y6rUwCAJEojfF1RkWviG2OsTgIAQMsxRpozRyoosDoJAFAa4cOqZ5orKbE6CQAALa+83PXGaFWV1UkABDhKI3zX/PlSTo7VKQAA8Jx9+6Sff7Y6BYAAR2mEb9qwQVq/3uoUAAB43po10tatVqcAEMAojfA9eXmuUUYAAALF999Lhw5ZnQJAgKI0wrdUVrrO7+DCxwCAQFJR4TqPn/MbAViA0gjf8vPP0oEDVqcAAKD15eZyiSkAlqA0wnds3y6tXWt1CgAArLN2rbR5s9UpAAQYSiN8Q2Gh63wOAAAC3Y8/Svn5VqcAEEAojfB+Tqf03XdSWZnVSQAAsF5FhevvotNpdRIAAYLSCO/3669SVpbVKQAA8B779klLl1qdAkCAoDTCu+3dKy1bZnUKAAC8z/LlvKkKoFVQGuG9ysuluXMlY6xOAgCA9zHG9XeyvNzqJAD8HKUR3mvBAqmoyOoUAAB4r4IC199LAPAgSiO8086d0saNVqcAAMD7bdzouiwVAHgIpRHep6xM+uEHq1MAAOA7fvhBKimxOgUAP0VphPeZP18qLrY6BQAAvqO01HX9RgDwAEojvMu2bdLmzVanAADA92zfzqkdADyC0gjvUVoq/fST1SkAAPBdCxdymCqAFkdphPf46Sf+0AEA0BxlZcymCqDFURrhHbZskbZutToFAAC+b8sW1yzkANBCKI2wHu+KAgDQsn78UaqosDoFAD9BaYT1Fi3isFQAAFpSUZH0yy9WpwDgJyiNsFZWlrR+vdUpAADwP2vXStnZVqcA4AcojbCO08lsqQAAeIox0g8/SFVVVicB4OMojbDOypXSgQNWpwAAwH8dPCgtW2Z1CgA+jtIIaxQUSL/+anUKAAD83/LlUl6e1SkA+DBKI6wxf75UWWl1CgAA/J/TySzlAJqF0ojWt20b148CAKA17d4tbd9udQoAPorSiNZVXs67nQAAWGHhQo7yAdAklEa0rmXLXNeOAgAAraugwDUJHQA0EqURrefQIWn1aqtTAAAQuJYvlwoLrU4BwMdQGtF6Fi3iWlEAAFipslL6+WerUwDwMZRGtI7MTNcEOAAAwFpbt0p791qdAoAPoTTC84xxnXwPAAC8w/z5rktxAEADUBrheRs3Svv3W50CAABUO3hQWrvW6hQAfASlEZ5VUSEtXmx1CgAAcKRff3VdCgsAjoHSCM9atkwqLrY6BQAAOFJpKZfgANAglEZ4TkGBtGqV1SkAAEB9Vq7kzV0Ax0RphOcsXswlNgAA8GaVla7DVAHgKCiN8IwDB6QtW6xOAQAAjmXdOik/3+oUALwYpRGesWSJ61IbAADAuxnDpHUAjorSiJa3b5+0fbvVKQAAQENt3Srl5FidAoCXojSi5S1ZYnUCAADQWL/8YnUCAF6K0oiWlZUl7dpldQoAANBYe/fyNxxAnSiNaFm8SwkAgO/iaCEAdaA0ouXs2uUaaQQAAL5p3z5GGwHUQmlEy+HdSQAAfB/XbQRwBEojWsb27a53JwEAgG/Lzpb27LE6BQAvQmlEy1i2zOoEAACgpTDaCOAwlEY03549jDICAOBPMjNds6kCgCiNaAmMMgIA4H/4+w7g/1Aa0Tw5ObwTCQCAP9qzh1nRAUiiNKK5li+3OgEAAPAURhsBiNKI5jh40DVrKgAA8E+7djFvAQBKI5qBUUYAAPzfypVWJwBgMUojmqagQNq82eoUAADA07ZulQoLrU4BwEKURjTNypWSMVanAAAAnmaMtGaN1SkAWCjY6gDwQaWl0vr1VqdAA6Xefrt25ObWuv2a0aP1t1NOUdc77qjzfu9edZXOGzKkzq9Nfe01zVi4sMZtE/r00dd//askqayiQlfMnKlPVqyQIzZWz//hDzqpd2/3so9+8412HjigZy66qKm7BQBoTevWSYMHSyEhVicBYAFKIxpv/XqpqsrqFGigxbfdpiqn0/356r17dfKTT+q8IUPUqW1bZT7ySI3lX/zxRz06e7ZO7dv3qOud2Levpl9yifvzsODfnk5e/PFHLd25UwtvvVVfrV6tP7zyirIffVQ2m03b9u/XSz/9pCW3395CewgA8LjycmnDBikjw+okACxAaUTjOJ0couJjkmJianz+0Ndfq1tSkkanp8tms8kRF1fj6x8tX67zhw5VdHj4UdcbFhxc677V1mVl6cz+/dW3fXulJSbqbx98oP2FhUqKidGf33xTD//+94qNiGjejgEAWtfq1VLfvpLNZnUSAK2McxrRONu2SUVFVqdAE5VXVuqNRYt02fDhstXxR3/pjh1avmuXLh8x4pjrmrdxo9rdcot63n23/vzmm8o9bJKEAR076qfNm1VSXq5v1q5VSlycEqOj9eaiRQoPCdHZgwa16H4BAFrBoUPSjh1WpwBgAUYa0TirV1udAM3w8fLlyisp0dThw+v8+ivz56t3SoqGd+t21PVM7NtXvx80SF0TE7Vl3z7d/vHHOvWZZ7Tw1lsVZLfrshEjtHL3bvWZNk2J0dF696qrdLC4WHd/+qnm3Xyz7vz4Y81askTdkpL06sUXq0ObNp7YXQBAS1u5UkpNtToFgFZmM4YpMNFA+/ZJH31kdQo0w4SnnlJoUJA+u+66Wl8rKS9Xyt//rrtOP103n3xyo9a7dd8+dbvzTn17ww0af9iEN4e79LXXNLBTJ3VNTNTtH3+sRf/4hx755hut3rtXH1x9dZP2BwBggbPPlpKSrE4BoBVxeCoajnMZfdqO3Fx9u26drjjxxDq//v6vv6q4vFwX/+53jV53WlKSEqOjtXnfvjq/PnfDBq3JzNR1Y8dq3oYNOi0jQ1FhYTp/6FDN27ix0dsDAFiIo46AgENpRMOUlkpbtlidAs0wfcECtYuJ0en9+tX59Vfmz9eZAwbUmjinIXYfPKjcoiKl1DExTmlFha59+239d8oUBdntqjJGFf83+25FVVWNmV0BAD5g61aprMzqFABaEaURDbNhA5fZ8GFOp1PTFyzQJcOGKTgoqNbXN+fk6IdNm3RFPRPg9Lr7bn20bJkkqbC0VH97/339vHWrtu/frznr1ums559X96QkTejTp9Z9//nFFzotI0ODOneWJI3o1k0fLlumlbt369m5czXiGOdPAgC8TFWVtGmT1SkAtCImwsGxGSOtXWt1CjTDt+vXa+eBA7qsnlL46vz56hgfr1PqKH2StCE7W/klJZKkILtdK/fs0Yyff1ZecbHax8frlN699c+zzlLYERd9Xr1nj95dulTL77zTfdu5gwdr3saNGvnoo+rpcOityy9vob0EALSadeu4ZiMQQJgIB8e2a5f01VdWpwAAAN7kzDMlh8PqFABaAYen4tg2bLA6AQAA8Dbr1lmdAEAroTTi6EpLuZAvAACojQlxgIBBacTRbd7MBDgAAKA2JsQBAgalEUfHoakAAKA+HKIKBARKI+q3f7+Um2t1CgAA4K0OHpSysqxOAcDDKI2oH6OMAADgWDZutDoBAA+jNKJuVVWu8xkBAACOZutW5j8A/BylEXXbvp0Z0QAAwLGVl0s7d1qdAoAHURpRNw41AQAADcUsqoBfozSituJiafduq1MAAABfsWsXRygBfozSiNq2bZOMsToFAADwFVVVrtcPAPwSpRG1bd1qdQIAAOBrOEQV8FuURtRUVMT1lgAAQONlZkqFhVanAOABlEbUtHUrh6YCAICm2bLF6gQAPIDSiJo4NBUAADQVh6gCfonSiN8UFkrZ2VanAAAAvurAASkvz+oUAFoYpRG/4ZASAADQXMyiCvgdSiN+w6GpAACguSiNgN+hNMLl0CFp3z6rUwAAAF+3fz+zqAJ+htIIl+3brU4AAAD8BaONgF+hNMJlxw6rEwAAAH/Bm9GAX6E0Qiork7KyrE4BAAD8RVaWVFpqdQoALYTSCGnXLskYq1MAAAB/YYy0c6fVKQC0EEojeFIHAAAtj0NUAb9BaQx0TqdrpBEAAKAl7d4tVVVZnQJAC6A0BrrsbNc5jQAAAC2pslLau9fqFABaAKUx0DFrKgAA8JTdu61OAKAFUBoDHeczAgAAT6E0An6B0hjIDh2S8vKsTgEAAPzVwYNScbHVKQA0E6UxkDEBDgAA8DRGGwGfR2kMZHv2WJ0AAAD4O0oj4PMojYHKGCkz0+oUAADA3+3Z43rdAcBnURoDVW4ul9oAAACeV1Liet0BwGdRGgMV100CAACthUNUAZ9GaQxUnM8IAABaC687AJ9GaQxETqeUlWV1CgAAECiysqTKSqtTAGgiSmMg2rdPqqiwOgUAAAgUVVWu1x8AfBKlMRBxPiMAAGht2dlWJwDQRJTGQERpBAAArY1TYwCfRWkMNJzPCAAArJCdzfUaAR9FaQw0+/e7zisAAABoTWVl0sGDVqcA0ASUxkCTk2N1AgAAEKg4rxHwSZTGQENpBAAAVuEUGcAnURoDDaURAABYhdII+CRKYyApLZUOHbI6BQAACFQFBVJxsdUpADQSpTGQMMoIAACsxmgj4HMojYGE0ggAAKy2b5/VCQA0EqUxkFAaAQCA1fbvtzoBgEaiNAYKY3hnDwAAWC831+oEABqJ0hgo8vNdF9UFAACwUmmpVFhodQoAjUBpDBQcCgIAALwFr0sAn0JpDBQHDlidAAAAwIVDVAGfQmkMFJRGAADgLRhpBHwKpTFQUBoBAIC3oDQCPoXSGAjKyznhHAAAeI+iIteEOAB8AqUxEDDKCAAAvA2jjYDPoDQGAkojAADwNrw+AXwGpTEQMEMZAADwNnl5VicA0ECUxkDAO3kAAMDbUBoBn0FpDASURgAA4G3y861OAKCBKI3+rrBQqqiwOgUAAEBNJSVSWZnVKQA0AKXR3x06ZHUCAACAunGIKuATKI3+jkM/AACAt+J1CuATKI3+jpFGAADgrRhpBHwCpdHfURoBAIC3ojQCPoHS6O8ojQAAwFtxeCrgEyiN/o7SCAAAvFV+vuR0Wp0CwDFQGv1ZSQmX2wAAAN7L6ZSKi61OAeAYKI3+jFFGAADg7QoLrU4A4Bgojf6M0ggAALxdUZHVCQAcA6XRn1EaAQCAt2OkEfB6lEZ/VlBgdQIAAICjozQCXo/S6M843AMAAHg7Xq8AXo/S6M+YjQwAAHg7RhoBr0dp9Ge8cwcAALwdpRHwepRGf1VRIZWXW50CAADg6EpLpcpKq1MAOApKo7/i0FQAAOArODoK8GqURn9FaQQAAL6C0gh4NUqjvyopsToBAABAw5SWWp0AwFFQGv0VI40AAMBXUBoBr0Zp9FeURgAA4CsojYBXozT6K558AQCAr+B1C+DVKI3+iidfAADgK3jdAng1SqO/qqiwOgEAAEDDlJVZnQDAUVAa/RVPvgAAwFcw0gh4NUqjvyovtzoBAABAw1AaAa9GafRXjDQCAABfQWkEvBql0V8x0ggAAHxFRYXkdFqdAkA9KI3+qKJCMsbqFAAAAA3HG96A16I0+iOedAEAgK+prLQ6AYB6UBr9EaURAAD4Gkoj4LUojf6ISXAAAICvoTQCXovS6I940gUAAL6G1y+A16I0+qOqKqsTAAAANA6lEfBalEZ/RGkEAAC+htIIeC1Koz/iOkcAAMDX8KY34LUojf6I0ggAAHwNI42A16I0+iPeqQMAAL6G0gh4LUqjP2KkEQAA+BpKI+C1KI3+iJFGAADga4yxOgGAelAa/REjjQAAwNdQGgGvRWn0R5RGAADgayiNgNeiNPojSiMAAACAFkJpBAAAgPUYaQS8VrDVAeABNpvVCQD4qY1D0hXrOKTknP2yOZnpEEALSrE6AID6MNLoj+x8WwF4RlVmuL5Pdur9jGAdSHLI2Hi+AdBCeNMb8Fr8tfdHPOkC8BDHob3av3WQDoaU6v3OWfqsb4QOtU2WEc87AJqL5xHAW1Ea/REjjQA8pE3hfm3c0lkxVQmSpKywIs3qmq3/9YlRcVySxekA+DTe9Aa8Fu3CH/GkC8CD2oVXqmDHwBq3bY84pDe679MPPduoLLqtNcEA+DhevwDeitLojxhpBOBBDnuJfl2bpmhnfK2vrY8+qBk9D2hx90RVRsS1fjgAvos3vQGvRbvwRzzpAvAgh/OQjGwq2TWw3mWWxe3Xq73ztbJrO1WFxbReOAC+i4m1AK/Fb6c/YqQRgAc5ynIlSUvWdFek8yiF0Cb93DZH0/sWaGNnh5whEa2UEAAAtCTahT+iNALwoJTCLEmS02lXVeaAYy7vtEnzkrL0ekaZdnRIkQkK83REAL6IkUbAa/Hb6Y8ojQA8qF3eHtltRpK0eFVPhZvIBt2v3O7UN45MvdmvSpkpKTL2YE/GBOBrgkKtTgCgHrQLfxTMCzEAnhPsrFRimFOSVFEZJFt2/0bdvzioUp+1z9T7GcHa384hw+gCAInSCHgx/lL7o1CedAF4VnJImfv/S1b2Vphp/CGnB0NK9WGnLH3SN1z5CckyTLcPBDZKI+C1KI3+KCTE6gQA/JxDhe7/l5aHKHh/vyavKyesWO+kZuvrPtEqim/XEvEA+CJKI+C1KI3+iJFGAB7mKD9Y4/NfV/ZViGneG1a7Igr0ZrcczesVr9KYhGatC4APojQCXovS6I8YaQTgYY7inBqfF5aEKfxg3xZZ98aoPL2enqufeySoIjK+RdYJwAcwszLgtSiN/oiRRgAelpK/u9Zty1b0V7BpuYm4VsbmanrvPC1PS1JV+FGuBwnAD9ikIN70BrwVpdEfBQdLNiaUAOA5UaUFigkxNW7LLwpX5KFeLb6tX9rs0/Q+BVrfJVnO0IZd3gOAj+HQVMCrURr9FYeoAvCw5LDyWretXDlAdtPyf1qcNumHxGzN6FuqbR0dMsEcxgb4FUoj4NUojf6KQ1QBeJjDVlzrttz8KMUWpntsmxV2p/6XnKU3Mqq0JyVFxs4bZIBf4I0gwKtRGv0VI40APMxRlV/n7WtWDZTNePYQ+ZKgSn3RPlPv9LNpX3KKjC3Io9sD4GGMNAJejdLor8J4xw6AZzlK99d5e9aBWMUVd2+VDIeCy/VRx0x9lBGqg4kOGXE+N+CTKI2AV6M0+quICKsTAPBzjkN76/3axjUDJVPvl1vc/tASvdclS1/2jVJhm3atuWkALYHSCHg1SqO/ojQC8LCEgmyF2OuuZ7ty2qhNaddWTiTtCS/UW2k5mts7XiWxia2+fQBNRGkEvBql0V9FMi09AM+yG6N24VX1fn3rukGtmKamzZF5mtljvxakt1V5VBvLcgBooCBOqwG8GaXRXzHSCKAVOIJK6/3a1r2Jii/r1Ippalsdc0Cv9Tqopd0SVRkRZ2kWAEfBSCPg1SiN/orSCKAVOMyho3591wbrRhsPtzR+v6b3ztea1GQ5Q6OsjgPgSFxyA/BqlEZ/xeGpAFqBo+zAUb++cadDceUprZTm6IxNmp+QrekZxdrcySETHG51JADVQqOtTgDgKCiN/oqRRgCtwFGUdcxlsjd7x2hjtSqb0XftsvR6vwrtap8iw2FxgPUojYBXozT6K0ojgFbgyNsj2zEucLFma0fFVia1UqKGK7NX6auUTM3KkLIdKTL2YKsjAQHKRmkEvByl0V8FB0shIVanAODnQivL1Cbs2FdFPLDNu0YbD1cQXK5POmTqw4wQHUhyyNj40wi0qpBIid87wKvxG+rPOK8RQCtwhJQdc5mVG7oopqptK6RputyQEr3fOUtf9I3UobbJMrJZHQkIDIwyAl6P0ujPonkSBuB5DlvRMZcxsqlgp/eONh5ub1ihZnXN1re9Y1Qc532H1QJ+JyzG6gQAjoHS6M9ieBIG4HmOioMNWu7XNWmKcvrOtRK3RR7SG9336ceebVQW7d2jpIBPY6QR8HqURn8WG2t1AgABwFGyr0HLGdlUtnugZ8N4wLrog5rR84AWd09UZYTvlF7AZ4TyJjfg7SiN/oyRRgCtwJG/p8HLLlndQ5FO3xxVWBa3X6/2zteqru1UFeab+wB4JUYaAa/H/OL+jNIIoBXEFR9UZKJRceWxJ46pctpVlTlA6jC/FZJ5gE1a2DZHi9pIo/Y71D0zX/aKEqtT+aTUSbdrR2ZurduvOW+0nrv1D7VuH3PVY/r+1421bj9tRIa+eOovkqR/z5ytR16fLUm69ZIJuvmPJ7uXW7R6m6556C0teu0fCg4OaqndQEvgnEbA61Ea/RmHpwJoJclhFdpWGdqgZZes6qnj2v+qUpvvli2nTZqXlKUFCXaNzUlR56xc2arKrY7lUxa/fpuqqpzuz1dv2auTr31S540fUufyHz56tcorKt2f5+YXacAf/qnzTnItv3LTbt39wqf6/MnrZIzRGTc+p1N+10f9undQZWWVrn7gTb14xx8pjN6IkUbA61Ea/Vl4uOtajRUVVicB4Occ9hJtU8NKY3llsGw5/aXkRR5O5Xnldqe+cWQqKilE47JS5MjZJ5uz8th3hJLa1BxdemjG1+rWMUmjh6TXuXzbuKgan8+avViR4aHu0rh+e5b69+ioccf1kiT1795B67dnqV/3Dnp05myNGtxDx/VNbfkdQfMER0h2Xo4C3o5zGv0dh6gCaAUOZ36jll+6oo9CTZiH0rS+oqAKfdYhU+9nBGt/uxQZLlTeKOUVlXrjy0W67Mzhstkadn3MVz6ZrwtPGaqoCNfPUb/uHbRxZ7Z2Zh3QjsxcbdyZo4xu7bVl9z5N/2yB7v/zWZ7cBTQVo4yAT+Cvmr+jNAJoBY7S2uemHU1JeYhCczM8lMY6B0NK9WGnTH3SN1z5CckyalgBCnQfz1uuvMISTZ00vEHL/7J6m1Zv2asrzjrRfVvvril64JrJOvmaJ3XKtU/pwWsnq3fXFP2/B97QI9efo28WrlHG+fdq0B/u1w91nBsJi1AaAZ/A8QD+jtIIoBU4CjKlyEGNus/SFRnKGLdSFTb/O4Q+J6xY76QWq3NyrEbuDVdUXo7VkbzaK5/M16nD+6p9UnyDl+/XvYOOz+ha4/arzx2tq88d7f58xucLFRMZrmH90tTznLu1+PXbtDsnTxfe/rK2ffovhYWGtORuoCmYBAfwCYw0+rs4rikGwPOS8vcqyGYadZ/CkjBF5PX1UCLvsDPikN7slqN5veJVGpNgdRyvtCMzV9/+sq7GqOHRFJWUadbsxbr8rBFHXW5/XqHufelzPfO3C7Vo9Tald05Wj87JGju0pyoqq7RxJ0XeKzDSCPgESqO/a9PG6gQAAkCQcSop3HnsBY+wbEU/BRn/n81yY1SeXk/P1c89ElQRGW91HK8y/dMFatcmRqef2K9By7/37VKVVVTqj6eecNTlbnzsXd140Xh1TG6jKqdTFZVV7q9VVjlrzNwKC4Ux0zvgCyiN/o7SCKCVOIJLG32fvMIIRR/q7YE03mllbK6m987T8rQkVYVzWJ7T6dT0zxbokjOG1boUxsV3T9dtz35U6z6vfDJfk0cPVEJ8/SNU//t5rTbuzNa154+RJB3XJ1Xrd2Tpq/mr9eKHPyjIblPPLsktui9oooi2VicA0ACc0+jvIiJcl94obfyLOQBoDIcpkBR1zOWOtHJlf3U9ca2ctsAZ+fmlzT4tiZdOzE1WemaB7OXFVkeyxLe/rNfOrAO67Mzah5ruzDogu73mREIbtmfpp+WbNfvZv9a7zpLScl33yCy98+CVsttd7413TG6jZ/52oS69b4bCQoI1495LFRHesEvEwIOCwjg8FfARNmNM405Cge/57DMpM9PqFAD83MLUkXqtvGmjhuNH/6C8mPUtnMg3hDjtGrOvnVKzDspWWWZ1HKD1xLSX0s+wOgWABuDw1EDAIaoAWoGjOLvJ9127eqBsJjAvT1Fhd+p/yVl6I6NKe1JSZOzM6IkAEcHkUICvoDQGgracLwDA8xz5e5p838zcWMUVd2vBNL6nJKhSX7TP1Dv9bNrXLkXG5v8TBCHARVIaAV9BaQwEjDQCaAURZUWKC236eYmb1g6UOGFCh4LL9VGnTH2UEaq8RIeMAnMEFgGASXAAn0FpDASURgCtxBFa0eT77sxuq/iy1JYL4+P2h5bo3S5Z+rJvlArbtKNPw7/Y7FI4r08AX0FpDATh4a5ZVAHAwxy2ombdf9vawS2UxH/sCS/UW2k5mts7XiWxiVbHAVpGeLxk5xBswFdQGgMF5zUCaAWOyrxm3X/r3kTFl3VqmTB+ZnNknmb22K8F6W1VHsUIDXwck+AAPoXSGCgSeHIG4HmOkn3NXsfujYNaIIn/Wh1zQK/1OqhfuyWpMjzW6jhA0zAJDuBTKI2BIpFDmgB4nuPQ3mavY8MOh+IqUlogjX9bEr9P0/sc0prUZDlDo6yOAzQOk+AAPoXSGCiSkqxOACAAtCncp7Cg5k/Zkr2Z0caGMDZpfkK2pmcUa0snh0xwuNWRgIbh8FTAp1AaA0VsrBQaanUKAH7OJqldWFWz17NmS0fFVvJmV0NV2YzmtMvS6/0qtKt9ikwQz/fwYiGRUggT9AG+hNIYKGw2DlEF0CpSgktaZD0HtzHa2Fhl9ip9lZKpWRlSdnKKjI3ZKeGFGGUEfA6lMZC0a2d1AgABwFGV3yLrWbGhi2KqmCW0KQqCy/VJx0x92C9UBxIdMjb+3MOLMAkO4HP4KxJIOK8RQCtwlOW2yHqMbCrcyWhjc+SGlOj9Lln6om+kCtomq/lnmwItgElwAJ9DaQwkjDQCaAWOwqwWW9eva9MU5YxrsfUFqr1hhXq7a7a+7R2r4jjeQITFIvkZBHwNpTGQREW5PgDAg9rl75Wthca0nMausj0DWmRdkLZFHtIb3ffpx55tVBbNaA8sEBwhhfNGEOBrKI2BhtFGAB4WUlWhhPCWOxByyap0RTqjW2x9kNZFH9SMnge0uHuiKiN4AY9WFMM1WAFfRGkMNMnJVicAEAAcIWUttq4qp11VWf1bbH34zbK4/Xq1d75Wd22nqjCKOVpBtMPqBACagNIYaFJ4hw+A5zlU2KLrW7Kyl8IN13XzCJu0oG2Opvct1MbODjm5fh48idII+CRKY6BJSJBCQqxOAcDPpVQcbNH1lVcGy57Tr0XXiZqcNmleUpZezyjTjg4OmaBQqyPB3wSFco1GwEdRGgON3S45eJcPgGc5irJbfJ1LVvRVqAlr8fWipnK7U984svRWP6NMR4qMPdjqSPAXUcmSzWZ1CgBNQGkMRO3bW50AgJ9z5O9p8XWWlIcoNDejxdeLuhUFVeizDpl6PyNYuUkOGRsvGdBMHJoK+Cz+AgQizmsE4GHRpYcUFdLyl5JfuiJDIYZD7FvTwZBSfdA5S5/1jVB+22QZMVKEJmLmVHiJ1NRUPfnkk1bHaJLt27fLZrNp+fLlkqR58+bJZrMpLy+vwetoyv5TGgNRYiLnNQLwOEdYRYuvs7AkTBF5fVp8vTi2rLAivdM1W7P7xKgonss3oZHswVJU6/7c7Nu3T3/+85/VuXNnhYWFyeFwaMKECZo/f36r5vBnr732muLj462O4TZmzBjdcMMNx1xu8eLFuuqqq5q9LZvNJpvNpvDwcPXp00fPP/98s9bpzSiNgYjzGgG0Aoe92CPrXb6yn4JMkEfWjWPbEXFIb3bL0fe92qgshklN0EDRDqmVD3E+55xztGzZMs2YMUMbN27Up59+qjFjxig3N7dVc8D7JCUlKTIystnrufLKK5WZmam1a9fq/PPP17XXXqu33367SesqLy9vdh5PojQGKg5RBeBhjsp8j6z3YEGkog/18si60XAbog5qRnquFvVIUEVkvNVx4O1iWnc+hby8PP344496+OGHNXbsWHXp0kXHH3+8brvtNp155pk1lrviiiuUlJSk2NhYjRs3TitWrKixroceekjJycmKiYnR5Zdfrn/84x8aOHCg++t1jW5NnjxZU6dOdX9eVlamW265RR06dFBUVJROOOEEzZs3z/316hG7b775Rr1791Z0dLQmTpyozMzMGut99dVX1bdvX4WFhSklJUXXXXddo/blcMOHD9ett95a47Z9+/YpJCREP/zwgyTp4MGDuvjii9WmTRtFRkbq1FNP1aZNmyS5Dou89NJLlZ+f7x5xmzZtWoP2ty42m00vv/yyzj77bEVGRqpHjx769NNPayzz/fff6/jjj3fv/z/+8Q9VVlZKkqZOnarvv/9eTz31lDvP9u3b69zWkYdnNmTbdYmMjJTD4VBaWpqmTZtW43633nqr0tPTFRkZqbS0NN11112qqPjtCJxp06Zp4MCBevnll9W1a1eFh4dLkr7++mudeOKJio+PV0JCgs444wxt2bLlmFkO99NPP2nkyJGKiIhQp06ddP3116uoqKhR6zgSpTFQMRkOAA9zlO732LpXrhwgu+FPmDdYEZur6b3ztCKtnarCY6yOA28V06FVNxcdHa3o6Gh9/PHHKisrq3e58847Tzk5Ofrqq6+0dOlSDR48WOPHj9eBAwckSe+++66mTZumBx54QEuWLFFKSkqTDkG87rrrtHDhQs2aNUsrV67Ueeedp4kTJ7oLmCQVFxfr3//+t2bOnKkffvhBO3fu1C233OL++n/+8x9de+21uuqqq7Rq1Sp9+umn6t69e4P35UhTpkzRrFmzZMxv55+/8847at++vUaOHCnJVcSWLFmiTz/9VAsXLpQxRqeddpoqKio0fPhwPfnkk4qNjVVmZqYyMzPdeRuyv3W59957df7552vlypU67bTTNGXKFHf+PXv26LTTTtNxxx2nFStW6D//+Y9eeeUV3X///ZKkp556SsOGDXOP/mVmZqpTp04N/h4dbdsNFRER4R4xjImJ0Wuvvaa1a9fqqaee0ksvvaQnnniixvKbN2/WBx98oA8//NB9jmJRUZFuuukmLVmyRHPmzJHdbtfZZ58tp9PZoAxbtmzRxIkTdc4552jlypV655139NNPP9V4g6Ep+IsbqDivEYCHpRRkHnuhJtqfH63Yoh4eWz8ab1GbHE3vU6ANXRxyhjT/sC/4kaAwKTKxVTcZHBys1157TTNmzFB8fLxGjBih22+/XStXrnQv89NPP+mXX37Re++9p6FDh6pHjx7697//rfj4eL3//vuSpCeffFKXX365Lr/8cvXs2VP333+/+vRp3HnVO3fu1PTp0/Xee+9p5MiR6tatm2655RadeOKJmj59unu5iooKvfDCCxo6dKgGDx6s6667TnPmzHF//f7779fNN9+sv/71r0pPT9dxxx3nHuFsyL4c6fzzz9fevXv1008/uW976623dNFFF8lms2nTpk369NNP9fLLL2vkyJEaMGCA3nzzTe3Zs0cff/yxQkNDFRcXJ5vNJofDIYfDoejo6Abvb12mTp2qiy66SN27d9cDDzygwsJC/fLLL5Kk559/Xp06ddKzzz6rXr16afLkybr33nv12GOPyel0Ki4uTqGhoe7RP4fDoaCghp/KcLRtH0tVVZXeeOMNrVy5UuPGjZMk3XnnnRo+fLhSU1M1adIk3XLLLXr33Xdr3K+8vFyvv/66Bg0apP79+0tyHVb9+9//Xt27d9fAgQP16quvatWqVVq7dm2Dsjz44IOaMmWKbrjhBvXo0UPDhw/X008/rddff12lpaUNfjyORGkMVHa71KF13/UDEFgSDmUq2N7yM6hWW7dqoGyGmTy9idMmfZ+YpRkZpdrW0SETzHU1IdesqRZcn/Gcc87R3r179emnn2rixImaN2+eBg8erNdee02StGLFChUWFiohIcE9MhkdHa1t27a5Dwdct26dTjjhhBrrHTZsWKNyrFq1SlVVVUpPT6+xne+//77GYYeRkZHq1q2b+/OUlBTl5ORIknJycrR3716NHz++zm00ZF+OlJSUpFNOOUVvvvmmJGnbtm1auHChpkyZ4t734ODgGvufkJCgnj17at26dc3e37pUFydJioqKUmxsrPsxWLdunYYNGybbYT9LI0aMUGFhoXbv3n3U9TbE0bZdn+eff17R0dGKiIjQlVdeqRtvvFF//vOfJblGbUeMGOEu03feead27txZ4/5dunRRUlJSjds2bdqkiy66SGlpaYqNjVVqaqok1bpvfVasWKHXXnutxmM/YcIEOZ1Obdu2rUHrqAtX7A1knTpJ9RzrDQDNZTdG7cKrtLfYM39q9ubGqXdJmvIiG3euBzyvwu7U/5KzFJEYrHHZKWqfvV82Z8vPpgsf0crnMx4uPDxcJ598sk4++WTddddduuKKK3TPPfdo6tSpKiwsVEpKSp3n2jVmRlC73V7jEE9JNc5dKywsVFBQkJYuXVpr5Cs6Otr9/5AjjgCz2Wzu9UZERBw1Q1P3ZcqUKbr++uv1zDPP6K233lK/fv3Ur1+/o27rWBq6v3Wp6zFo6GGZzdWUbU+ZMkV33HGHIiIilJKSIrvdNR5XXb7vvfdeTZgwQXFxcZo1a5Yee+yxGvePioqqtc5JkyapS5cueumll9S+fXs5nU5lZGQ0eKKcwsJC/b//9/90/fXX1/pa586dG7SOulAaA1kzfnAAoCEcQaXaq6O/SGiOTWsGKWnoFnHpQO9UElSpL9pnKq5dmMZlpihxX45spsrqWGhtrXw+49H06dNHH3/8sSRp8ODBysrKUnBwsHs050i9e/fWokWLdPHFF7tv+/nnn2ssk5SUVGPCmqqqKq1evVpjx46VJA0aNEhVVVXKyclxnyvYWDExMUpNTdWcOXPc6z1cQ/alLmeddZauuuoqff3113rrrbdq7Gfv3r1VWVmpRYsWafjw4ZKk3NxcbdiwwX2IbmhoqKqqav5Ot8T+1qV379764IMPZIxxjzbOnz9fMTEx6tixY715PCkuLq7GeaXVFixYoC5duuiOO+5w37Zjx45jrq/68X3ppZfcj93hhw83xODBg7V27do6czUHh6cGsqgoqW1bq1MA8GMOU+DR9e/Mbqs2Zake3QaaLz+4TB91ytTHGaHKS3DI0PIDR1isFNGm1Tebm5urcePGuc8z27Ztm9577z098sgjOuussyRJJ510koYNG6bJkydr9uzZ2r59uxYsWKA77rhDS5YskST99a9/1auvvqrp06dr48aNuueee7RmzZoa2xo3bpy++OILffHFF1q/fr3+/Oc/17jQenp6uqZMmaKLL75YH374obZt26ZffvlFDz74oL744osG79O0adP02GOP6emnn9amTZv066+/6plnnmnwvtQlKipKkydP1l133aV169bpoosucn+tR48eOuuss3TllVfqp59+0ooVK/THP/5RHTp0cD+GqampKiws1Jw5c7R//34VFxe32P4e6ZprrtGuXbv0l7/8RevXr9cnn3yie+65RzfddJN7hC81NVWLFi3S9u3btX///lYbpTxSjx49tHPnTs2aNUtbtmzR008/rY8++uiY92vTpo0SEhL04osvavPmzfruu+900003NWrbt956qxYsWKDrrrtOy5cv16ZNm/TJJ58wEQ6aidFGAB7kKG/czHNNsW3dII9vAy1jX2iJ3k3N0ld9o1QY306eO+MVXiM+1ZLNRkdH64QTTtATTzyhUaNGKSMjQ3fddZeuvPJKPfvss5Jchx9++eWXGjVqlC699FKlp6frwgsv1I4dO5ScnCxJuuCCC3TXXXfp73//u4YMGaIdO3a4z1mrdtlll+mSSy7RxRdfrNGjRystLa3WaOD06dN18cUX6+abb1bPnj01efJkLV68uFGHC15yySV68skn9fzzz6tv374644wz3LORNmRf6jNlyhStWLFCI0eOrJVn+vTpGjJkiM444wwNGzZMxhh9+eWX7kM5hw8frquvvloXXHCBkpKS9Mgjj7TY/h6pQ4cO+vLLL/XLL79owIABuvrqq3X55ZfrzjvvdC9zyy23KCgoSH369FFSUlKDzwNsaWeeeaZuvPFGXXfddRo4cKAWLFigu+6665j3s9vtmjVrlpYuXaqMjAzdeOONevTRRxu17f79++v777/Xxo0bNXLkSA0aNEh333232jfzygk2c+RB2AgsmZnSZ59ZnQKAn9qR1F0PhIzz+HbGn/Kl8kKbPxECWlf3ongN3xus8EOeuzwLLNbzTCnaYXWKFjVt2jR9/PHH7kskAIGAkcZAl5wshYZanQKAn3Ic3C1bK4wn7d7IaKMv2hyVp9d77NeC9LYqj2r9QxjhYcERUtTRR7kA+AZKY6Cz26X/O3kYAFpaWGWp4sM8Xxo3bE9RXIV/jWYEktUxB/Rar4P6tVuSKsNjrY6DlhLfxZJLbQBoeRyeCmnDBun7761OAcBPPdnzYq0rCPf4djK671JYr688vh14ls1IIw4kq9feQtnLi6yOg+boPlGKY+4EwB8w0gjX9RoBwEMcap0X/qs3d1JsZdKxF4RXMzbpp4Rsvda3WFs6OWSCPf+GAzzAHuJVl9oA0DyURkiRka5zGwHAAxyVB1ttWwe3D2y1bcGzKu1Gc9plaWZGhXa1T5EJCjn2neA9YjtK9qBjLwfAJ1Aa4ZKWZnUCAH7KUbKv1ba1Yn2qYqqYUMWflAZV6auUTM3KsCk7OUXGRhHxCW26Wp0AQAuiNMKlK0/uADzDkb+31bZlZFPhTmZS9UcFweX6pGOmPswI0YFEh4yYYMVr2eycywj4GUojXKKjOUQVgEfEF+UqPLj15lz7dW2aopzMwOmvckNL9X6XLH2REaWCNsmtcEEXNFp0ihTE5bwAf0JpxG8YbQTgIY6wylbbltPYVb5nYKttD9bYG1aot9OyNad3nErimADJq8SnWp0AQAujNOI3nNcIwEMc9pJW3d7S1T0U4Yxq1W3CGlsj8zWz+z791LOtyqPbWh0HEqUR8EOURvwmOlpq187qFAD8kMOZ36rbq6gKkjNrQKtuE9ZaG31Ar/U8oCXdE1UZEWd1nMAVmSSF8oYN4G8ojaiJQ1QBeICjLLfVt7lkZS+FmYhW3y6s9Wvcfr3aO1+ru7ZTVVi01XECD6OMgF+iNKImDlEF4AGOgsxW32Z5ZbCC9vVr9e3CC9ikBW1zNL1voTZ1dsgZwpsHrYbSCPglSiNqiomRkphQAEDLape/V3Zb689zuXRFH4WasFbfLryD0ybNTcrS6xll2tHBIcOMnp4VmShFcJ1UwB9RGlFb9+5WJwDgZ4KcVUoKd7b6dovLQhV6oG+rbxfepdzu1DeOLL3VzyjTkSJjD7Y6kn9KSLc6AQAPoTSitu7dJTs/GgBaliO4zJLt/roiQ8EmxJJtw7sUBVXosw6Zej8jWLlJDhkbf+tajC1IatvD6hQAPIRnS9QWESF16mR1CgB+JtkUWLLdguJwReb1tmTb8E4HQ0r1QecsfdY3Qvltk2VkszqS74vvIgVzKDjgryiNqFs6h5gAaFmOioOWbXv5yv4KMkGWbR/eKSusSO90zdbsPjEqjuN8/mZJ6Gl1AgAeRGlE3bp0kcLDrU4BwI+kFGVbtu2DBZGKLuBFLeq2I+KQ3ui+T9/3bKOymASr4/iekCgptqPVKQB4EKURdbPbpW7drE4BwI848vdYuv1VKwfKbvizh/ptiD6oGem5WtQjQRWR8VbH8R0J6ZKNQ3wBf8ZfT9SvJ+/KA2g5kWWFig1t/ctuVNuXF63YIibqwLGtiM3V9F55WpHWTlVhMVbH8X6JvF4A/B2lEfVLTJTatrU6BQA/4ggtt3T761YPlM0wIoIGsEmL2uRoet8CbeiSLGdIpNWJvFN0ihQWa3UKAB5GacTRMSEOgBbksBVZuv29++MUV5JmaQb4FqdN+j4xWzMySrW9Y4oMM4TWxCgjEBAojTi67t05TwFAi0muyrc6gjavHSRZd5QsfFSF3anZyZl6I6NKe1McMnau/Sl7iNSGN2GAQEBpxNFFRrpmUgWAFuAo2Wd1BO3Iaqv4Mp7X0DQlQZX6vH2W3u1n1752DhlbAF/KpW03yR5sdQoArYDSiGPr29fqBAD8hONQptURJEnb1w2yOgJ8XH5wmT7qlKWPM0KVl+CQUQAelcO1GYGAQWnEsXXoIMXHW50CgB9IKMhWaJD1x4Zu2dNO8eUdrI4BP7AvtETvpmbp677RKoxvFzhHPofHS9HJVqcA0EoojWiYPn2sTgDAD9gkJYdVWR1DkrR3I6ONaDm7wgv0Vrccze0Vr9LYRKvjeF4CE+UBgYTSiIZJT5dCOOkfQPM5gkqsjiBJWre9veIqGClBy9oclafXe+zXwvQEVUS1sTqOh9gojUCAoTSiYUJDXTOpAkAzJZtDVkdw27eF0UZ4xqqYXE3vdVC/dktSZbifXcewbTeJ61YCAYXSiIZjQhwALcBRdsDqCG6rNndWbGUAHEoIyyyJ36fpfQ5pbWqynKFRVsdpGcn9rU4AoJVRGtFwbdtKKSlWpwDg4xyFWVZHqCFvO6ON8Cxjk35KyNZrfYu1pZNDJjjc6khNF9NeiuSNFiDQUBrROEyIA6CZkvP2yOZFc0wuX5+q6Cp/PfcM3qTSbjSnXZZmZlRod/sUmSAfnCuAUUYgIFEa0Thdu0qRnMcAoOlCq8rVNsx7SqORTcW7BlodAwGkNKhKX6ZkalaGTdnJKTK2IKsjNUx4Gymus9UpAFiA0ojGsduljAyrUwDwcSmhZVZHqGHpmm6KcsZYHQMBpiC4XJ90zNSHGSE6kOiQkc3qSEfHKCMQsCiNaLw+fbj8BoBmSVah1RFqcBq7yvcOtDoGAlRuaKne75KlL/pGqaBNshcdvH2YkEipLbOoA4GK0ojGCw2Veve2OgUAH+aoOGh1hFqWrkpXhNP7Z7fc+MNGPTvpWf29/d/1/2z/T8s/Xl7j68YYfXr3p/pbyt90XcR1euKkJ5S9KbtZ65Sk2f+erVva3aJb2t2i/z32vxpf27Zom/415F+qqqxq7u4FtL3hhXo7LVtzesepJDbJ6jg1JfWV7D5yGC2AFkdpRNP06+c6VBUAmsBRnGN1hFoqqoJksr3/8LvyonJ1HNBRFz13UZ1f/+aRb/Td099pygtT9I9F/1BYVJienvC0KkormrzO3St369O7P9UVs67Q5W9frk/u/ER7Vu2RJFVVVunNq9/UlBemKCiYUtEStkbma2aPffopva3Ko9taHUeyh0hJTIQHBLJgqwPAR0VFSd27Sxs3Wp0EgA9y5O+VvHDC0iUre2uIY5nKbKVWR6lXxqkZyji17nPLjTGa8+QcnXbnaRp41kBJ0qWvX6pbkm/R8o+X67gLj2v0OiUpa32WOvbvqF7jekmSOvTvoKz1WerQr4NmPzpbPUb1UOpxqc3aL9S2NuaA1vaUBucnauCeCgWX5FsTJLGnFBxmzbYBeAWGitB0AwdanQCAj4otyVNUiPeduVVWEazgff2sjtFk+7ft16GsQ+p90m+nEETERajrCV21deHWJq+3Q78Oyt6YrQM7Dyh3R65yNuaofUZ77duyTwumL9BZ95/VEvFRj1/j9uvV3vla3bWdnGHRrbx1m9TOd38nALQMRhrRdPHxUpcu0o4dVicB4IOSQyu0tSLU6hi1LFnRVwNOWqFyW7nVURrtUNYhSVJscmyN22OTY5Wf1fRRqpTeKZr8wGQ9efKTkqTJD05WSu8UPXHSEzrnkXO05ps1+nza5woKCdL5T52v9FHpTd4W6mGTFrTN0aI2No3a71C3zHzZK0o8v902XaUwZhYGAh2lEc0zYAClEUCTOOzF2irvK43FZaEKO5Ch8oRfrY7iVUZfPVqjrx7t/nzhjIUKjwlX2rA03d3zbt22+Dbl7c7Tyxe+rH9t+5dCwphl2xOqbEZzk7I0P8GucTkp6pSVK1uVB9/gSB7guXUD8BkcnormcTik5GSrUwDwQY4qi87PaoClKzIUbHzvfdVYh2uE8VD2oRq3H8o+pDhHXIttp3B/oT6/93Nd+MyF2rZom5LTk5XcI1k9x/ZUVUWVcjZ630RH/qbc7tTXjky9nWGU5UiRsXvg5zU6RYrysllcAViC0ojmGzTI6gQAfJCjdL/VEepVUByuyHzfmy0ysWuiYh2xWj9nvfu2kkMl2rZom9KGpbXYdt698V2Nv3G82nRsI2eVU1UVv11qw1nplLPK2WLbwtEVBlfo0w6Zej8jWLlJDhlbC760S/b+2YQBtA7fexsV3qdzZykpSdq3z+okAHyIoyBT8uLLIq5Y0V/dR61Rlc27rj1YWliqfZt/e77dv22/di3fpai2UWrbua3G3zBeX97/pdr1aKfEron65K5PFN8+XgMnD3Tf5/Hxj2vQ2YM09rqxDVrn4db+b62yN2Zr6oypkqTU41KVtT5Lq79arQO7DsgWZFNyT45AaW0HQ0r1QecsOZKjNGZvtGIO5MimZkw2FdFWiuvccgEB+DRKI1rG0KHSV19ZnQKAD0k6lKXgaKNKY7M6Sp0OFEQquqCn8mPXWh2lhh1LdujxsY+7P3/vpvckScMuGaapr03VhL9PUHlRud646g0V5xWr+4nddf3X1ysk/LdzDPdv2a/C/YUNXme18pJyzbpulq5850rZ/+9avW06ttGFz1yoGZfOUHBYsC6dcalCI7zvXNVAkRVWpFldi9TFEauRe8IUmd/EN3RThkg27/zdBND6bMYY75vzHL7pk0+k7GyrUwDwIdO6XabMEu99/7JdmwJ1Hj5LxsafSvimnoVt9Ls9doUV5jb8TpGJUu/fey4UAJ/DOY1oOUOHWp0AgI9xBJdZHeGocg7GKK64h9UxgCbbEH1QM3rm6pceiaqIjG/Yndrz9xxATZRGtJwOHaSUFKtTAPAhDlNgdYRjWr9qoGxeeggt0FDLY/dreq88rUhrp6qjXXcxKplzGQHUQmlEy2K0EUAjOMoPWB3hmPbsj1dcaVerYwDNZ5MWtcnR9L4F2tAlWc6QyNrLdDiu9XMB8HqURrSslBTXiCMANICj2DfOg96yZpCaMxEl4E2cNun7xGzNyCjV9o4OmeAw1xdi2rs+AOAIlEa0PEYbATSQ4+BuqyM0yPasBMWXc8ge/EuF3anZyVl6I6NKe1NSZDiXEUA9KI1oecnJUqdOVqcA4APCK0oUH+obF4LfsW6w1REAjygJqtTK9iGyRTusjgLAS1Ea4RnHH8/1nQA0iCO03OoIDbJ5dzvFl3P4PfyPTTYdr+OtjgHAi1Ea4RkJCVIPpqkHcGwOW5HVERps76ZBVkcAWlwP9VBbtbU6BgAvRmmE5wwdKgUFWZ0CgJdzVOZZHaHB1m1rr7iKZKtjAC0mSEEaKs5lBHB0lEZ4TnS01K+f1SkAeDlHyT6rIzTK/q2MNsJ/9FVfRSva6hgAvBylEZ41cKAUHm51CgBezHFor9URGmXlps6KrUqwOgbQbBGK0GAxwROAY6M0wrNCQ7kEB4CjalO4X+FBvnURxPztjDbC9w3VUIUq1OoYAHwApRGe16uX1KaN1SkAeLHk8EqrIzTKsnVdFV0Vb3UMoMkSlahe6mV1DAA+gtIIz7PbpWHDrE4BwIs57CVWR2gUI5tKdg20OgbQZMM1XDZxaSwADUNpROvo2FHq1MnqFAC8lMOZb3WERluytrsinTFWxwAarZu6ySGH1TEA+BBKI1rPsGGuUUcAOIKjLNfqCI3mdNpVuXeA1TGARglWsE7QCVbHAOBjeAWP1hMfL/Xvb3UKAF7IUZhtdYQmWbK6pyJMpNUxgAYboAFcYgNAo1Ea0boGD5ZiOJwLQE3t8vbIbvOtGVQlqaIySCabN8PgG6IVrQFidBxA41Ea0bqCg6Xhw61OAcDLBDsrlRjmtDpGkyxZ0UdhhuvRwvv9Tr9TsIKtjgHAB1Ea0fq6dHF9AMBhHCFlVkdokrKKYAXv72d1DOCo2qu90pRmdQwAPorSCGsMH+4adQSA/+MwBVZHaLKlK/oqxHCRdHinIAVppEZaHQOAD6M0whoxMdKgQVanAOBFHBUHrY7QZEWloQo/2NfqGECdBmuw4hRndQwAPozSCOsMGOCaURUAJDmKc6yO0CzLVvRTsOEICniXtmrL5DcAmo3SCOvY7dKJJ1qdAoCXcOTvsTpCs+QXhSsyv7fVMQA3m2wapVGy83IPQDPxLAJrtW8vpadbnQKAF4gqLVBMiO9dduNwK1YMUJAJsjoGIEnqq75qp3ZWxwDgByiNsN6wYVIkF8cGICWHlVsdoVkOFEQqupA3wmC9KEXpOB1ndQwAfoLSCOuFhUkjmdUNgOSwFVsdodnWrBwom7FZHQMB7kSdqBCFWB0DgJ+gNMI7dOkide9udQoAFkupyrc6QrNlH4xRXDHPZ7BOmtLURVwPGUDLoTTCewwfLkVEWJ0CgIUcpfusjtAi1q8axGgjLBGmMA3XcKtjAPAzlEZ4j/BwDlMFApzjUGaT7rf8vYf04iSbFrx0Q73LfHbbGL04yVbr46t7T3cvs+LDf+v1P7bT639sp5UfPVbj/jkbFunDG4bIWVV5zDx79scrvrRrk/YFaI4RGqFIMU8AgJbFBaXgXVJTpW7dpC1brE4CwAJtC7IVEmtU4Wz4KF3OxsVa9/V/1Ta1/1GXO/n2D+Ws/G2indJDufrg+gFKG3GeJCl320otefNuTbz7c0lGX993hjoOOkVtU/vJWVWpH5+/WiOvfVH2oIb96dyydqDaDtna4P0AmitNaeouDo0G0PIYaYT3GTGCw1SBAGU3RsnhVQ1evqKkUHMfm6KRf3lJYdFtjrpseExbRbZxuD/2LP+fgsMilXaiqzTm7V6vhK791WHAOHUYMF5tU/srb/d6SdKKDx9VSt9Rapfe8Nkot2UmKr6sc4OXB5ojUpEaKY7WAeAZlEZ4n/Bw6cQTrU4BwCLJQaUNXvanF65Vp6Gnq+PAkxq9nfX/e0XdRl2okPAoSVLb1H7K37NRhTk7VZCzQ/l7NqpNlwwdytyijd9O19A/3t/obexYP6jR9wGaYrRGK0xhVscA4KcojfBOXbsymyoQoBzmUIOW2/zDLO3f8quOv+TBRm8jZ+MvOrhjtXqdcoX7tjadeuu4ix/QF3efrC/vPkXHX/Kg2nTqrR+f+386Yeoj2r3sG713bYY++OsgZa7+oWEZdyUrvrx9o/MBjdFHfdRJnayOAcCPcU4jvNeJJ0rZ2VJBgdVJALQiR9kBSUcvWoX7dmnhS3/Vaff9T8Gh4Y3exvrZr6htaj+1Sz++xu19Tr1afU692v35xjkzFBIRo3a9hundP/fU2Y8vVtH+3Zrz6IW66OVtCgo59shO5qZBiui7t9EZgYaIU5x+p99ZHQOAn2OkEd4rNFQaN06yMW09EEhSirKOucz+zUtVkpejD28YrJfOCtZLZwUrc/X3Wv3Z03rprGA5q+o/L7KitEhbfpylnidfftRtlObv19K379Xw//eMcjYuUlz7dMW176H2/cfKWVmh/D0bG7Q/a7d1UFxluwYtCzSGTTaN1VgFMwYAwMN4loF3S06WhgyRliyxOgmAVpJ8cLdsyUZG9b9h1H7AeJ377Koat33/5KWK69hLA8+9VfagoHrvu/Wn9+SsKFOPMX88ao4FL9+ofmfdqOjEjtq3abGcVRXurzmrKuV0NnzCnv1bBykk/ZsGLw80xCANUjvxhgQAz6M0wvsNGiTt2SNlNu36bQB8S2hVudqGGeWW1V8aQyNj1LZLRo3bgsOjFB6b4L597uMXKyqhQ61zHjf87xV1+d1khccm1Lv+3cv+p/y9GzX2xhmSpKQexylv93rtXPKVivbvks0epPgOPRu8Tys3dtGYbgkqCMpt8H2Ao0lSkgZrsNUxAAQIDk+F97PZpLFjpTBmhQMCRXJoWbPXUbhvp4oP1HyzKW/3BmWt/Um9jnJoamVZieb/9zqNvPa/stldfyajEztqxFXP6PunLtWyd/+lsTfOUHBY4y4NVLCdmVTRMkIUonEaJzsv4wC0EpsxxlgdAmiQrVulb7+1OgWAVvBOz9/ru4JEq2O0KJuMRp32ngrteVZHgY87SScpTWlWxwAQQHiLCr4jLU3q2fDDwQD4LkfFQasjtDgjm0p2DbQ6BnxcH/WhMAJodZRG+Jbhw6W4OKtTAPAwR8k+qyN4xJI13RXpjLE6BnxUohI1TMOsjgEgAFEa4VtCQqSTT5aCmcMJ8GeO/D1WR/AIp9OuyswBVseADwpVqE7SSQpS/TMDA4CnUBrhe9q2lUaNsjoFAA+KKz6oyGD/POV+yaqeijCRVseAjxmt0YpVrNUxAAQoSiN8U/fuUt++VqcA4EHJYRXHXsgHVVQGSdn9rY4BH9JXfdVVXa2OASCAURrhu4YNk5KTrU4BwEMc9hKrI3jMkpW9FWa4jBCOLUlJ+p1+Z3UMAAGO0gjfZbdLJ50kRTTuWmkAfIPDmW91BI8pLQ9R8P5+VseAlwtVqMZrPOcxArAcpRG+LSpKGj9estmsTgKghTlK91sdwaOWrshQiAm1Oga8lE02jdd4zmME4BUojfB97dtLxx9vdQoALcxRkGV1BI8qKg1V+ME+VseAlzpBJ6iTOlkdAwAkURrhLwYMkLoySQDgT5Ly9yrI5p8zqFZbtqK/gg2XEEJNPdRD/cVkSQC8B6UR/mP0aNflOAD4hSDjVFK40+oYHpVfFK7IQ72sjgEvkqQkjdRIq2MAQA2URviP0FBpwgQmxgH8iCO41OoIHrdy5QDZDX+OIUUqUqfoFAWL0WcA3oW/UvAvMTHSKadIQcw0B/gDhymwOoLH5eZHKbYw3eoYsFiQgnSKTlGUoqyOAgC1UBrhf5KTXYeqAvB5jvIDVkdoFWtWDZTNMAt0IBupkWqndlbHAIA6URrhn7p3lwYNsjoFgGZyFOdYHaFVZB2IVVxxd6tjwCL91E/pYrQZgPeiNMJ/DR0qpaVZnQJAMzjydlsdodVsXDNQ8u/JYlGHTuqkE3SC1TEA4KgojfBfNps0ZoyUlGR1EgBNFFFerLhQ/55BtdqunDZqU8qlgwJJkpJ0kk6SnZdjALwcz1Lwb8HBrhlVo5hYAPBVjtAKqyO0mi1rOaw+UMQoRhM1USEKsToKABwTpRH+LzJSmjhRCuEPM+CLHLYiqyO0mm2ZiYov62R1DHhYuMJ1qk5VhLhEFADfQGlEYEhIcI04cikOwOc4KvOsjtCqdm1gtNGfBSlIEzRB8Yq3OgoANBilEYGjfXtp7FjXuY4AfIajZJ/VEVrVxp0OxZWnWB0DHmCTTeM1XslKtjoKADQKpRGBJS1NGjHC6hQAGsFxaK/VEVpd1mZGG/3RcA1XqlKtjgEAjUZpRODp00caPNjqFAAaqE3hPoUFBda1KNZu7ai4Si707k8GaqD6qq/VMQCgSSiNCExDh0q9e1udAkAD2CQlh1VaHaPV5W5ltNFf9FAPHafjrI4BAE1GaUTgOvFEqSvXRAN8gSOoxOoIrW7lxs6KqWprdQw0U6pSNVqjZRPn0wPwXZRGBC6bTRo3TkphwgnA2zmch6yO0OqMbCrYyWijL+ukThqv8bLzcguAj+NZDIEtKMh1KY6kJKuTADgKR1mu1REs8euaNEU546yOgSZIUYpO1skKEpd6AuD7KI1AaKh02mlSYqLVSQDUw1GYZXUESxjZVLp7oNUx0EjJStZETVSwgq2OAgAtgtIISFJYmKs4JiRYnQRAHdrl75XdFlgzqFZbsrqHIp3RVsdAAyUqUafqVIUoxOooANBiKI1AtfBw6fTTpTZtrE4C4AghVRVKCHNaHcMSTqddVZkDrI6BBmijNjpNpylUoVZHAYAWRWkEDhceLp1xhhQfb3USAEdwhJRZHcEyS1b1VLiJsDoGjiJOcTpdpytc4VZHAYAWR2kEjhQR4SqOcUw+AXgThwqtjmCZ8spg2XL6Wx0D9YhRjE7X6YpUpNVRAMAjKI1AXSIjXcUxNtbqJAD+j6P8oNURLLVkRR+FmTCrY+AIMYrRJE1StDjvFID/ojQC9YmKchXHmBirkwCQ5CjOsTqCpUrLQxSS28/qGDhMnOJ0ps6kMALwe5RG4Giio6VJkzhUFfACjvw9Vkew3NIVfRVimJXTG8QrXpM0SVGKsjoKAHgcpRE4luri2Lat1UmAgBZdekhRIYF52Y1qhSVhisjra3WMgNdWbTVJkziHEUDAoDQCDVF9jmNSktVJgICWElZhdQTLLVveT8GGi8ZbJUlJOkNnKELMZgsgcFAagYaqvo6jw2F1EiBgOWxFVkewXF5RhKIO9bI6RkByyMFlNQAEJEoj0BihodJpp0mdOlmdBAhIjqp8qyN4hRUrB8hu+BPemjqqo07TaQpVqNVRAKDV8RcHaKzgYGnCBCktzeokQMBxlO63OoJXyM2PUmxhutUxAkZXddUETVCwOCwYQGCiNAJNYbdL48dLvThEDGhNjkOZVkfwGmtXD5TN2KyO4ff6qq9O0kkKUpDVUQDAMpRGoKlsNmnUKGnwYKuTAAEjoSBLwfbAnkG1WmZurOKKu1kdw68dr+M1QiNkE+UcQGCjNALNNXSoqzzaeFEBeJrdGLULr7I6htfYuGaQRIducXbZNVZjNVADrY4CAF6B0gi0hF69pFNPlUK46DbgaY6gUqsjeI1dOW0UX5pqdQy/EqIQTdRE9VAPq6MAgNegNAItpWNHadIk1zUdAXhMiimwOoJX2baOQ+RbSqQidabOVEd1tDoKAHgVSiPQkhITpcmTpTZtrE4C+C1HWa7VEbzK1r2Jii/jMkDNFa94naWzlKAEq6MAgNehNAItLTpaOussqX17q5MAfslRlG11BK+za8MgqyP4NIccOktnKUYxVkcBAK9EaQQ8ITRUOu00qQfnxAAtLTlvj2zM/lLDxp0OxVWkWB3DJ6UrXafrdIUpzOooAOC1KI2Ap9jt0tixrtlVAbSYsMpSxYdRGo+UvZnRxsawyabf6XcaozFcgxEAjoHSCHja4MHShAnMrAq0IEdoudURvM6aLR0VW5lkdQyfEKpQTdRE9Vd/q6N4BZvNpo8//liStH37dtlsNi1fvrzB9x8zZoxuuOEGj2RrrNdee03x8fFWxwD8DqURaA1durgmyImLszoJ4BccKrI6glc6uI3RxmOJU5wma7I6ybsmD5o6dapsNptsNptCQ0PVvXt33XfffaqsrLQ6mleYN2+ebDab8vLy/n979x5e053vcfy9E0l27hfCToiE5kIQdohLU0JoXU4MotWLGlpHOy5Dx+BUO1XpoWc6h2m1pzWKYkw72nN6YZxO6dVoShV1T91GUIIKShIikn3+WCe7NgmRJlYun9fz/B7W2mut33et5ZF89+92w+Puv/9+9u3b97PrW7hwIe3bt8fPz4+goCDsdjv/8R//8bOvKz+5+ssKqfkamB2ASL0RHGwkjp99BkePmh2NSK1mu3IWNMvldbbvjSSlZQgX3M+YHUqNFEEEvemNJ55mh1Kmfv36sWTJEgoLC/nwww8ZP348Hh4eTJ8+/ZavVVxcjMViwc2tfrUPeHt74+3t/bOu8cYbb/DEE0/w8ssvk5KSQmFhITt27GDXrl1VFKVI7VO//icRMZuXF/TrB+3bmx2JSK0WdvEHs0OokRxYyDvSwewwaqQEEuhHvxqbMAJ4eXlhs9mIjIxk7Nix9OnTh1WrVgHwxz/+kXbt2uHr60tERATjxo0jLy/PeW5pt8xVq1YRHx+Pl5cXR44c4ZtvvuHuu++mUaNGBAYGkpKSwtatW28prl27dtG/f3/8/Pxo0qQJI0aM4PTp0xU+f+bMmXTo0IHly5cTFRVFYGAgDzzwABcu/LTmamFhIRMnTqRx48ZYrVbuuusuvvnmG8DoMturVy8AgoODsVgsjBo1qsy6ru2eWpG6r7Vq1SqGDRvG6NGjiY6Opk2bNjz44IPMnj3b5bhFixbRunVrrFYrrVq14rXXXnP5fNOmTdjtdqxWK506deL999936fpbVlfaDz74AIvF4rJv5cqVJCYmYrVaadmyJRkZGS4t0BaLhUWLFjFkyBB8fHyIiYlx/rsptXv3btLS0ggICMDf35/u3btz8ODBCt/L1V5//XXCw8MpKSlx2T9o0CAeffRR5/b8+fO544478PT0JC4ujuXLlzs/i4qKAmDIkCFYLBbndkXuV8yhpFHkdrNYoEsXSE0Fd02+IFIZtnPHzA6hxtqy+w58S9QVvpQ77vSkJ13pigXLzU+oQby9vbl82Ri/6+bmxssvv8zu3btZtmwZn332GdOmTXM5vqCggBdeeIFFixaxe/duGjduzIULFxg5ciRffvklGzduJCYmhgEDBtwwabrauXPnSE1NxW63s3nzZj766CNOnjzJsGHDbuleDh48yAcffMDq1atZvXo169at4/e//73z82nTpvHuu++ybNkytm7dSnR0NH379uXMmTNERETw7rvvArB3715ycnKYN29eldV9LZvNxsaNGzl8+HC5x7z55pvMmDGD2bNnk5WVxfPPP88zzzzDsmXLAMjLyyMtLY34+Hi2bNnCzJkzmTJlSoVjLrV+/Xp++ctfMmnSJPbs2cOCBQtYunTpdQlsRkYGw4YNY8eOHQwYMIDhw4dz5ozR4+DYsWP06NEDLy8vPvvsM7Zs2cKjjz7qTMRudi/Xuu+++8jNzeXzzz937jtz5gwfffQRw4cPB+D9999n0qRJ/Pa3v2XXrl08/vjjPPLII85zSr8QWLJkCTk5Oc7tit6v3H5KGkXMEh1trOfo52d2JCK1TmDBGbwbaAbVsjiwUHhMvRkA/PFnEIOIJdbsUG6Jw+Hgk08+Yc2aNaSmpgLwxBNP0KtXL6KiokhNTWXWrFm88847LucVFRXx2muvceeddxIXF4ePjw+pqak8/PDDtGrVitatW/P6669TUFDAunXrKhTLf/3Xf2G323n++edp1aoVdrudN954g88///yWxg6WlJSwdOlS2rZtS/fu3RkxYgSffvopAPn5+cyfP5///M//pH///sTHx7Nw4UK8vb1ZvHgx7u7uhISEANC4cWNsNhuBtzBHwI3qLsuzzz5LUFAQUVFRxMXFMWrUKN555x2XlrVnn32WuXPnkp6eTosWLUhPT+c3v/kNCxYsAOCtt96ipKSExYsX06ZNG9LS0pg6dWqFYy6VkZHBk08+yciRI2nZsiV33303//7v/+6sp9SoUaN48MEHiY6O5vnnnycvL49NmzYB8OqrrxIYGMiKFSvo1KkTsbGxPPLII8TFxVXoXq4VHBxM//79eeutt5z7/ud//odGjRo5W4TnzJnDqFGjGDduHLGxsUyePJn09HTmzJkDQGioMWlXUFAQNpvNuV3R+5XbT0mjiJkaNYL0dGje3OxIRGqdJl7qrlSezTtj8Smp319IRRHFUIbSiEZmh1Jhq1evxs/PD6vVSv/+/bn//vuZOXMmAJ988gm9e/emadOm+Pv7M2LECHJzcykoKHCe7+npSUKC64ywJ0+eZMyYMcTExBAYGEhAQAB5eXkcOXKkQjFt376dzz//HD8/P2dp1aoVgEv3xpuJiorC39/fuR0WFsapU6ec1ykqKiI5Odn5uYeHB507dyYrK6vCdVSm7rKEhYWxYcMGdu7cyaRJk7hy5QojR46kX79+lJSUkJ+fz8GDBxk9erTLc5k1a5bzmWRlZZGQkIDVanVet1u3brcc+/bt23nuuedc6hkzZgw5OTku7/7q9+7r60tAQIDzHrdt20b37t3xKGMW94rcS1mGDx/Ou+++S2FhIWC0Vj7wwAPOMbRZWVku7xMgOTn5pu+zovcrt58mwhExm9VqLMmxYwds2gQOtZ6IVITNvYBs1A2zLMUlbhSfSIDwr8wO5bZzw40udKEd7cwO5Zb16tWL+fPn4+npSXh4OA0aGL+mZWdnk5aWxtixY5k9ezYhISF8+eWXjB49msuXL+Pj4wMY3VmvHQ83cuRIcnNzmTdvHpGRkXh5edGtWzdnt9ebycvLY+DAgbzwwgvXfRYWFlbhe7s2YbFYLNeNiasula27bdu2tG3blnHjxvGrX/2K7t27s27dOuLj4wFjhtUuXbq4nON+C8NO3NzccFzzM7+oqMhlOy8vj4yMDNLT0687/+qE9Eb3eKOJgUrHxd7qvQwcOBCHw8H//u//kpSUxPr163nxxRfLPb6iKnq/cvspaRSpCSwWY3Icmw0++QTytZyAyM3Yis+DksZybd7RiqSwb7lkuWh2KLeNH370oQ+NaWx2KJXi6+tLdHT0dfu3bNlCSUkJc+fOdbbkXNs1tTyZmZm89tprDBgwAICjR4/e0iQ2iYmJvPvuu0RFRTmT2KpWOllKZmYmkZGRgJE8ffPNN871Hz09jQmMiouLqyWGmylNFPPz82nSpAnh4eH885//dI7hu1br1q1Zvnw5ly5dciY7GzdudDkmNDSUCxcukJ+fj6+vL8B162MmJiayd+/eMv9dVFRCQgLLli2jqKjouuSyIvdSFqvVSnp6Om+++SYHDhwgLi6OxMRE5+etW7cmMzOTkSNHOvdlZmY6nyMYie6177Mq7leqh5JGkZqkSRMYOhS++AIq2HVIpL6yFeZCDVtrrya5fKUBbqcSoMnXZodyWzSnOT3piZW61xoRHR1NUVERr7zyCgMHDiQzM5M//elPFTo3JiaG5cuX06lTJ86fP8/UqVNvaUmK8ePHs3DhQh588EGmTZtGSEgIBw4cYMWKFSxatOiWWtbK4+vry9ixY5k6dSohISE0b96cP/zhDxQUFDB69GgAIiMjsVgsrF69mgEDBuDt7Y1fNc0JMHbsWMLDw0lNTaVZs2bk5OQwa9YsQkNDnV1MMzIymDhxIoGBgfTr14/CwkI2b97M2bNnmTx5Mg899BBPP/00Y8aMYfr06WRnZzvH85Xq0qULPj4+PPXUU0ycOJGvv/6apUuXuhwzY8YM0tLSaN68Offeey9ubm5s376dXbt2MWvWrArdz4QJE3jllVd44IEHmD59OoGBgWzcuJHOnTsTFxd303spz/Dhw0lLS2P37t08/PDDLp9NnTqVYcOGYbfb6dOnD3/729947733+OSTT5zHREVF8emnn5KcnIyXlxfBwcFVcr9SPTSmUaSmKe2u2qWL0QIpImWyXcgxO4Qab/P2eDwdXmaHUa0sWOhMZ/rSt04mjADt27fnj3/8Iy+88AJt27blzTffrPBC84sXL+bs2bMkJiYyYsQI57IWFRUeHk5mZibFxcXcc889tGvXjieeeIKgoKAqXQPy97//PUOHDmXEiBEkJiZy4MAB1qxZQ3BwMABNmzZ1TpLSpEkTJkyYUGV1X6tPnz5s3LiR++67j9jYWIYOHYrVauXTTz+lYUNjfdh//dd/ZdGiRSxZsoR27dqRkpLC0qVLadGiBQB+fn787W9/Y+fOndjtdp5++unruviGhITwl7/8hQ8//JB27drx17/+1TmGtVTfvn1ZvXo1a9euJSkpia5du/Liiy86W2QromHDhnz22Wfk5eWRkpJCx44dWbhwobPV8Wb3Up7U1FRCQkLYu3cvDz30kMtngwcPZt68ecyZM4c2bdqwYMEClixZQs+ePZ3HzJ07l48//piIiAjsdnuV3a9UD4vj2s7UIlJznDyp7qoi5Sh2c2dC2KOUOPTlyo2kdN1CXqMtZodRLXzxJZVUwqj42DoRs2RnZ9OiRQu+/fZbOnToYHY4IrdELY0iNVlpd9WbfNsnUh+5lxQTar09E2nUZlu2t8XDcf2sibXdHdzBvdyrhFFE5DZQ0ihS01mtcPfd0KsX/P9EACJisDUoNDuEGi/vohfe5+JvfmAt4YUXqaTSm954Ube73oqI1BTqnipSm+TlGZPkHD9udiQiNcJ7cYNYc6GJ2WHUeEF+F4lNeYtiizkzT1aVpjSlJz3xxdfsUERE6hW1NIrUJn5+8C//At26QRXMWCdS29kunzU7hFrhXJ43fudbmR1Gpbnjzp3cyQAGKGEUETGBkkaR2sZigXbtID0dGjUyOxoRU9nyT5odQq2xY0d73By178d+IxqRTjptaYsFTXokImKG2vfTQ0QMwcEweDAkJmppDqm3bD8eMzuEWuP0j34E5MeYHUaFWbBgx85gBhNMsNnhiIjUa0oaRWozNzfo1AkGDYKQELOjEbntfArzCPDU0PyK2rPTjqUWLFESQgiDGEQSSbjpVxUREdPpf2KRuqBxY6O7aqdOGuso9Y7N87LZIdQaObkBBF28w+wwyuWOO0kkkU46jan4AvQiIlK9lDSK1BVubkZX1aFDIUzrlkn9YbPkmx1CrbJvdweogY2z4YRzL/dix67WRRGRGkb/K4vUNUFBkJYGPXpoXUepF2zFP5odQq1y5GQIwYVRZofh5IUXPehBGmkEEmh2OCIiUgYljSJ1kcUCrVrBsGHQsqXZ0YhUK9vFH8wOodY5lGU3OwQAWtKS+7iPVtTe5UBEROoDJY0idZmPD/TpA337gq/WNpO6yXb+uNkh1DoHj4USVNjMtPp98aUvfelDH3zwMS0OERGpmAZmByAit0FkJISHw7ffws6dUFxsdkQiVSbkwik8gxxcLq75s4LWJN/vs+PX7vvbWqc77rSjHXbseOBxW+sWEZHKU0ujSH3h4QGdO8N990Hz5mZHI1JlLEATL30Rcqv2Hg4jsMh22+prTnPu4z4601kJo4hILaOkUaS+CQiAfv2gf38I1KQTUjfY3C+aHUKtdOpg9Y9tDCKI/vSnH/0IIKDa6xMRkaqnpFGkvoqIMFodu3Y1WiFFajGb47zZIdRKuw5EEHAltFqu7YknXenKvdxLBBHVUoeIiNweGtMoUp+5uUFCAkRHw6ZNsG+f2RGJVIqtMBdoanYYtdLZQ3bcY9ZW6TXjiKMznfHGu0qvKyIi5lBLo4gYs6z27AmDB0NYmNnRiNwyW95Js0OotbbvjcS/OLhKrmXDxhCGkEKKEkYRkTrE4nA4HGYHISI1zJEjRsvjmTNmRyJSIUXunvy6yUgcaAbVyujU5gCOFp9V+vwQQkgiiUgiqzAqERGpKdQ9VUSu17y5MebxwAHYvBkuXDA7IpEb8ii+TEOrg9OXlDRWxtY9LbkrcjP5brc2NtQffzrRiWiisShhFxGps5Q0ikjZLBaIiYGWLSErC7ZuhUuXzI5KpFw2j0JOX1KXyMoocbhReKwDRPyjQsd7440dO/HE46aRLiIidZ6SRhG5MXd3aNsW4uJgxw6jFBWZHZXIdZqQxy6No6u0zTtj6dZ0Cxfd8ss9xgMP2tOedrTTWosiIvWIkkYRqRgPD+jYEeLjYds2o/XxyhWzoxJxshWdBapn+Yj6oLjEDceJ9hD+1XWfueNOG9rQgQ5YsZoQnYiImEkT4YhI5RQUGK2Oe/YoeZQaYZ8tnrlud5kdRq3m2eAKnfr+lULLRQAa0IB44kkgAR98TI5ORETMopZGEakcHx/o2hXat/8peVS3VTFR2I/HoGpWjqi3Ll9pgPsP7fBo/C1taEMCCWpZFBERtTSKSBW5dAl274Zdu6Cw0OxopJ6aHDmG/CLN4llZvh5wT0wRvVqW4IWX2eGIiEgNoZZGEakaVqsx5jEhwWh13LEDLl40OyqpZ2yeRRws8jQ7jFonyAv63AHdm4O1gSa4ERERV0oaRaRqeXgYXVbbtoX9+2HnTjh71uyopJ6wuRVwECWNFRXmB31aQtdm0EArZ4iISDmUNIpI9XB3h1atjPL990byePSo2VFJHdek+EcgyOwwajQL0CYUUltAfKixJKuIiMiNKGkUkerXrJlRzp0zxjzu26cZV6Va2C6dBiLNDqNG8nI3WhRTW4DNz+xoRESkNtFEOCJy+126BN99Z0yck1/+QuIit+pkYDgzfNPMDqNGCbZCryi4qzn4queuiIhUgpJGETFPSQn885+QlQU5OWZHI3VAicWNX4eP5opDfS5jQqBnFNht4K7xiiIi8jOoe6qImMfNDaKjjfLjj0br4759mnVVKs3NUUJjazHHL9bPH2/+nkYX1LuaqwuqiIhUHbU0ikjNUlIC2dlGAvn992ZHI7XQgriH2Hqh/mRMFqB1KNwVAR3UqigiItWgfn4VKyI1l5sbtGxplAsXjORx714oKDA7MqklmjguAHU/aQyywp0RkBwBjXzMjkZEROoytTSKSM1XUmIs17F/Pxw5oplX5YY2RiWz5HIbs8OoFh5ukNDE6ILatjG4aeimiIjcBmppFJGaz80NIiONUlRkdF89cMDovqrvveQatvyT4FF3kkY3C7RuBJ2bGt1PrfrJLSIit5l+9IhI7eLhATExRrl40Zh99cABOHnS7MikhrCdOwahZkfx87UMhs7h0DEcArzMjkZEROozJY0iUnt5e0ObNkY5fx4OHjQSyLNnzY5MTGQtukiQZwnnLte+GWHC/SEp3GhV1DhFERGpKZQ0ikjdEBAAdrtRzp83urBmZxstkOrCWu/YPC9z7rLV7DBuygJEBRlrKdrDoLGv2RGJiIhcT0mjiNQ9AQGQkGCUixeNyXOys40xkMXFZkcnt4HNks931MyksYEbxDWE9k2gvc2YBVVERKQmU9IoInWbtzfExRnlyhUjcczONhLJS5fMjk6qie3KOaCh2WE4+XlC21AjSYwP1WQ2IiJSu+jHlojUHw0aQFSUURwOOH3aSCKPHYMTJ4ylPaROsF08BdxhWv0N3OCOYCNBjA+FiACwaHkMERGppZQ0ikj9ZLFAaKhR7HajFTInx0ggv/8ezpwxO0L5GWw/HofA21tnuL+xNEZ8KMQ2BE/321u/iIhIdVHSKCICRitkRIRRAAoKjATy2DEjmbxwwdz45JYE5+diDXFwqbj6mvca+8AdIcb4xNahGpsoIiJ1l5JGEZGy+Pj8tB4kGEnkiRPGbKwnTkBurrqz1nBNrFc4nO9RJddyt0BEoNHlNDrEKFo7UURE6gsljSIiFeHjAy1bGgWM7qw//PBTInnyJBQWmhujuLC5XeQwlUsafTyMpTCiQyA6GFoEq7upiIjUX0oaRUQqo0EDCAszChgT65w/b0yuk5trlNOnjSU/xBS2kh+BgJseF+AFzQOMlsTm/18a+VR/fCIiIrWFkkYRkapgsUBgoFHuuGrWzoIC1yQyN9dILh0O82KtJ2yFuUCEc9sCNPSBZv4/JYfNAyFQYxFFRERuyOJw6DcXEZHbqqgIzp27vpw/D8XFpoZWJ7i7Q2AgZ2wtWB/akTA/CPODJn7qYioiIlIZShpFRGoKhwPy8+HHH38qFy5AXp6xX11dDRYLeHuDn99Pxd//p5ZePz8tiigiIlKFlDSKiNQWxcVG8lhaSpPJ0r9fvGhMxnPlitmRVp6Hh5EQWq1G8fFxTQ5Li5ub2ZGKiIjUG0oaRUTqmuJiuHTJSCDL+vPyZSOxvHLFOPbav1+9r6Tkp1a7q1vvytrXoEHZxcPj+u3SpLC0lCaKSgZFRERqHCWNIiIiIiIiUi59pSsiIiIiIiLlUtIoIiIiIiIi5VLSKCIiIiIiIuVS0igiIiIiIiLlUtIoIiIiIiIi5VLSKCIiIiIiIuVS0igiIiI1ysyZM+nQoYPZYVSpqKgoXnrpJbPDuKm6+OxF5OfTOo0iIiI12KhRozh37hwffPBBhc+xWCy8//77DB48uNriqiplxZqXl0dhYSENGzY0L7AK6tmzJx06dLhpQvjDDz/g6+uLj4/Pz6pr3bp1zu3GjRvTo0cP5syZQ2RkZKWve7Xa9OxF5PZRS6OIiIiUqaioyJR6/fz86lzSEhoa+rMSxlJjxowhJyeH48ePs3LlSo4ePcrDDz9cBREa6uKzF5GfT0mjiIhILdKzZ08mTpzItGnTCAkJwWazMXPmTOfnUVFRAAwZMgSLxeLcBli5ciWJiYlYrVZatmxJRkYGV65ccX5usViYP38+v/jFL/D19WX27NmcPXuW4cOHExoaire3NzExMSxZssR5ztGjRxk2bBhBQUGEhIQwaNAgsrOzXWJ+4403aNOmDV5eXoSFhTFhwoQbxnptF8mSkhKee+45mjVrhpeXFx06dOCjjz5yfp6dnY3FYuG9996jV69e+Pj40L59ezZs2HDDZ2mxWFi0aBFDhgzBx8eHmJgYVq1a5XLMunXr6Ny5szP2J5980vnMRo0axbp165g3bx4WiwWLxXLdvV/9Xq5ujaxI3WXx8fHBZrMRFhZG165dmTBhAlu3bnV+XlxczOjRo2nRogXe3t7ExcUxb948l2t88cUXdO7cGV9fX4KCgkhOTubw4cNA2d1Ty3t/IlJ/KGkUERGpZZYtW4avry9ff/01f/jDH3juuef4+OOPAfjmm28AWLJkCTk5Oc7t9evX88tf/pJJkyaxZ88eFixYwNKlS5k9e7bLtWfOnMmQIUPYuXMnjz76KM888wx79uzh73//O1lZWcyfP59GjRoBRktk37598ff3Z/369WRmZuLn50e/fv24fPkyAPPnz2f8+PE89thj7Ny5k1WrVhEdHX3DWK81b9485s6dy5w5c9ixYwd9+/blF7/4Bfv373c57umnn2bKlCls27aN2NhYHnzwQZekuCwZGRkMGzaMHTt2MGDAAIYPH86ZM2cAOHbsGAMGDCApKYnt27czf/58Fi9ezKxZs5xxdevWzdn6l5OTQ0RERAXe4M3rrogzZ87wzjvv0KVLF+e+kpISmjVrxn//93+zZ88eZsyYwVNPPcU777wDwJUrVxg8eDApKSns2LGDDRs28Nhjj2GxWMqs40bvT0TqEYeIiIjUWCNHjnQMGjTIuZ2SkuK46667XI5JSkpy/Nu//ZtzG3C8//77Lsf07t3b8fzzz7vsW758uSMsLMzlvCeeeMLlmIEDBzoeeeSRMmNbvny5Iy4uzlFSUuLcV1hY6PD29nasWbPG4XA4HOHh4Y6nn3663PsrK9Znn33W0b59e+d2eHi4Y/bs2S7HJCUlOcaNG+dwOByOQ4cOOQDHokWLnJ/v3r3bATiysrJuWPfvfvc753ZeXp4DcPz97393OBwOx1NPPXXd/b366qsOPz8/R3FxscPhMN7HpEmTyq2jVGRkpOPFF1+scN1lSUlJcXh4eDh8fX0dPj4+DsARGxvrOHTo0A3rHj9+vGPo0KEOh8PhyM3NdQCOL774osxjy3r2N3p/IlI/qKVRRESklklISHDZDgsL49SpUzc8Z/v27Tz33HP4+fk5S2kLWUFBgfO4Tp06uZw3duxYVqxYQYcOHZg2bRpfffWVyzUPHDiAv7+/85ohISFcunSJgwcPcurUKY4fP07v3r0rfa/nz5/n+PHjJCcnu+xPTk4mKyvLZd/VzyUsLAzgps/l6nN8fX0JCAhwnpOVlUW3bt1cWuGSk5PJy8vj+++/r9wNVbDu8gwfPpxt27axfft2vvzyS6Kjo7nnnnu4cOGC85hXX32Vjh07Ehoaip+fH6+//jpHjhwBICQkhFGjRtG3b18GDhzIvHnzyMnJKbOuqnh/IlI3KGkUERGpZTw8PFy2LRYLJSUlNzwnLy+PjIwMtm3b5iw7d+5k//79WK1W53G+vr4u5/Xv35/Dhw/zm9/8xplATJkyxXnNjh07ulxz27Zt7Nu3j4ceeghvb+8quuOKufq5lCZ6N3sulXmWVaUydQcGBhIdHU10dDTJycksXryY/fv38/bbbwOwYsUKpkyZwujRo1m7di3btm3jkUcecXYXBqM78IYNG7jzzjt5++23iY2NZePGjdfVdbvfn4jUXEoaRURE6hgPDw+Ki4td9iUmJrJ3715nwnF1cXO78a8DoaGhjBw5kr/85S+89NJLvP76685r7t+/n8aNG193zcDAQPz9/YmKiuLTTz+9pVivFhAQQHh4OJmZmS77MzMziY+Pv9mj+Flat27Nhg0bcFy1OllmZib+/v40a9YMAE9PzxvGX93c3d0BuHjxojO+O++8k3HjxmG324mOjubgwYPXnWe325k+fTpfffUVbdu25a233rrumIq8PxGpH5Q0ioiI1DGlv+ifOHGCs2fPAjBjxgz+/Oc/k5GRwe7du8nKymLFihX87ne/u+G1ZsyYwcqVKzlw4AC7d+9m9erVtG7dGjC6SjZq1IhBgwaxfv16Dh06xBdffMHEiROd3TdnzpzJ3Llzefnll9m/fz9bt27llVdeuWGs15o6dSovvPACb7/9Nnv37uXJJ59k27ZtTJo0qSoeV7nGjRvH0aNH+fWvf813333HypUrefbZZ5k8ebIz0Y6KiuLrr78mOzub06dPV3srZUFBASdOnODEiRNs376dsWPHYrVaueeeewCIiYlh8+bNrFmzhn379vHMM8+4TDB06NAhpk+fzoYNGzh8+DBr165l//79znd6rZu9PxGpH5Q0ioiI1DFz587l448/JiIiArvdDkDfvn1ZvXo1a9euJSkpia5du/Liiy/edFF4T09Ppk+fTkJCAj169MDd3Z0VK1YAxvIP//jHP2jevDnp6em0bt2a0aNHc+nSJQICAgAYOXIkL730Eq+99hpt2rQhLS3NZdbTsmK91sSJE5k8eTK//e1vadeuHR999BGrVq0iJiamKh5XuZo2bcqHH37Ipk2baN++Pb/61a8YPXq0S6I9ZcoU3N3diY+PJzQ01Dl2sLosXLiQsLAwwsLC6NWrF6dPn+bDDz8kLi4OgMcff5z09HTuv/9+unTpQm5uLuPGjXOe7+Pjw3fffcfQoUOJjY3lscceY/z48Tz++ONl1nez9yci9YPFcXWfCxEREREREZGrqKVRREREREREyqWkUURERERERMqlpFFERERERETKpaRRREREREREyqWkUURERERERMqlpFFERERERETKpaRRREREREREyqWkUURERERERMqlpFFERERERETKpaRRREREREREyqWkUURERERERMqlpFFERERERETKpaRRREREREREyqWkUURERERERMqlpFFERERERETKpaRRREREREREyqWkUURERERERMqlpFFERERERETKpaRRREREREREyvV/OBDLljf2upwAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 1000x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import json\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 文件路径\n",
    "basic_path=\"/home/tianqiu/tts_schedule/batch_infer/results/mathhard/Qwen_Qwen2.5-7B-Instruct/Majority/output/acc4_new.jsonl\"\n",
    "parallel_path=\"/home/tianqiu/tts_schedule/batch_infer/results/mathhard/Qwen_Qwen2.5-7B-Instruct/Majority/output/acc8.jsonl\"\n",
    "sequence_vote_path=\"/home/tianqiu/tts_schedule/batch_infer/results/mathhard/Qwen_Qwen2.5-7B-Instruct/Sequence_vote/output_data/acc4_new.jsonl\"\n",
    "\n",
    "# 加载数据\n",
    "with open(basic_path, 'r') as f:\n",
    "    basic_data = json.load(f)\n",
    "\n",
    "with open(parallel_path, 'r') as f:\n",
    "    parallel_data = json.load(f)\n",
    "\n",
    "with open(sequence_vote_path, 'r') as f:\n",
    "    sequence_vote_data = json.load(f)\n",
    "\n",
    "# 获取正确索引\n",
    "correct_indices_basic = basic_data['correct_indices']\n",
    "correct_indices_parallel = parallel_data['correct_indices']\n",
    "correct_indices_sequence_vote = sequence_vote_data['correct_indices']\n",
    "\n",
    "# 计算parallel和sequence vote的交集\n",
    "intersection = set(correct_indices_parallel) & set(correct_indices_sequence_vote)\n",
    "\n",
    "# 计算basic在intersection中的部分\n",
    "basic_in_intersection = set(correct_indices_basic) & intersection\n",
    "intersection_not_basic = intersection - set(correct_indices_basic)\n",
    "\n",
    "# 打印统计信息\n",
    "print(f\"Intersection: {len(intersection)}\")\n",
    "print(f\"Parallel not in Sequence vote: {len(correct_indices_parallel) - len(intersection)}\")\n",
    "print(f\"Sequence vote not in Parallel: {len(correct_indices_sequence_vote) - len(intersection)}\")\n",
    "print(f\"Basic in intersection: {len(basic_in_intersection)}\")\n",
    "print(f\"Intersection not in basic: {len(intersection_not_basic)}\")\n",
    "\n",
    "# 绘制饼图 - 将intersection分成两部分：basic在intersection中的部分，和intersection中不在basic中的部分\n",
    "plt.figure(figsize=(10, 8))\n",
    "plt.pie([len(basic_in_intersection), len(intersection_not_basic), \n",
    "         len(correct_indices_parallel) - len(intersection), \n",
    "         len(correct_indices_sequence_vote) - len(intersection)], \n",
    "        labels=['Basic in Intersection', 'Intersection not in Basic', \n",
    "                'Parallel not in Sequence vote', 'Sequence vote not in Parallel'], \n",
    "        autopct='%1.1f%%',\n",
    "        colors=['#ff9999', '#66b3ff', '#99ff99', '#ffcc99'])\n",
    "plt.title('Comparison of Correct Answers Across Different Methods')\n",
    "plt.axis('equal')\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2754face",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "879\n"
     ]
    }
   ],
   "source": [
    "# 并集合有多少长度\n",
    "\n",
    "conjunction=set(correct_indices_parallel) | set(correct_indices_sequence_vote)\n",
    "\n",
    "print(len(conjunction))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "62a06708",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6638972809667674"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "879/1324"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "25db0e17",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intersection: 722\n",
      "Parallel not in Sequence vote: 89\n",
      "Sequence vote not in Parallel: 68\n",
      "Basic in intersection: 681\n",
      "Intersection not in basic: 41\n",
      "差集结果已保存到: /home/tianqiu/tts_schedule/batch_infer/results/mathhard/Qwen_Qwen2.5-7B-Instruct/diff_result.json\n"
     ]
    }
   ],
   "source": [
    "import json\n",
    "\n",
    "# 文件路径\n",
    "basic_path = \"/home/tianqiu/tts_schedule/batch_infer/results/mathhard/Qwen_Qwen2.5-7B-Instruct/Majority/output/acc4_new.json\"\n",
    "parallel_path = \"/home/tianqiu/tts_schedule/batch_infer/results/mathhard/Qwen_Qwen2.5-7B-Instruct/Majority/output/acc8.json\"\n",
    "sequence_vote_path = \"/home/tianqiu/tts_schedule/batch_infer/results/mathhard/Qwen_Qwen2.5-7B-Instruct/Sequence_vote/output_data/acc4_new.json\"\n",
    "output_diff_path = \"/home/tianqiu/tts_schedule/batch_infer/results/mathhard/Qwen_Qwen2.5-7B-Instruct/diff_result.json\"\n",
    "\n",
    "# 加载数据（每个文件中只包含一个 JSON 对象）\n",
    "with open(basic_path, 'r') as f:\n",
    "    basic_data = json.load(f)\n",
    "\n",
    "with open(parallel_path, 'r') as f:\n",
    "    parallel_data = json.load(f)\n",
    "\n",
    "with open(sequence_vote_path, 'r') as f:\n",
    "    sequence_vote_data = json.load(f)\n",
    "\n",
    "# 获取正确索引\n",
    "correct_indices_basic = basic_data['correct_indices']\n",
    "correct_indices_parallel = parallel_data['correct_indices']\n",
    "correct_indices_sequence_vote = sequence_vote_data['correct_indices']\n",
    "\n",
    "# 计算交集和差集\n",
    "intersection = set(correct_indices_parallel) & set(correct_indices_sequence_vote)\n",
    "basic_in_intersection = set(correct_indices_basic) & intersection\n",
    "intersection_not_basic = intersection - set(correct_indices_basic)\n",
    "\n",
    "# 差集保存\n",
    "sequence_vote_not_in_basic = list(set(correct_indices_sequence_vote) - set(correct_indices_basic))\n",
    "parallel_not_in_basic = list(set(correct_indices_parallel) - set(correct_indices_basic))\n",
    "\n",
    "# 保存差集到 JSON 文件\n",
    "diff_result = {\n",
    "    \"sequence_vote_not_in_basic\": sequence_vote_not_in_basic,\n",
    "    \"parallel_not_in_basic\": parallel_not_in_basic\n",
    "}\n",
    "with open(output_diff_path, 'w') as f:\n",
    "    json.dump(diff_result, f, indent=2)\n",
    "\n",
    "# 打印统计信息\n",
    "print(f\"Intersection: {len(intersection)}\")\n",
    "print(f\"Parallel not in Sequence vote: {len(correct_indices_parallel) - len(intersection)}\")\n",
    "print(f\"Sequence vote not in Parallel: {len(correct_indices_sequence_vote) - len(intersection)}\")\n",
    "print(f\"Basic in intersection: {len(basic_in_intersection)}\")\n",
    "print(f\"Intersection not in basic: {len(intersection_not_basic)}\")\n",
    "print(f\"差集结果已保存到: {output_diff_path}\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "df7de783",
   "metadata": {},
   "outputs": [],
   "source": [
    "import json\n",
    "parallel_data_path=\"E:/copy/tts_schedule_730/batch_infer/src/memory_bank/similarity_retrieval/data/mathhard_train_level.jsonl\"\n",
    "\n",
    "sequence_data_path=\"E:/copy/tts_schedule_730/batch_infer/src/memory_bank/similarity_retrieval/data/mathhard_train_sequence_vote.jsonl\"\n",
    "\n",
    "merged_data=[]\n",
    "merged_data_path=\"E:/copy/tts_schedule_730/batch_infer/src/memory_bank/llm_rank/data/mathhard_train_merged.jsonl\"\n",
    "\n",
    "with open(parallel_data_path, 'r') as f1,open(sequence_data_path, 'r') as f2:\n",
    "    for line1,line2 in zip(f1,f2):\n",
    "        data1 = json.loads(line1)\n",
    "        data2 = json.loads(line2)\n",
    "        data1[\"sequence_outputs\"]= data2[\"outputs\"]\n",
    "        merged_data.append(data1)\n",
    "        \n",
    "with open(merged_data_path, 'w') as f:\n",
    "    for data in merged_data:\n",
    "        f.write(json.dumps(data) + \"\\n\")\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "2534b325",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'problem': 'If $x$, $y$, and $z$ are positive integers such that $6xyz+30xy+21xz+2yz+105x+10y+7z=812$, find $x+y+z$.', 'solution': \"Usually when we apply Simon's Favorite Factoring Trick, we have two variables. Maybe we can find an adaptation for three variables. We notice that four of the terms on the left hand side have a factor of $z$ in them, so we can factor it out as: $$z(6xy+21x+2y+7)+30xy+105x+10y=812.$$This looks promising! Add $35$ to each side and continue factoring: \\\\begin{align*}\\nz(6xy+21x+2y+7)+30xy+105x+10y+35&=812+35 \\\\quad \\\\Rightarrow \\\\\\\\\\nz(6xy+21x+2y+7)+5(6xy+21x+2y+7)&=812+35 \\\\quad \\\\Rightarrow \\\\\\\\\\n(z+5)(6xy+21x+2y+7)&=847.\\n\\\\end{align*}Now we can proceed with the two-variable version of Simon's Favorite Factoring Trick on the remaining four-term factor: \\\\begin{align*}\\n(z+5)(3x(2y+7)+2y+7)&=847 \\\\quad \\\\Rightarrow \\\\\\\\\\n(z+5)(3x+1)(2y+7)&=847.\\n\\\\end{align*}The prime factorization of $847$ is $7\\\\cdot 11^2$. We must find $3$ numbers which multiply to $847$ and assign them to $z+5$, $3x+1$, and $2y+7$. We know none of the factors can be negative, since then we would have a negative solution for $x$, $y$ or $z$, which must be positive numbers. Similarly, no factor can be $1$ because that would give either $z=-4$, $x=0$, or $y=-3$, none of which is allowable. There are only $3$ non-one factors which multiply to $847$, so in some order our three factors must be $7$, $11$, and $11$.\\n\\nWe examine the $3x+1$ term. If this factor is equal to $11$, then $x=\\\\frac{10}{3}$, which is not an integer. So $3x+1=7$ and $x=2$. The remaining factors must equal $11$. Setting $2y+7=11$ gives $y=2$, and setting $z+5=11$ gives $z=6$. Thus $x+y+z=2+2+6=\\\\boxed{10}$.\", 'answer': \"[10, '10']\", 'outputs': [\"To solve the equation \\\\(6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = 812\\\\) for positive integers \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\), we start by factoring the left-hand side of the equation.\\n\\nFirst, observe that we can factor out common terms from the expression:\\n\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z.\\\\]\\n\\nWe can group the terms to see if there is a common factor:\\n\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = (6xyz + 30xy + 21xz) + (2yz + 105x + 10y + 7z).\\\\]\\n\\nNotice that \\\\(6xyz + 30xy + 21xz = 3x(2yz + 10y + 7z)\\\\). So the equation becomes:\\n\\n\\\\[3x(2yz + 10y + 7z) + 2yz + 105x + 10y + 7z = 812.\\\\]\\n\\nWe can rewrite this as:\\n\\n\\\\[3x(2yz + 10y + 7z) + (2yz + 105x + 10y + 7z) = 812.\\\\]\\n\\nNow, let's try some small values for \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\).\\n\\nIf \\\\(x = 1\\\\), the equation simplifies to:\\n\\n\\\\[3(2yz + 10y + 7z) + (2yz + 105 + 10y + 7z) = 812.\\\\]\\n\\nThis further simplifies to:\\n\\n\\\\[3(2yz + 10y + 7z) + 2yz + 105 + 10y + 7z = 812,\\\\]\\n\\\\[5(2yz + 10y + 7z) + 105 + 10y = 812,\\\\]\\n\\\\[5(2yz + 10y + 7z) + 10y = 707.\\\\]\\n\\nNow, let's try \\\\(y = 4\\\\):\\n\\n\\\\[5(2(4)z + 10(4) + 7z) + 10(4) = 707,\\\\]\\n\\\\[5(8z + 40 + 7z) + 40 = 707,\\\\]\\n\\\\[5(15z + 40) + 40 = 707,\\\\]\\n\\\\[75z + 200 + 40 = 707,\\\\]\\n\\\\[75z + 240 = 707,\\\\]\\n\\\\[75z = 467,\\\\]\\n\\\\[z = \\\\frac{467}{75}.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(z = 467/75\\\\) is not an integer. So, let's try another value for \\\\(y\\\\).\\n\\nIf \\\\(y = 3\\\\):\\n\\n\\\\[5(2(3)z + 10(3) + 7z) + 10(3) = 707,\\\\]\\n\\\\[5(6z + 30 + 7z) + 30 = 707,\\\\]\\n\\\\[5(13z + 30) + 30 = 707,\\\\]\\n\\\\[65z + 150 + 30 = 707,\\\\]\\n\\\\[65z + 180 = 707,\\\\]\\n\\\\[65z = 527,\\\\]\\n\\\\[z = \\\\frac{527}{65}.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(z = 527/65\\\\) is not an integer. So, let's try \\\\(y = 2\\\\):\\n\\n\\\\[5(2(2)z + 10(2) + 7z) + 10(2) = 707,\\\\]\\n\\\\[5(4z + 20 + 7z) + 20 = 707,\\\\]\\n\\\\[5(11z + 20) + 20 = 707,\\\\]\\n\\\\[55z + 100 + 20 = 707,\\\\]\\n\\\\[55z + 120 = 707,\\\\]\\n\\\\[55z = 587,\\\\]\\n\\\\[z = \\\\frac{587}{55}.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(z = 587/55\\\\) is not an integer. So, let's try \\\\(y = 1\\\\):\\n\\n\\\\[5(2(1)z + 10(1) + 7z) + 10(1) = 707,\\\\]\\n\\\\[5(2z + 10 + 7z) + 10 = 707,\\\\]\\n\\\\[5(9z + 10) + 10 = 707,\\\\]\\n\\\\[45z + 50 + 10 = 707,\\\\]\\n\\\\[45z + 60 = 707,\\\\]\\n\\\\[45z = 647,\\\\]\\n\\\\[z = \\\\frac{647}{45}.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(z = 647/45\\\\) is not an integer. So, let's try \\\\(x = 2\\\\):\\n\\nIf \\\\(x = 2\\\\), the equation simplifies to:\\n\\n\\\\[12(2yz + 10y + 7z) + 2yz + 210 + 10y + 7z = 812,\\\\]\\n\\\\[12(2yz + 10y + 7z) + 2yz + 210 + 10y + 7z = 812,\\\\]\\n\\\\[24yz + 120y + 84z + 2yz + 210 + 10y + 7z = 812,\\\\]\\n\\\\[26yz + 130y + 91z + 210 = 812,\\\\]\\n\\\\[26yz + 130y + 91z = 602.\\\\]\\n\\nNow, let's try \\\\(y = 2\\\\):\\n\\n\\\\[26(2)z + 130(2) + 91z = 602,\\\\]\\n\\\\[52z + 260 + 91z = 602,\\\\]\\n\\\\[143z + 260 = 602,\\\\]\\n\\\\[143z = 342,\\\\]\\n\\\\[z = \\\\frac{342}{143}.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(z = 342/143\\\\) is not an integer. So, let's try \\\\(y = 1\\\\):\\n\\n\\\\[26z + 130 + 91z = 602,\\\\]\\n\\\\[117z + 130 = 602,\\\\]\\n\\\\[117z = 472,\\\\]\\n\\\\[z = \\\\frac{472}{117}.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(z = 472/117\\\\) is not an integer. So, let's try \\\\(x = 3\\\\):\\n\\nIf \\\\(x = 3\\\\), the equation simplifies to:\\n\\n\\\\[18(2yz + 10y + 7z) + 2yz + 315 + 10y + 7z = 812,\\\\]\\n\\\\[36yz + 180y + 126z + 2yz + 315 + 10y + 7z = 812,\\\\]\\n\\\\[38yz + 190y + 133z + 315 = 812,\\\\]\\n\\\\[38yz + 190y + 133z = 497.\\\\]\\n\\nNow, let's try \\\\(y = 1\\\\):\\n\\n\\\\[38z + 190 + 133z = 497,\\\\]\\n\\\\[171z + 190 = 497,\\\\]\\n\\\\[171z = 307,\\\\]\\n\\\\[z = \\\\frac{307}{171}.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(z = 307/171\\\\) is not an integer. So, let's try \\\\(y = 2\\\\):\\n\\n\\\\[38(2)z + 190(2) + 133z = 497,\\\\]\\n\\\\[76z + 380 + 133z = 497,\\\\]\\n\\\\[209z + 380 = 497,\\\\]\\n\\\\[209z = 117,\\\\]\\n\\\\[z = \\\\frac{117}{209}.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer\", \"To solve the equation \\\\(6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = 812\\\\) for positive integers \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\), we will start by factoring the left-hand side of the equation.\\n\\nFirst, let's group and factor the terms:\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z.\\\\]\\n\\nWe can rewrite it as:\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = (6xyz + 30xy + 21xz) + (2yz + 105x + 10y + 7z).\\\\]\\n\\nNotice that we can factor out common terms from each group:\\n\\\\[6xyz + 30xy + 21xz = 3x(2yz + 10y + 7z),\\\\]\\n\\\\[2yz + 105x + 10y + 7z = 2yz + 10y + 7z + 105x.\\\\]\\n\\nSo the equation becomes:\\n\\\\[3x(2yz + 10y + 7z) + (2yz + 10y + 7z) + 105x = 812.\\\\]\\n\\nWe can factor out \\\\((2yz + 10y + 7z)\\\\) from the first two terms:\\n\\\\[(3x + 1)(2yz + 10y + 7z) + 105x = 812.\\\\]\\n\\nLet's denote \\\\(A = 2yz + 10y + 7z\\\\). Then the equation simplifies to:\\n\\\\[(3x + 1)A + 105x = 812.\\\\]\\n\\nRearrange to isolate \\\\(A\\\\):\\n\\\\[(3x + 1)A = 812 - 105x.\\\\]\\n\\nSince \\\\(A\\\\) must be an integer, \\\\(812 - 105x\\\\) must be divisible by \\\\(3x + 1\\\\). We will test possible values of \\\\(x\\\\) to find an integer solution for \\\\(A\\\\).\\n\\nFirst, let's try \\\\(x = 3\\\\):\\n\\\\[(3(3) + 1)A + 105(3) = 812,\\\\]\\n\\\\[10A + 315 = 812,\\\\]\\n\\\\[10A = 497,\\\\]\\n\\\\[A = 49.7.\\\\]\\nSince \\\\(A\\\\) is not an integer, \\\\(x = 3\\\\) is not a solution.\\n\\nNext, let's try \\\\(x = 4\\\\):\\n\\\\[(3(4) + 1)A + 105(4) = 812,\\\\]\\n\\\\[13A + 420 = 812,\\\\]\\n\\\\[13A = 392,\\\\]\\n\\\\[A = \\\\frac{392}{13}.\\\\]\\nSince \\\\(A\\\\) is not an integer, \\\\(x = 4\\\\) is not a solution.\\n\\nNext, let's try \\\\(x = 5\\\\):\\n\\\\[(3(5) + 1)A + 105(5) = 812,\\\\]\\n\\\\[16A + 525 = 812,\\\\]\\n\\\\[16A = 287,\\\\]\\n\\\\[A = \\\\frac{287}{16}.\\\\]\\nSince \\\\(A\\\\) is not an integer, \\\\(x = 5\\\\) is not a solution.\\n\\nNext, let's try \\\\(x = 6\\\\):\\n\\\\[(3(6) + 1)A + 105(6) = 812,\\\\]\\n\\\\[19A + 630 = 812,\\\\]\\n\\\\[19A = 182,\\\\]\\n\\\\[A = \\\\frac{182}{19}.\\\\]\\nSince \\\\(A\\\\) is not an integer, \\\\(x = 6\\\\) is not a solution.\\n\\nNext, let's try \\\\(x = 7\\\\):\\n\\\\[(3(7) + 1)A + 105(7) = 812,\\\\]\\n\\\\[22A + 735 = 812,\\\\]\\n\\\\[22A = 77,\\\\]\\n\\\\[A = \\\\frac{77}{22}.\\\\]\\nSince \\\\(A\\\\) is not an integer, \\\\(x = 7\\\\) is not a solution.\\n\\nNext, let's try \\\\(x = 8\\\\):\\n\\\\[(3(8) + 1)A + 105(8) = 812,\\\\]\\n\\\\[25A + 840 = 812,\\\\]\\n\\\\[25A = -28.\\\\]\\nSince \\\\(A\\\\) is not an integer, \\\\(x = 8\\\\) is not a solution.\\n\\nFinally, let's try \\\\(x = 2\\\\):\\n\\\\[(3(2) + 1)A + 105(2) = 812,\\\\]\\n\\\\[7A + 210 = 812,\\\\]\\n\\\\[7A = 602,\\\\]\\n\\\\[A = 86.\\\\]\\nSince \\\\(A\\\\) is an integer, \\\\(x = 2\\\\) is a solution. Now we need to find \\\\(y\\\\) and \\\\(z\\\\) such that \\\\(2yz + 10y + 7z = 86\\\\).\\n\\nRewrite the equation:\\n\\\\[2yz + 10y + 7z = 86.\\\\]\\n\\nWe will test possible values for \\\\(y\\\\) and \\\\(z\\\\):\\n\\nIf \\\\(y = 3\\\\):\\n\\\\[2(3)z + 10(3) + 7z = 86,\\\\]\\n\\\\[6z + 30 + 7z = 86,\\\\]\\n\\\\[13z + 30 = 86,\\\\]\\n\\\\[13z = 56,\\\\]\\n\\\\[z = \\\\frac{56}{13}.\\\\]\\nSince \\\\(z\\\\) is not an integer, \\\\(y = 3\\\\) is not a solution.\\n\\nIf \\\\(y = 4\\\\):\\n\\\\[2(4)z + 10(4) + 7z = 86,\\\\]\\n\\\\[8z + 40 + 7z = 86,\\\\]\\n\\\\[15z + 40 = 86,\\\\]\\n\\\\[15z = 46,\\\\]\\n\\\\[z = \\\\frac{46}{15}.\\\\]\\nSince \\\\(z\\\\) is not an integer, \\\\(y = 4\\\\) is not a solution.\\n\\nIf \\\\(y = 5\\\\):\\n\\\\[2(5)z + 10(5) + 7z = 86,\\\\]\\n\\\\[10z + 50 + 7z = 86,\\\\]\\n\\\\[17z + 50 = 86,\\\\]\\n\\\\[17z = 36,\\\\]\\n\\\\[z = \\\\frac{36}{17}.\\\\]\\nSince \\\\(z\\\\) is not an integer, \\\\(y = 5\\\\) is not a solution.\\n\\nIf \\\\(y = 6\\\\):\\n\\\\[2(6)z + 10(6) + 7z = 86,\\\\]\\n\\\\[12z + 60 + 7z = 86,\\\\]\\n\\\\[19z + 60 = 86,\\\\]\\n\\\\[19z = 26,\\\\]\\n\\\\[z = \\\\frac{26}{19}.\\\\]\\nSince \\\\(z\\\\) is not an integer, \\\\(y = 6\\\\) is not a solution.\\n\\nIf \\\\(y = 7\\\\):\\n\\\\[2(7)z + 10(7) + 7z = 86,\\\\]\\n\\\\[14z + 70 + 7z = 86,\\\\]\\n\\\\[21z + 70 = 86,\\\\]\\n\\\\[21z = 16,\\\\]\\n\\\\[z = \\\\frac{16}{21}.\\\\]\\nSince \\\\(z\\\\) is not an integer, \\\\(y = 7\\\\) is not a solution.\\n\\nIf \\\\(y = 2\\\\):\\n\\\\[2(2)z + 10(2) + 7z = 86,\\\\]\\n\\\\[4z + 20 + 7z = 86,\\\\]\\n\\\\[11z + 20 = 86,\\\\]\\n\\\\[11z = 66,\\\\]\\n\\\\[z = 6.\\\\]\\nSince \\\\(z\\\\) is an integer, \\\\(y = 2\\\\) and \\\\(z = 6\\\\) is a solution.\\n\\nThus, the solution is \\\\(x = 2\\\\), \\\\(y = 2\\\\), and \\\\(z = 6\\\\). Therefore, \\\\(x + y + z = 2 + 2 + 6 = 10\\\\).\\n\\nThe final answer is \\\\(\\\\boxed{10}\\\\).\", \"To solve the equation \\\\(6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = 812\\\\) for positive integers \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\), we will first try to simplify and factorize the given expression.\\n\\nFirst, let's rewrite the equation:\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = 812.\\\\]\\n\\nWe can group the terms in a way that might help us factorize:\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = (6xyz + 30xy + 21xz + 2yz) + (105x + 10y + 7z) = 812.\\\\]\\n\\nNotice that we can factor out common terms from the first part of the equation:\\n\\\\[6xyz + 30xy + 21xz + 2yz = xyz(6) + xy(30) + xz(21) + yz(2) = xyz(6) + xy(30) + xz(21) + yz(2).\\\\]\\n\\nHowever, a more useful approach is to look for a pattern or substitution that simplifies the equation. Let's test some small values for \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\).\\n\\nFirst, let's try \\\\(x = 1\\\\):\\n\\\\[6(1)yz + 30(1)y + 21(1)z + 2yz + 105(1) + 10y + 7z = 812,\\\\]\\n\\\\[6yz + 30y + 21z + 2yz + 105 + 10y + 7z = 812,\\\\]\\n\\\\[8yz + 40y + 28z + 105 = 812,\\\\]\\n\\\\[8yz + 40y + 28z = 707.\\\\]\\n\\nNow, let's try \\\\(y = 7\\\\):\\n\\\\[8(7)z + 40(7) + 28z = 707,\\\\]\\n\\\\[56z + 280 + 28z = 707,\\\\]\\n\\\\[84z + 280 = 707,\\\\]\\n\\\\[84z = 427,\\\\]\\n\\\\[z = \\\\frac{427}{84} \\\\approx 5.0952.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 7\\\\) does not work. Let's try \\\\(y = 5\\\\):\\n\\\\[8(5)z + 40(5) + 28z = 707,\\\\]\\n\\\\[40z + 200 + 28z = 707,\\\\]\\n\\\\[68z + 200 = 707,\\\\]\\n\\\\[68z = 507,\\\\]\\n\\\\[z = \\\\frac{507}{68} \\\\approx 7.4412.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 5\\\\) does not work. Let's try \\\\(y = 4\\\\):\\n\\\\[8(4)z + 40(4) + 28z = 707,\\\\]\\n\\\\[32z + 160 + 28z = 707,\\\\]\\n\\\\[60z + 160 = 707,\\\\]\\n\\\\[60z = 547,\\\\]\\n\\\\[z = \\\\frac{547}{60} \\\\approx 9.1167.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 4\\\\) does not work. Let's try \\\\(y = 3\\\\):\\n\\\\[8(3)z + 40(3) + 28z = 707,\\\\]\\n\\\\[24z + 120 + 28z = 707,\\\\]\\n\\\\[52z + 120 = 707,\\\\]\\n\\\\[52z = 587,\\\\]\\n\\\\[z = \\\\frac{587}{52} \\\\approx 11.2885.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 3\\\\) does not work. Let's try \\\\(y = 2\\\\):\\n\\\\[8(2)z + 40(2) + 28z = 707,\\\\]\\n\\\\[16z + 80 + 28z = 707,\\\\]\\n\\\\[44z + 80 = 707,\\\\]\\n\\\\[44z = 627,\\\\]\\n\\\\[z = \\\\frac{627}{44} \\\\approx 14.25.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 2\\\\) does not work. Let's try \\\\(y = 1\\\\):\\n\\\\[8(1)z + 40(1) + 28z = 707,\\\\]\\n\\\\[8z + 40 + 28z = 707,\\\\]\\n\\\\[36z + 40 = 707,\\\\]\\n\\\\[36z = 667,\\\\]\\n\\\\[z = \\\\frac{667}{36} \\\\approx 18.5278.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 1\\\\) does not work. Let's try \\\\(x = 2\\\\):\\n\\\\[6(2)yz + 30(2)y + 21(2)z + 2yz + 105(2) + 10y + 7z = 812,\\\\]\\n\\\\[12yz + 60y + 42z + 2yz + 210 + 10y + 7z = 812,\\\\]\\n\\\\[14yz + 70y + 49z + 210 = 812,\\\\]\\n\\\\[14yz + 70y + 49z = 602.\\\\]\\n\\nNow, let's try \\\\(y = 7\\\\):\\n\\\\[14(7)z + 70(7) + 49z = 602,\\\\]\\n\\\\[98z + 490 + 49z = 602,\\\\]\\n\\\\[147z + 490 = 602,\\\\]\\n\\\\[147z = 112,\\\\]\\n\\\\[z = \\\\frac{112}{147} \\\\approx 0.7619.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 7\\\\) does not work. Let's try \\\\(y = 6\\\\):\\n\\\\[14(6)z + 70(6) + 49z = 602,\\\\]\\n\\\\[84z + 420 + 49z = 602,\\\\]\\n\\\\[133z + 420 = 602,\\\\]\\n\\\\[133z = 182,\\\\]\\n\\\\[z = \\\\frac{182}{133} = 1.3671.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 6\\\\) does not work. Let's try \\\\(y = 5\\\\):\\n\\\\[14(5)z + 70(5) + 49z = 602,\\\\]\\n\\\\[70z + 350 + 49z = 602,\\\\]\\n\\\\[119z + 350 = 602,\\\\]\\n\\\\[119z = 252,\\\\]\\n\\\\[z = \\\\frac{252}{119} \\\\approx 2.11.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 5\\\\) does not work. Let's try \\\\(y = 4\\\\):\\n\\\\[14(4)z + 70(4) + 49z = 602,\\\\]\\n\\\\[56z + 280 + 49z = 602,\\\\]\\n\\\\[105z + 280 = 602,\\\\]\\n\\\\[105z = 322,\\\\]\\n\\\\[z = \\\\frac{322}{105} \\\\approx 3.0671.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 4\\\\) does not work. Let's try \\\\(y = 3\\\\):\\n\\\\[14(3)z + 70(3) + 49z = 602,\\\\]\\n\\\\[42z + 210 + 49z = 602,\\\\]\\n\\\\[91z + 210 = 602,\\\\]\\n\\\\[91z = 392,\\\\]\\n\\\\[z = \\\\frac{392}{91} = 4.31.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 3\\\\) does not work. Let's try \\\\(y = 2\\\\):\\n\\\\[14(2)z + 70(2) + 49z = 60\", \"To solve the equation \\\\(6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = 812\\\\) for positive integers \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\), we start by factoring the left-hand side of the equation.\\n\\nFirst, let's group the terms in a way that might help us factor them:\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = (6xyz + 30xy + 21xz) + (2yz + 105x + 10y + 7z).\\\\]\\n\\nWe can factor out common terms from each group:\\n\\\\[6xyz + 30xy + 21xz = 3x(2yz + 10y + 7z),\\\\]\\n\\\\[2yz + 105x + 10y + 7z = 2yz + 7z + 10y + 105x = z(2y + 7) + 10(y + 10.5x).\\\\]\\n\\nHowever, this approach seems complicated. Instead, let's try to find values for \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\) by testing small positive integers.\\n\\nLet's start with \\\\(x = 1\\\\):\\n\\\\[6(1)yz + 30(1)y + 21(1)z + 2yz + 105(1) + 10y + 7z = 812,\\\\]\\n\\\\[6yz + 30y + 21z + 2yz + 105 + 10y + 7z = 812,\\\\]\\n\\\\[8yz + 40y + 28z + 105 = 812,\\\\]\\n\\\\[8yz + 40y + 28z = 707.\\\\]\\nDivide the entire equation by 4:\\n\\\\[2yz + 10y + 7z = 176.5.\\\\]\\nSince \\\\(2yz + 10y + 7z\\\\) must be an integer, \\\\(x = 1\\\\) is not a solution. Let's try \\\\(x = 2\\\\):\\n\\\\[6(2)yz + 30(2)y + 21(2)z + 2yz + 105(2) + 10y + 7z = 812,\\\\]\\n\\\\[12yz + 60y + 42z + 2yz + 210 + 10y + 7z = 812,\\\\]\\n\\\\[14yz + 70y + 49z + 210 = 812,\\\\]\\n\\\\[14yz + 70y + 49z = 602.\\\\]\\nDivide the entire equation by 7:\\n\\\\[2yz + 10y + 7z = 86.\\\\]\\nNow, let's test \\\\(y = 1\\\\):\\n\\\\[2(1)z + 10(1) + 7z = 86,\\\\]\\n\\\\[2z + 10 + 7z = 86,\\\\]\\n\\\\[9z + 10 = 86,\\\\]\\n\\\\[9z = 76,\\\\]\\n\\\\[z = \\\\frac{76}{9},\\\\]\\nwhich is not an integer. Let's try \\\\(y = 2\\\\):\\n\\\\[2(2)z + 10(2) + 7z = 86,\\\\]\\n\\\\[4z + 20 + 7z = 86,\\\\]\\n\\\\[11z + 20 = 86,\\\\]\\n\\\\[11z = 66,\\\\]\\n\\\\[z = 6.\\\\]\\nSo, \\\\(x = 2\\\\), \\\\(y = 2\\\\), and \\\\(z = 6\\\\) is a solution. Let's verify:\\n\\\\[6(2)(2)(6) + 30(2)(2) + 21(2)(6) + 2(2)(6) + 105(2) + 10(2) + 7(6) = 144 + 120 + 252 + 24 + 210 + 20 + 42 = 812.\\\\]\\nThe solution is correct. Therefore, \\\\(x + y + z = 2 + 2 + 6 = 10\\\\).\\n\\nThe final answer is \\\\(\\\\boxed{10}\\\\).\", \"To solve the equation \\\\(6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = 812\\\\) for positive integers \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\), we start by factoring the left-hand side of the equation.\\n\\nFirst, observe that the equation can be rewritten as:\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = 812.\\\\]\\n\\nWe can factor out common terms to simplify the expression. Notice that each term on the left-hand side has at least one factor of \\\\(x\\\\), \\\\(y\\\\), or \\\\(z\\\\). Let's try to group the terms in a way that allows us to factor them:\\n\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = (6xyz + 30xy + 21xz) + (2yz + 105x + 10y + 7z).\\\\]\\n\\nWe can factor out \\\\(3x\\\\) from the first three terms:\\n\\\\[6xyz + 30xy + 21xz = 3x(2yz + 10y + 7z).\\\\]\\n\\nNow, let's look at the remaining terms:\\n\\\\[2yz + 105x + 10y + 7z.\\\\]\\n\\nWe can rewrite the entire equation as:\\n\\\\[3x(2yz + 10y + 7z) + 2yz + 105x + 10y + 7z = 812.\\\\]\\n\\nNotice that we can factor out \\\\(2yz + 10y + 7z\\\\) from the last three terms:\\n\\\\[2yz + 105x + 10y + 7z = (2yz + 10y + 7z) + 105x.\\\\]\\n\\nSo the equation becomes:\\n\\\\[3x(2yz + 10y + 7z) + (2yz + 10y + 7z) + 105x = 812.\\\\]\\n\\nWe can factor out \\\\(2yz + 10y + 7z\\\\) from the first two terms:\\n\\\\[(3x + 1)(2yz + 10y + 7z) + 105x = 812.\\\\]\\n\\nNow, let's test some small values for \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\). Start with \\\\(x = 2\\\\):\\n\\\\[(3 \\\\cdot 2 + 1)(2yz + 10y + 7z) + 105 \\\\cdot 2 = 812,\\\\]\\n\\\\[7(2yz + 10y + 7z) + 210 = 812,\\\\]\\n\\\\[7(2yz + 10y + 7z) = 602,\\\\]\\n\\\\[2yz + 10y + 7z = 86.\\\\]\\n\\nNow, we need to find positive integers \\\\(y\\\\) and \\\\(z\\\\) that satisfy this equation. Let's try \\\\(y = 3\\\\):\\n\\\\[2(3)z + 10(3) + 7z = 86,\\\\]\\n\\\\[6z + 30 + 7z = 86,\\\\]\\n\\\\[13z + 30 = 86,\\\\]\\n\\\\[13z = 56,\\\\]\\n\\\\[z = \\\\frac{56}{13},\\\\]\\nwhich is not an integer. So, \\\\(y = 3\\\\) does not work. Let's try \\\\(y = 4\\\\):\\n\\\\[2(4)z + 10(4) + 7z = 86,\\\\]\\n\\\\[8z + 40 + 7z = 86,\\\\]\\n\\\\[15z + 40 = 86,\\\\]\\n\\\\[15z = 46,\\\\]\\nwhich is not an integer. So, \\\\(y = 4\\\\) does not work. Let's try \\\\(y = 5\\\\):\\n\\\\[2(5)z + 10(5) + 7z = 86,\\\\]\\n\\\\[10z + 50 + 7z = 86,\\\\]\\n\\\\[17z + 50 = 86,\\\\]\\n\\\\[17z = 36,\\\\]\\nwhich is not an integer. So, \\\\(y = 5\\\\) does not work. Let's try \\\\(y = 6\\\\):\\n\\\\[2(6)z + 10(6) + 7z = 86,\\\\]\\n\\\\[12z + 60 + 7z = 86,\\\\]\\n\\\\[19z + 60 = 86,\\\\]\\n\\\\[19z = 26,\\\\]\\nwhich is not an integer. So, \\\\(y = 6\\\\) does not work. Let's try \\\\(y = 7\\\\):\\n\\\\[2(7)z + 10(7) + 7z = 86,\\\\]\\n\\\\[14z + 70 + 7z = 86,\\\\]\\n\\\\[21z + 70 = 86,\\\\]\\n\\\\[21z = 16,\\\\]\\nwhich is not an integer. So, \\\\(y = 7\\\\) does not work. Let's try \\\\(y = 2\\\\):\\n\\\\[2(2)z + 10(2) + 7z = 86,\\\\]\\n\\\\[4z + 20 + 7z = 86,\\\\]\\n\\\\[11z + 20 = 86,\\\\]\\n\\\\[11z = 66,\\\\]\\n\\\\[z = 6.\\\\]\\n\\nSo, \\\\(y = 2\\\\) and \\\\(z = 6\\\\) work. Therefore, the solution is \\\\(x = 2\\\\), \\\\(y = 2\\\\), and \\\\(z = 6\\\\). The sum \\\\(x + y + z\\\\) is:\\n\\\\[x + y + z = 2 + 2 + 6 = 10.\\\\]\\n\\nThus, the answer is \\\\(\\\\boxed{10}\\\\).\", \"To solve the equation \\\\(6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = 812\\\\) for positive integers \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\), we will start by factoring the left-hand side of the equation.\\n\\nFirst, let's group and factor the terms:\\n\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = 812.\\\\]\\n\\nWe can rewrite the equation as:\\n\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = 812.\\\\]\\n\\nNotice that we can factor out common terms from groups of terms:\\n\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = (6xy + 21x + 2y + 7)(z) + 30xy + 105x + 10y.\\\\]\\n\\nHowever, this approach seems complex, so let's try another method by testing small values for \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\).\\n\\nLet's start with \\\\(x = 1\\\\):\\n\\n\\\\[6(1)yz + 30(1)y + 21(1)z + 2yz + 105(1) + 10y + 7z = 812,\\\\]\\n\\\\[6yz + 30y + 21z + 2yz + 105 + 10y + 7z = 812,\\\\]\\n\\\\[8yz + 40y + 28z + 105 = 812,\\\\]\\n\\\\[8yz + 40y + 28z = 707.\\\\]\\n\\nNow, let's try \\\\(y = 1\\\\):\\n\\n\\\\[8(1)z + 40(1) + 28z = 707,\\\\]\\n\\\\[8z + 40 + 28z = 707,\\\\]\\n\\\\[36z + 40 = 707,\\\\]\\n\\\\[36z = 667,\\\\]\\n\\\\[z = \\\\frac{667}{36},\\\\]\\nwhich is not an integer. So, \\\\(y = 1\\\\) does not work.\\n\\nNext, let's try \\\\(y = 2\\\\):\\n\\n\\\\[8(2)z + 40(2) + 28z = 707,\\\\]\\n\\\\[16z + 80 + 28z = 707,\\\\]\\n\\\\[44z + 80 = 707,\\\\]\\n\\\\[44z = 627,\\\\]\\n\\\\[z = \\\\frac{627}{44},\\\\]\\nwhich is not an integer. So, \\\\(y = 2\\\\) does not work.\\n\\nNext, let's try \\\\(y = 3\\\\):\\n\\n\\\\[8(3)z + 40(3) + 28z = 707,\\\\]\\n\\\\[24z + 120 + 28z = 707,\\\\]\\n\\\\[52z + 120 = 707,\\\\]\\n\\\\[52z = 587,\\\\]\\n\\\\[z = \\\\frac{587}{52},\\\\]\\nwhich is not an integer. So, \\\\(y = 3\\\\) does not work.\\n\\nNext, let's try \\\\(y = 4\\\\):\\n\\n\\\\[8(4)z + 40(4) + 28z = 707,\\\\]\\n\\\\[32z + 160 + 28z = 707,\\\\]\\n\\\\[60z + 160 = 707,\\\\]\\n\\\\[60z = 547,\\\\]\\n\\\\[z = \\\\frac{547}{60},\\\\]\\nwhich is not an integer. So, \\\\(y = 4\\\\) does not work.\\n\\nNext, let's try \\\\(y = 5\\\\):\\n\\n\\\\[8(5)z + 40(5) + 28z = 707,\\\\]\\n\\\\[40z + 200 + 28z = 707,\\\\]\\n\\\\[68z + 200 = 707,\\\\]\\n\\\\[68z = 507,\\\\]\\n\\\\[z = \\\\frac{507}{68},\\\\]\\nwhich is not an integer. So, \\\\(y = 5\\\\) does not work.\\n\\nNext, let's try \\\\(y = 6\\\\):\\n\\n\\\\[8(6)z + 40(6) + 28z = 707,\\\\]\\n\\\\[48z + 240 + 28z = 707,\\\\]\\n\\\\[76z + 240 = 707,\\\\]\\n\\\\[76z = 467,\\\\]\\n\\\\[z = \\\\frac{467}{76},\\\\]\\nwhich is not an integer. So, \\\\(y = 6\\\\) does not work.\\n\\nNext, let's try \\\\(y = 7\\\\):\\n\\n\\\\[8(7)z + 40(7) + 28z = 707,\\\\]\\n\\\\[56z + 280 + 28z = 707,\\\\]\\n\\\\[84z + 280 = 707,\\\\]\\n\\\\[84z = 427,\\\\]\\n\\\\[z = \\\\frac{427}{84},\\\\]\\nwhich is not an integer. So, \\\\(y = 7\\\\) does not work.\\n\\nNext, let's try \\\\(y = 8\\\\):\\n\\n\\\\[8(8)z + 40(8) + 28z = 707,\\\\]\\n\\\\[64z + 320 + 28z = 707,\\\\]\\n\\\\[92z + 320 = 707,\\\\]\\n\\\\[92z = 387,\\\\]\\n\\\\[z = \\\\frac{387}{92},\\\\]\\nwhich is not an integer. So, \\\\(y = 8\\\\) does not work.\\n\\nNext, let's try \\\\(y = 9\\\\):\\n\\n\\\\[8(9)z + 40(9) + 28z = 707,\\\\]\\n\\\\[72z + 360 + 28z = 707,\\\\]\\n\\\\[100z + 360 = 707,\\\\]\\n\\\\[100z = 347,\\\\]\\n\\\\[z = \\\\frac{347}{100},\\\\]\\nwhich is not an integer. So, \\\\(y = 9\\\\) does not work.\\n\\nFinally, let's try \\\\(y = 10\\\\):\\n\\n\\\\[8(10)z + 40(10) + 28z = 707,\\\\]\\n\\\\[80z + 400 + 28z = 707,\\\\]\\n\\\\[108z + 400 = 707,\\\\]\\n\\\\[108z = 307,\\\\]\\n\\\\[z = \\\\frac{307}{108},\\\\]\\nwhich is not an integer. So, \\\\(y = 10\\\\) does not work.\\n\\nAfter trying several values, we find that \\\\(x = 1\\\\), \\\\(y = 7\\\\), and \\\\(z = 10\\\\) works:\\n\\n\\\\[6(1)(7)(10) + 30(1)(7) + 21(1)(10) + 2(7)(10) + 105(1) + 10(7) + 7(10) = 420 + 210 + 210 + 140 + 105 + 70 + 70 = 1025 - 213 = 812.\\\\]\\n\\nSo, \\\\(x + y + z = 1 + 7 + 10 = 18\\\\).\\n\\nThe answer is \\\\(\\\\boxed{18}\\\\).\", \"To solve the equation \\\\(6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = 812\\\\) for positive integers \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\), we will start by factoring the left-hand side of the equation.\\n\\nFirst, let's rewrite the equation:\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = 812.\\\\]\\n\\nWe can factor out common terms to simplify the expression. Notice that each term contains at least one of \\\\(x\\\\), \\\\(y\\\\), or \\\\(z\\\\). Let's group the terms in a way that might help us factor:\\n\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = (6xyz + 30xy + 21xz + 2yz) + (105x + 10y + 7z).\\\\]\\n\\nWe can factor out \\\\(xy\\\\) from the first four terms:\\n\\\\[6xyz + 30xy + 21xz + 2yz = xy(6z + 30 + 21/x + 2/z).\\\\]\\n\\nHowever, this form is not immediately helpful. Instead, let's try another grouping:\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = (6xyz + 21xz + 105x) + (30xy + 2yz + 10y) + 7z.\\\\]\\n\\nWe can factor out \\\\(3x\\\\) from the first group, \\\\(10y\\\\) from the second group, and leave the last term as it is:\\n\\\\[6xyz + 21xz + 105x = 3x(2yz + 7z + 35),\\\\]\\n\\\\[30xy + 2yz + 10y = 10y(3x + z + 1).\\\\]\\n\\nSo the equation becomes:\\n\\\\[3x(2yz + 7z + 35) + 10y(3x + z + 1) + 7z = 812.\\\\]\\n\\nNow, let's test some small values for \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\) to see if we can find a solution. Start with \\\\(x = 2\\\\):\\n\\\\[3(2)(2yz + 7z + 35) + 10y(6 + z + 1) + 7z = 812,\\\\]\\n\\\\[6(2yz + 7z + 35) + 10y(7 + z) + 7z = 812,\\\\]\\n\\\\[12yz + 42z + 210 + 70y + 10yz + 7z = 812,\\\\]\\n\\\\[22yz + 49z + 70y + 210 = 812,\\\\]\\n\\\\[22yz + 49z + 70y = 602.\\\\]\\n\\nNow, let's test \\\\(y = 3\\\\):\\n\\\\[22(3)z + 49z + 70(3) = 602,\\\\]\\n\\\\[66z + 49z + 210 = 602,\\\\]\\n\\\\[115z + 210 = 602,\\\\]\\n\\\\[115z = 392,\\\\]\\n\\\\[z = \\\\frac{392}{115}.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(z = 3\\\\) does not work. Let's try \\\\(y = 2\\\\):\\n\\\\[22(2)z + 49z + 70(2) = 602,\\\\]\\n\\\\[44z + 49z + 140 = 602,\\\\]\\n\\\\[93z + 140 = 602,\\\\]\\n\\\\[93z = 462,\\\\]\\n\\\\[z = \\\\frac{462}{93}.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(z = 2\\\\) does not work either. Let's try \\\\(y = 4\\\\):\\n\\\\[22(4)z + 49z + 70(4) = 602,\\\\]\\n\\\\[88z + 49z + 280 = 602,\\\\]\\n\\\\[137z + 280 = 602,\\\\]\\n\\\\[137z = 322,\\\\]\\n\\\\[z = \\\\frac{322}{137}.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(z = 2\\\\) does not work. Let's try \\\\(y = 1\\\\):\\n\\\\[22(1)z + 49z + 70(1) = 602,\\\\]\\n\\\\[22z + 49z + 70 = 602,\\\\]\\n\\\\[71z + 70 = 602,\\\\]\\n\\\\[71z = 532,\\\\]\\n\\\\[z = \\\\frac{532}{71}.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(z = 7\\\\) works:\\n\\\\[22(7) + 49(7) + 70 = 602,\\\\]\\n\\\\[154 + 343 + 70 = 602,\\\\]\\n\\\\[567 + 35 = 602.\\\\]\\n\\nSo, \\\\(x = 2\\\\), \\\\(y = 1\\\\), and \\\\(z = 7\\\\) is a solution. Therefore, \\\\(x + y + z = 2 + 1 + 7 = 10\\\\).\\n\\nThe answer is \\\\(\\\\boxed{10}\\\\).\", \"To solve the equation \\\\(6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = 812\\\\) for positive integers \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\), we will start by factoring the left-hand side of the equation.\\n\\nFirst, let's rewrite the equation:\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = 812.\\\\]\\n\\nWe can factor out common terms from groups of terms:\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = (6xy + 21x + 2y + 7)(z) + 30xy + 105x + 10y + 7z - 7(6xy + 21x + 2y + 7) + 812.\\\\]\\nHowever, this approach seems complex, so let's try another method by testing small values for \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\).\\n\\nLet's start with \\\\(x = 1\\\\):\\n\\\\[6(1)yz + 30(1)y + 21(1)z + 2yz + 105(1) + 10y + 7z = 812,\\\\]\\n\\\\[6yz + 30y + 21z + 2yz + 105 + 10y + 7z = 812,\\\\]\\n\\\\[8yz + 40y + 28z + 105 = 812,\\\\]\\n\\\\[8yz + 40y + 28z = 707.\\\\]\\n\\nNow, let's test \\\\(y = 1\\\\):\\n\\\\[8(1)z + 40(1) + 28z = 707,\\\\]\\n\\\\[8z + 40 + 28z = 707,\\\\]\\n\\\\[36z + 40 = 707,\\\\]\\n\\\\[36z = 667,\\\\]\\n\\\\[z = \\\\frac{667}{36},\\\\]\\nwhich is not an integer. So, \\\\(y = 1\\\\) does not work.\\n\\nNext, let's test \\\\(y = 2\\\\):\\n\\\\[8(2)z + 40(2) + 28z = 707,\\\\]\\n\\\\[16z + 80 + 28z = 707,\\\\]\\n\\\\[44z + 80 = 707,\\\\]\\n\\\\[44z = 627,\\\\]\\n\\\\[z = \\\\frac{627}{44},\\\\]\\nwhich is not an integer. So, \\\\(y = 2\\\\) does not work.\\n\\nNext, let's test \\\\(y = 3\\\\):\\n\\\\[8(3)z + 40(3) + 28z = 707,\\\\]\\n\\\\[24z + 120 + 28z = 707,\\\\]\\n\\\\[52z + 120 = 707,\\\\]\\n\\\\[52z = 587,\\\\]\\n\\\\[z = \\\\frac{587}{52},\\\\]\\nwhich is not an integer. So, \\\\(y = 3\\\\) does not work.\\n\\nNext, let's test \\\\(y = 4\\\\):\\n\\\\[8(4)z + 40(4) + 28z = 707,\\\\]\\n\\\\[32z + 160 + 28z = 707,\\\\]\\n\\\\[60z + 160 = 707,\\\\]\\n\\\\[60z = 547,\\\\]\\n\\\\[z = \\\\frac{547}{60},\\\\]\\nwhich is not an integer. So, \\\\(y = 4\\\\) does not work.\\n\\nNext, let's test \\\\(y = 5\\\\):\\n\\\\[8(5)z + 40(5) + 28z = 707,\\\\]\\n\\\\[40z + 200 + 28z = 707,\\\\]\\n\\\\[68z + 200 = 707,\\\\]\\n\\\\[68z = 507,\\\\]\\n\\\\[z = \\\\frac{507}{68},\\\\]\\nwhich is not an integer. So, \\\\(y = 5\\\\) does not work.\\n\\nNext, let's test \\\\(y = 6\\\\):\\n\\\\[8(6)z + 40(6) + 28z = 707,\\\\]\\n\\\\[48z + 240 + 28z = 707,\\\\]\\n\\\\[76z + 240 = 707,\\\\]\\n\\\\[76z = 467,\\\\]\\n\\\\[z = \\\\frac{467}{76},\\\\]\\nwhich is not an integer. So, \\\\(y = 6\\\\) does not work.\\n\\nNext, let's test \\\\(y = 7\\\\):\\n\\\\[8(7)z + 40(7) + 28z = 707,\\\\]\\n\\\\[56z + 280 + 28z = 707,\\\\]\\n\\\\[84z + 280 = 707,\\\\]\\n\\\\[84z = 427,\\\\]\\n\\\\[z = \\\\frac{427}{84},\\\\]\\nwhich is not an integer. So, \\\\(y = 7\\\\) does not work.\\n\\nNext, let's test \\\\(y = 8\\\\):\\n\\\\[8(8)z + 40(8) + 28z = 707,\\\\]\\n\\\\[64z + 320 + 28z = 707,\\\\]\\n\\\\[92z + 320 = 707,\\\\]\\n\\\\[92z = 387,\\\\]\\n\\\\[z = \\\\frac{387}{92},\\\\]\\nwhich is not an integer. So, \\\\(y = 8\\\\) does not work.\\n\\nNext, let's test \\\\(y = 9\\\\):\\n\\\\[8(9)z + 40(9) + 28z = 707,\\\\]\\n\\\\[72z + 360 + 28z = 707,\\\\]\\n\\\\[100z + 360 = 707,\\\\]\\n\\\\[100z = 347,\\\\]\\n\\\\[z = \\\\frac{347}{100},\\\\]\\nwhich is not an integer. So, \\\\(y = 9\\\\) does not work.\\n\\nFinally, let's test \\\\(y = 10\\\\):\\n\\\\[8(10)z + 40(10) + 28z = 707,\\\\]\\n\\\\[80z + 400 + 28z = 707,\\\\]\\n\\\\[108z + 400 = 707,\\\\]\\n\\\\[108z = 307,\\\\]\\n\\\\[z = \\\\frac{307}{108},\\\\]\\nwhich is not an integer. So, \\\\(y = 10\\\\) does not work.\\n\\nAfter testing these values, we find that \\\\(x = 2\\\\), \\\\(y = 3\\\\), and \\\\(z = 7\\\\) works:\\n\\\\[6(2)(3)(7) + 30(2)(3) + 21(2)(7) + 2(3)(7) + 105(2) + 10(3) + 7(7) = 812,\\\\]\\n\\\\[252 + 180 + 294 + 42 + 210 + 30 + 49 = 812.\\\\]\\n\\nSo, \\\\(x + y + z = 2 + 3 + 7 = 12\\\\).\\n\\nThe answer is \\\\(\\\\boxed{12}\\\\).\", \"To solve the equation \\\\(6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = 812\\\\) for positive integers \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\), we will use a method of factoring and trial and error.\\n\\nFirst, let's rewrite the equation in a more manageable form by grouping terms:\\n\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = 812.\\\\]\\n\\nWe can factor out common terms from groups of terms to see if we can simplify the expression. Notice that we can group the terms as follows:\\n\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = (6xy + 21x + 2y + 7)(z + 5) - 35z - 35 + 105x + 10y + 7z.\\\\]\\n\\nHowever, this approach seems complex. Instead, let's try to find values for \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\) by testing small positive integers.\\n\\nLet's start with \\\\(x = 1\\\\):\\n\\n\\\\[6(1)yz + 30(1)y + 21(1)z + 2yz + 105(1) + 10y + 7z = 812,\\\\]\\n\\\\[6yz + 30y + 21z + 2yz + 105 + 10y + 7z = 812,\\\\]\\n\\\\[8yz + 40y + 28z + 105 = 812,\\\\]\\n\\\\[8yz + 40y + 28z = 707.\\\\]\\n\\nNow, let's try \\\\(y = 1\\\\):\\n\\n\\\\[8(1)z + 40(1) + 28z = 707,\\\\]\\n\\\\[8z + 40 + 28z = 707,\\\\]\\n\\\\[36z + 40 = 707,\\\\]\\n\\\\[36z = 667.\\\\]\\n\\nSince 667 is not divisible by 36, \\\\(y = 1\\\\) does not work. Let's try \\\\(y = 2\\\\):\\n\\n\\\\[8(2)z + 40(2) + 28z = 707,\\\\]\\n\\\\[16z + 80 + 28z = 707,\\\\]\\n\\\\[44z + 80 = 707,\\\\]\\n\\\\[44z = 627.\\\\]\\n\\nSince 627 is not divisible by 44, \\\\(y = 2\\\\) does not work. Let's try \\\\(y = 3\\\\):\\n\\n\\\\[8(3)z + 40(3) + 28z = 707,\\\\]\\n\\\\[24z + 120 + 28z = 707,\\\\]\\n\\\\[52z + 120 = 707,\\\\]\\n\\\\[52z = 587.\\\\]\\n\\nSince 587 is not divisible by 52, \\\\(y = 3\\\\) does not work. Let's try \\\\(y = 4\\\\):\\n\\n\\\\[8(4)z + 40(4) + 28z = 707,\\\\]\\n\\\\[32z + 160 + 28z = 707,\\\\]\\n\\\\[60z + 160 = 707,\\\\]\\n\\\\[60z = 547.\\\\]\\n\\nSince 547 is not divisible by 60, \\\\(y = 4\\\\) does not work. Let's try \\\\(y = 5\\\\):\\n\\n\\\\[8(5)z + 40(5) + 28z = 707,\\\\]\\n\\\\[40z + 200 + 28z = 707,\\\\]\\n\\\\[68z + 200 = 707,\\\\]\\n\\\\[68z = 507.\\\\]\\n\\nSince 507 is not divisible by 68, \\\\(y = 5\\\\) does not work. Let's try \\\\(y = 6\\\\):\\n\\n\\\\[8(6)z + 40(6) + 28z = 707,\\\\]\\n\\\\[48z + 240 + 28z = 707,\\\\]\\n\\\\[76z + 240 = 707,\\\\]\\n\\\\[76z = 467.\\\\]\\n\\nSince 467 is not divisible by 76, \\\\(y = 6\\\\) does not work. Let's try \\\\(y = 7\\\\):\\n\\n\\\\[8(7)z + 40(7) + 28z = 707,\\\\]\\n\\\\[56z + 280 + 28z = 707,\\\\]\\n\\\\[84z + 280 = 707,\\\\]\\n\\\\[84z = 427.\\\\]\\n\\nSince 427 is not divisible by 84, \\\\(y = 7\\\\) does not work. Let's try \\\\(y = 8\\\\):\\n\\n\\\\[8(8)z + 40(8) + 28z = 707,\\\\]\\n\\\\[64z + 320 + 28z = 707,\\\\]\\n\\\\[92z + 320 = 707,\\\\]\\n\\\\[92z = 387.\\\\]\\n\\nSince 387 is not divisible by 92, \\\\(y = 8\\\\) does not work. Let's try \\\\(y = 9\\\\):\\n\\n\\\\[8(9)z + 40(9) + 28z = 707,\\\\]\\n\\\\[72z + 360 + 28z = 707,\\\\]\\n\\\\[100z + 360 = 707,\\\\]\\n\\\\[100z = 347.\\\\]\\n\\nSince 347 is not divisible by 100, \\\\(y = 9\\\\) does not work. Let's try \\\\(y = 10\\\\):\\n\\n\\\\[8(10)z + 40(10) + 28z = 707,\\\\]\\n\\\\[80z + 400 + 28z = 707,\\\\]\\n\\\\[108z + 400 = 707,\\\\]\\n\\\\[108z = 307.\\\\]\\n\\nSince 307 is not divisible by 108, \\\\(y = 10\\\\) does not work. Let's try \\\\(y = 11\\\\):\\n\\n\\\\[8(11)z + 40(11) + 28z = 707,\\\\]\\n\\\\[88z + 440 + 28z = 707,\\\\]\\n\\\\[116z + 440 = 707,\\\\]\\n\\\\[116z = 267.\\\\]\\n\\nSince 267 is not divisible by 116, \\\\(y = 11\\\\) does not work. Let's try \\\\(y = 12\\\\):\\n\\n\\\\[8(12)z + 40(12) + 28z = 707,\\\\]\\n\\\\[96z + 480 + 28z = 707,\\\\]\\n\\\\[124z + 480 = 707,\\\\]\\n\\\\[124z = 227.\\\\]\\n\\nSince 227 is not divisible by 124, \\\\(y = 12\\\\) does not work. Let's try \\\\(y = 13\\\\):\\n\\n\\\\[8(13)z + 40(13) + 28z = 707,\\\\]\\n\\\\[104z + 520 + 28z = 707,\\\\]\\n\\\\[132z + 520 = 707,\\\\]\\n\\\\[132z = 187.\\\\]\\n\\nSince 187 is not divisible by 132, \\\\(y = 13\\\\) does not work. Let's try \\\\(y = 14\\\\):\\n\\n\\\\[8(14)z + 40(14) + 28z = 707,\\\\]\\n\\\\[112z + 560 + 28z = 707,\\\\]\\n\\\\[140z + 560 = 707,\\\\]\\n\\\\[140z = 147.\\\\]\\n\\nSince 147 is not divisible by 140, \\\\(y = 14\\\\) does not work. Let's try \\\\(y = 15\\\\):\\n\\n\\\\[8(15)z + 40(15) + 28z = 707,\\\\]\\n\\\\[120z + 600 + 28z = 707,\\\\]\\n\\\\[148z + 600 = 707,\\\\]\\n\\\\[148z = 107.\\\\]\\n\\nSince 107 is not divisible by 148, \\\\(y = 15\\\\) does not work. Let\", \"To solve the equation \\\\(6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = 812\\\\) for positive integers \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\), we start by factoring the left-hand side of the equation.\\n\\nFirst, let's group the terms in a way that allows us to factor them:\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z.\\\\]\\n\\nWe can rewrite it as:\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = (6xyz + 30xy + 21xz) + (2yz + 105x + 10y + 7z).\\\\]\\n\\nNotice that we can factor out common terms from each group:\\n\\\\[6xyz + 30xy + 21xz = 3x(2yz + 10y + 7z),\\\\]\\n\\\\[2yz + 105x + 10y + 7z = 2yz + 10y + 7z + 105x.\\\\]\\n\\nHowever, a more straightforward approach is to look for a common factor or a pattern. Let's try to find a simpler factorization by testing small values for \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\).\\n\\nFirst, let's test \\\\(x = 1\\\\):\\n\\\\[6(1)yz + 30(1)y + 21(1)z + 2yz + 105(1) + 10y + 7z = 812,\\\\]\\n\\\\[6yz + 30y + 21z + 2yz + 105 + 10y + 7z = 812,\\\\]\\n\\\\[8yz + 40y + 28z + 105 = 812,\\\\]\\n\\\\[8yz + 40y + 28z = 707.\\\\]\\n\\nNow, let's test \\\\(y = 7\\\\):\\n\\\\[8(7)z + 40(7) + 28z = 707,\\\\]\\n\\\\[56z + 280 + 28z = 707,\\\\]\\n\\\\[84z + 280 = 707,\\\\]\\n\\\\[84z = 427,\\\\]\\n\\\\[z = \\\\frac{427}{84}.\\\\]\\n\\nSince \\\\(z\\\\) is not an integer, \\\\(y = 7\\\\) is not a solution. Let's try \\\\(y = 5\\\\):\\n\\\\[8(5)z + 40(5) + 28z = 707,\\\\]\\n\\\\[40z + 200 + 28z = 707,\\\\]\\n\\\\[68z + 200 = 707,\\\\]\\n\\\\[68z = 507,\\\\]\\n\\\\[z = \\\\frac{507}{68}.\\\\]\\n\\nSince \\\\(z\\\\) is not an integer, \\\\(y = 5\\\\) is not a solution. Let's try \\\\(y = 4\\\\):\\n\\\\[8(4)z + 40(4) + 28z = 707,\\\\]\\n\\\\[32z + 160 + 28z = 707,\\\\]\\n\\\\[60z + 160 = 707,\\\\]\\n\\\\[60z = 547,\\\\]\\n\\\\[z = \\\\frac{547}{60}.\\\\]\\n\\nSince \\\\(z\\\\) is not an integer, \\\\(y = 4\\\\) is not a solution. Let's try \\\\(y = 3\\\\):\\n\\\\[8(3)z + 40(3) + 28z = 707,\\\\]\\n\\\\[24z + 120 + 28z = 707,\\\\]\\n\\\\[52z + 120 = 707,\\\\]\\n\\\\[52z = 587,\\\\]\\n\\\\[z = \\\\frac{587}{52}.\\\\]\\n\\nSince \\\\(z\\\\) is not an integer, \\\\(y = 3\\\\) is not a solution. Let's try \\\\(y = 2\\\\):\\n\\\\[8(2)z + 40(2) + 28z = 707,\\\\]\\n\\\\[16z + 80 + 28z = 707,\\\\]\\n\\\\[44z + 80 = 707,\\\\]\\n\\\\[44z = 627,\\\\]\\n\\\\[z = \\\\frac{627}{44}.\\\\]\\n\\nSince \\\\(z\\\\) is not an integer, \\\\(y = 2\\\\) is not a solution. Let's try \\\\(y = 1\\\\):\\n\\\\[8(1)z + 40(1) + 28z = 707,\\\\]\\n\\\\[8z + 40 + 28z = 707,\\\\]\\n\\\\[36z + 40 = 707,\\\\]\\n\\\\[36z = 667,\\\\]\\n\\\\[z = \\\\frac{667}{36}.\\\\]\\n\\nSince \\\\(z\\\\) is not an integer, \\\\(y = 1\\\\) is not a solution. Finally, let's try \\\\(x = 2\\\\):\\n\\\\[6(2)yz + 30(2)y + 21(2)z + 2yz + 105(2) + 10y + 7z = 812,\\\\]\\n\\\\[12yz + 60y + 42z + 2yz + 210 + 10y + 7z = 812,\\\\]\\n\\\\[14yz + 70y + 49z + 210 = 812,\\\\]\\n\\\\[14yz + 70y + 49z = 602.\\\\]\\n\\nNow, let's test \\\\(y = 7\\\\):\\n\\\\[14(7)z + 70(7) + 49z = 602,\\\\]\\n\\\\[98z + 490 + 49z = 602,\\\\]\\n\\\\[147z + 490 = 602,\\\\]\\n\\\\[147z = 112,\\\\]\\n\\\\[z = \\\\frac{112}{147}.\\\\]\\n\\nSince \\\\(z\\\\) is not an integer, \\\\(y = 7\\\\) is not a solution. Let's try \\\\(y = 6\\\\):\\n\\\\[14(6)z + 70(6) + 49z = 602,\\\\]\\n\\\\[84z + 420 + 49z = 602,\\\\]\\n\\\\[133z + 420 = 602,\\\\]\\n\\\\[133z = 182,\\\\]\\n\\\\[z = \\\\frac{182}{133}.\\\\]\\n\\nSince \\\\(z\\\\) is not an integer, \\\\(y = 6\\\\) is not a solution. Let's try \\\\(y = 5\\\\):\\n\\\\[14(5)z + 70(5) + 49z = 602,\\\\]\\n\\\\[70z + 350 + 49z = 602,\\\\]\\n\\\\[119z + 350 = 602,\\\\]\\n\\\\[119z = 252,\\\\]\\n\\\\[z = \\\\frac{252}{119}.\\\\]\\n\\nSince \\\\(z\\\\) is not an integer, \\\\(y = 5\\\\) is not a solution. Let's try \\\\(y = 4\\\\):\\n\\\\[14(4)z + 70(4) + 49z = 602,\\\\]\\n\\\\[56z + 280 + 49z = 602,\\\\]\\n\\\\[105z + 280 = 602,\\\\]\\n\\\\[105z = 322,\\\\]\\n\\\\[z = \\\\frac{322}{105}.\\\\]\\n\\nSince \\\\(z\\\\) is not an integer, \\\\(y = 4\\\\) is not a solution. Let's try \\\\(y = 3\\\\):\\n\\\\[14(3)z + 70(3) + 49z = 602,\\\\]\\n\\\\[42z + 210 + 49z = 602,\\\\]\\n\\\\[91z + 210 = 602,\\\\]\\n\\\\[91z = 392,\\\\]\\n\\\\[z = \\\\frac{392}{91}.\\\\]\\n\\nSince \\\\(z\\\\) is not an integer, \\\\(y = 3\\\\) is not a solution. Let's try \\\\(y = 2\\\\):\\n\\\\[14(2)z + 70(2) + 49z = 602,\\\\]\\n\\\\[28z + 140 + 49z = 602,\\\\]\\n\\\\[77z + 140 = 602,\\\\]\\n\\\\[77z = 462,\\\\]\\n\\\\[z = 6.\\\\]\\n\\nSo, \\\\(x = 2\\\\), \\\\(y = 2\\\\), and \\\\(z = 6\\\\) is a solution. Therefore,\", \"To solve the equation \\\\(6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = 812\\\\) for positive integers \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\), we start by factoring the left-hand side of the equation.\\n\\nFirst, let's group and factor terms:\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z.\\\\]\\n\\nWe can rewrite it as:\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = (6xyz + 30xy + 21xz) + (2yz + 105x + 10y + 7z).\\\\]\\n\\nNotice that we can factor out common terms in groups:\\n\\\\[6xyz + 30xy + 21xz = 3x(2yz + 10y + 7z),\\\\]\\n\\\\[2yz + 105x + 10y + 7z = 2yz + 7z + 105x + 10y = z(2y + 7) + 105x + 10y.\\\\]\\n\\nSo the equation becomes:\\n\\\\[3x(2yz + 10y + 7z) + z(2y + 7) + 105x + 10y = 812.\\\\]\\n\\nNow, let's try some small values for \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\) to see if we can find a solution. Start with \\\\(x = 1\\\\):\\n\\\\[6yz + 30y + 21z + 2yz + 10y + 7z + 105 + 10 + 7 = 812,\\\\]\\n\\\\[8yz + 40y + 28z + 122 = 812,\\\\]\\n\\\\[8yz + 40y + 28z = 690.\\\\]\\nDivide the entire equation by 2:\\n\\\\[4yz + 20y + 14z = 345.\\\\]\\n\\nNow, let's try \\\\(y = 1\\\\):\\n\\\\[4z + 20 + 14z = 345,\\\\]\\n\\\\[18z + 20 = 345,\\\\]\\n\\\\[18z = 325,\\\\]\\n\\\\[z = \\\\frac{325}{18},\\\\]\\nwhich is not an integer. So, \\\\(y = 1\\\\) does not work. Let's try \\\\(y = 2\\\\):\\n\\\\[8z + 40 + 14z = 345,\\\\]\\n\\\\[22z + 40 = 345,\\\\]\\n\\\\[22z = 305,\\\\]\\n\\\\[z = \\\\frac{305}{22},\\\\]\\nwhich is not an integer. So, \\\\(y = 2\\\\) does not work. Let's try \\\\(y = 3\\\\):\\n\\\\[12z + 60 + 14z = 345,\\\\]\\n\\\\[26z + 60 = 345,\\\\]\\n\\\\[26z = 285,\\\\]\\n\\\\[z = \\\\frac{285}{26},\\\\]\\nwhich is not an integer. So, \\\\(y = 3\\\\) does not work. Let's try \\\\(y = 4\\\\):\\n\\\\[16z + 80 + 14z = 345,\\\\]\\n\\\\[30z + 80 = 345,\\\\]\\n\\\\[30z = 265,\\\\]\\n\\\\[z = \\\\frac{265}{30},\\\\]\\nwhich is not an integer. So, \\\\(y = 4\\\\) does not work. Let's try \\\\(y = 5\\\\):\\n\\\\[20z + 100 + 14z = 345,\\\\]\\n\\\\[34z + 100 = 345,\\\\]\\n\\\\[34z = 245,\\\\]\\n\\\\[z = \\\\frac{245}{34},\\\\]\\nwhich is not an integer. So, \\\\(y = 5\\\\) does not work. Let's try \\\\(y = 6\\\\):\\n\\\\[24z + 120 + 14z = 345,\\\\]\\n\\\\[38z + 120 = 345,\\\\]\\n\\\\[38z = 225,\\\\]\\n\\\\[z = \\\\frac{225}{38},\\\\]\\nwhich is not an integer. So, \\\\(y = 6\\\\) does not work. Let's try \\\\(y = 7\\\\):\\n\\\\[28z + 140 + 14z = 345,\\\\]\\n\\\\[42z + 140 = 345,\\\\]\\n\\\\[42z = 205,\\\\]\\n\\\\[z = \\\\frac{205}{42},\\\\]\\nwhich is not an integer. So, \\\\(y = 7\\\\) does not work. Let's try \\\\(y = 8\\\\):\\n\\\\[32z + 160 + 14z = 345,\\\\]\\n\\\\[46z + 160 = 345,\\\\]\\n\\\\[46z = 185,\\\\]\\n\\\\[z = \\\\frac{185}{46},\\\\]\\nwhich is not an integer. So, \\\\(y = 8\\\\) does not work. Let's try \\\\(y = 9\\\\):\\n\\\\[36z + 180 + 14z = 345,\\\\]\\n\\\\[50z + 180 = 345,\\\\]\\n\\\\[50z = 165,\\\\]\\n\\\\[z = \\\\frac{165}{50} = \\\\frac{33}{10},\\\\]\\nwhich is not an integer. So, \\\\(y = 9\\\\) does not work. Let's try \\\\(y = 10\\\\):\\n\\\\[40z + 200 + 14z = 345,\\\\]\\n\\\\[54z + 200 = 345,\\\\]\\n\\\\[54z = 145,\\\\]\\n\\\\[z = \\\\frac{145}{54},\\\\]\\nwhich is not an integer. So, \\\\(y = 10\\\\) does not work. Let's try \\\\(y = 11\\\\):\\n\\\\[44z + 220 + 14z = 345,\\\\]\\n\\\\[58z + 220 = 345,\\\\]\\n\\\\[58z = 125,\\\\]\\n\\\\[z = \\\\frac{125}{58},\\\\]\\nwhich is not an integer. So, \\\\(y = 11\\\\) does not work. Let's try \\\\(y = 12\\\\):\\n\\\\[48z + 240 + 14z = 345,\\\\]\\n\\\\[62z + 240 = 345,\\\\]\\n\\\\[62z = 105,\\\\]\\n\\\\[z = \\\\frac{105}{62},\\\\]\\nwhich is not an integer. So, \\\\(y = 12\\\\) does not work. Let's try \\\\(y = 13\\\\):\\n\\\\[52z + 260 + 14z = 345,\\\\]\\n\\\\[66z + 260 = 345,\\\\]\\n\\\\[66z = 85,\\\\]\\n\\\\[z = \\\\frac{85}{66},\\\\]\\nwhich is not an integer. So, \\\\(y = 13\\\\) does not work. Let's try \\\\(y = 14\\\\):\\n\\\\[56z + 280 + 14z = 345,\\\\]\\n\\\\[70z + 280 = 345,\\\\]\\n\\\\[70z = 65,\\\\]\\n\\\\[z = \\\\frac{65}{70} = \\\\frac{13}{14},\\\\]\\nwhich is not an integer. So, \\\\(y = 14\\\\) does not work. Let's try \\\\(y = 15\\\\):\\n\\\\[60z + 300 + 14z = 345,\\\\]\\n\\\\[74z + 300 = 345,\\\\]\\n\\\\[74z = 45,\\\\]\\n\\\\[z = \\\\frac{45}{74},\\\\]\\nwhich is not an integer. So, \\\\(y = 15\\\\) does not work. Let's try \\\\(y = 16\\\\):\\n\\\\[64z + 320 + 14z = 345,\\\\]\\n\\\\[78z + 320 = 345,\\\\]\\n\\\\[78z = 25,\\\\]\\n\\\\[z = \\\\frac{25}{78},\\\\]\\nwhich is not an integer. So, \\\\(y = 16\\\\) does not work. Let's try \\\\(y = 17\\\\):\\n\\\\[68z + 340 + 14z = 345,\\\\]\\n\\\\[82z + 340 = 345,\\\\]\\n\\\\[82z = 5,\\\\]\\n\\\\[z = \\\\frac{5}{82},\\\\]\\nwhich is not an integer. So,\", \"To solve the equation \\\\(6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = 812\\\\) for positive integers \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\), we will start by factoring the left-hand side of the equation.\\n\\nFirst, let's group the terms in a way that might help us factor them:\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = (6xyz + 30xy + 21xz) + (2yz + 105x + 10y + 7z).\\\\]\\n\\nWe can factor out common terms from each group:\\n\\\\[6xyz + 30xy + 21xz = 3x(2yz + 10y + 7z),\\\\]\\n\\\\[2yz + 105x + 10y + 7z = 2yz + 7z + 105x + 10y = z(2y + 7) + 10(10.5x + y) = z(2y + 7) + 10(10.5x + y).\\\\]\\n\\nHowever, a simpler approach is to try specific values for \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\) and see if they satisfy the equation. Let's start with small values and check.\\n\\nAssume \\\\(x = 1\\\\):\\n\\\\[6(1)yz + 30(1)y + 21(1)z + 2yz + 105(1) + 10y + 7z = 812,\\\\]\\n\\\\[6yz + 30y + 21z + 2yz + 105 + 10y + 7z = 812,\\\\]\\n\\\\[8yz + 40y + 28z + 105 = 812.\\\\]\\nSubtract 105 from both sides:\\n\\\\[8yz + 40y + 28z = 707.\\\\]\\nDivide the entire equation by 7:\\n\\\\[ \\\\frac{8yz}{7} + \\\\frac{40y}{7} + 4z = 101.\\\\]\\nThis doesn't simplify nicely, so let's try another value for \\\\(x\\\\).\\n\\nAssume \\\\(x = 2\\\\):\\n\\\\[6(2)yz + 30(2)y + 21(2)z + 2yz + 105(2) + 10y + 7z = 812,\\\\]\\n\\\\[12yz + 60y + 42z + 2yz + 210 + 10y + 7z = 812,\\\\]\\n\\\\[14yz + 70y + 49z + 210 = 812.\\\\]\\nSubtract 210 from both sides:\\n\\\\[14yz + 70y + 49z = 602.\\\\]\\nDivide the entire equation by 7:\\n\\\\[2yz + 10y + 7z = 86.\\\\]\\nRearrange:\\n\\\\[2yz + 10y + 7z - 86 = 0.\\\\]\\nWe need to find integer solutions to this equation. Let's try \\\\(y = 5\\\\):\\n\\\\[2(5)z + 10(5) + 7z = 86,\\\\]\\n\\\\[10z + 50 + 7z = 86,\\\\]\\n\\\\[17z + 50 = 86,\\\\]\\n\\\\[17z = 36,\\\\]\\n\\\\[z = \\\\frac{36}{17},\\\\]\\nwhich is not an integer. So, let's try \\\\(y = 6\\\\):\\n\\\\[2(6)z + 10(6) + 7z = 86,\\\\]\\n\\\\[12z + 60 + 7z = 86,\\\\]\\n\\\\[19z + 60 = 86,\\\\]\\n\\\\[19z = 26,\\\\]\\n\\\\[z = \\\\frac{26}{19},\\\\]\\nwhich is not an integer. So, let's try \\\\(y = 7\\\\):\\n\\\\[2(7)z + 10(7) + 7z = 86,\\\\]\\n\\\\[14z + 70 + 7z = 86,\\\\]\\n\\\\[21z + 70 = 86,\\\\]\\n\\\\[21z = 16,\\\\]\\n\\\\[z = \\\\frac{16}{21},\\\\]\\nwhich is not an integer. So, let's try \\\\(y = 4\\\\):\\n\\\\[2(4)z + 10(4) + 7z = 86,\\\\]\\n\\\\[8z + 40 + 7z = 86,\\\\]\\n\\\\[15z + 40 = 86,\\\\]\\n\\\\[15z = 46,\\\\]\\n\\\\[z = \\\\frac{46}{15},\\\\]\\nwhich is not an integer. So, let's try \\\\(y = 3\\\\):\\n\\\\[2(3)z + 10(3) + 7z = 86,\\\\]\\n\\\\[6z + 30 + 7z = 86,\\\\]\\n\\\\[13z + 30 = 86,\\\\]\\n\\\\[13z = 56,\\\\]\\n\\\\[z = \\\\frac{56}{13},\\\\]\\nwhich is not an integer. So, let's try \\\\(y = 2\\\\):\\n\\\\[2(2)z + 10(2) + 7z = 86,\\\\]\\n\\\\[4z + 20 + 7z = 86,\\\\]\\n\\\\[11z + 20 = 86,\\\\]\\n\\\\[11z = 66,\\\\]\\n\\\\[z = 6.\\\\]\\nSo, \\\\(y = 2\\\\) and \\\\(z = 6\\\\) is a solution. Therefore, \\\\(x + y + z = 2 + 2 + 6 = 10\\\\).\\n\\nThe answer is \\\\(\\\\boxed{10}\\\\).\", \"To solve the equation \\\\(6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = 812\\\\) for positive integers \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\), we will start by factoring the left-hand side of the equation.\\n\\nFirst, let's group the terms in a way that allows us to factor by grouping:\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = (6xyz + 30xy + 21xz) + (2yz + 105x + 10y + 7z).\\\\]\\n\\nWe can factor out common factors from each group:\\n\\\\[6xyz + 30xy + 21xz = 3x(2yz + 10y + 7z),\\\\]\\n\\\\[2yz + 105x + 10y + 7z = 2yz + 10y + 7z + 105x.\\\\]\\n\\nNow, we need to find a way to factor the entire expression. Notice that if we rewrite the equation as:\\n\\\\[3x(2yz + 10y + 7z) + (2yz + 10y + 7z) + 105x - 105x + 10y - 10y + 7z - 7z = 812,\\\\]\\nwe can group it as:\\n\\\\[(3x + 1)(2yz + 10y + 7z) + 105x + 10y + 7z - 105x - 10y - 7z = 812.\\\\]\\nThis simplifies to:\\n\\\\[(3x + 1)(2yz + 10y + 7z) = 812 - 105x - 10y - 7z + 105x + 10y + 7z = 812.\\\\]\\n\\nWe need to find values of \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\) such that the left-hand side equals 812. Let's test some small values for \\\\(x\\\\).\\n\\nIf \\\\(x = 1\\\\):\\n\\\\[6(1)yz + 30(1)y + 21(1)z + 2yz + 105(1) + 10y + 7z = 812,\\\\]\\n\\\\[6yz + 30y + 21z + 2yz + 105 + 10y + 7z = 812,\\\\]\\n\\\\[8yz + 40y + 28z + 105 = 812,\\\\]\\n\\\\[8yz + 40y + 28z = 707.\\\\]\\nDividing the entire equation by 7:\\n\\\\[ \\\\frac{8yz + 40y + 28z}{7} = \\\\frac{707}{7},\\\\]\\n\\\\[ \\\\frac{8yz}{7} + \\\\frac{40y}{7} + 4z = 101.\\\\]\\nSince \\\\(y\\\\) and \\\\(z\\\\) are integers, \\\\(8yz\\\\) must be divisible by 7. The smallest possible value for \\\\(y\\\\) and \\\\(z\\\\) that satisfies this is \\\\(y = 7\\\\) and \\\\(z = 7\\\\):\\n\\\\[8(7)(7) + 40(7) + 28(7) = 392 + 280 + 196 = 868 - 61 = 707.\\\\]\\nSo, \\\\(y = 7\\\\) and \\\\(z = 7\\\\) works. Therefore, \\\\(x + y + z = 1 + 7 + 7 = 15\\\\).\\n\\nThus, the answer is \\\\(\\\\boxed{15}\\\\).\", \"To solve the equation \\\\(6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = 812\\\\) for positive integers \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\), we will start by factoring the left-hand side of the equation.\\n\\nFirst, let's group and factor terms:\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z.\\\\]\\n\\nWe can rewrite the equation as:\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = (6xy + 21x + 7)(3z + 5y + 15) - 105z - 35y - 35.\\\\]\\n\\nHowever, this approach seems complex. Instead, let's try to factor by grouping in a simpler way:\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = (2x + 7)(3y + 15)(z + 1) - 105z - 35y - 35 + 105z + 35y + 35 - 105z - 35 + 812.\\\\]\\nThis simplifies to:\\n\\\\[(2x + 7)(3y + 15)(z + 1) - 105z - 35y - 35 + 812 = (2x + 7)(3y + 15)(z + 1) - 105z - 35y - 35 + 812.\\\\]\\n\\nLet's simplify further by trial and error with small values for \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\).\\n\\nAssume \\\\(x = 2\\\\):\\n\\\\[6(2)yz + 30(2)y + 21(2)z + 2yz + 105(2) + 10y + 7z = 812,\\\\]\\n\\\\[12yz + 60y + 42z + 2yz + 210 + 10y + 7z = 812,\\\\]\\n\\\\[14yz + 70y + 49z + 210 = 812,\\\\]\\n\\\\[14yz + 70y + 49z = 602.\\\\]\\nDivide the entire equation by 7:\\n\\\\[2yz + 10y + 7z = 86.\\\\]\\nNow, assume \\\\(y = 3\\\\):\\n\\\\[2(3)z + 10(3) + 7z = 86,\\\\]\\n\\\\[6z + 30 + 7z = 86,\\\\]\\n\\\\[13z + 30 = 86,\\\\]\\n\\\\[13z = 56,\\\\]\\n\\\\[z = \\\\frac{56}{13}.\\\\]\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 3\\\\) is not a solution. Let's try \\\\(y = 4\\\\):\\n\\\\[2(4)z + 10(4) + 7z = 86,\\\\]\\n\\\\[8z + 40 + 7z = 86,\\\\]\\n\\\\[15z + 40 = 86,\\\\]\\n\\\\[15z = 46,\\\\]\\n\\\\[z = \\\\frac{46}{15}.\\\\]\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 4\\\\) is not a solution. Let's try \\\\(y = 5\\\\):\\n\\\\[2(5)z + 10(5) + 7z = 86,\\\\]\\n\\\\[10z + 50 + 7z = 86,\\\\]\\n\\\\[17z + 50 = 86,\\\\]\\n\\\\[17z = 36,\\\\]\\n\\\\[z = \\\\frac{36}{17}.\\\\]\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 5\\\\) is not a solution. Let's try \\\\(y = 6\\\\):\\n\\\\[2(6)z + 10(6) + 7z = 86,\\\\]\\n\\\\[12z + 60 + 7z = 86,\\\\]\\n\\\\[19z + 60 = 86,\\\\]\\n\\\\[19z = 26,\\\\]\\n\\\\[z = \\\\frac{26}{19}.\\\\]\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 6\\\\) is not a solution. Let's try \\\\(y = 7\\\\):\\n\\\\[2(7)z + 10(7) + 7z = 86,\\\\]\\n\\\\[14z + 70 + 7z = 86,\\\\]\\n\\\\[21z + 70 = 86,\\\\]\\n\\\\[21z = 16,\\\\]\\n\\\\[z = \\\\frac{16}{21}.\\\\]\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 7\\\\) is not a solution. Let's try \\\\(y = 8\\\\):\\n\\\\[2(8)z + 10(8) + 7z = 86,\\\\]\\n\\\\[16z + 80 + 7z = 86,\\\\]\\n\\\\[23z + 80 = 86,\\\\]\\n\\\\[23z = 6,\\\\]\\n\\\\[z = \\\\frac{6}{23}.\\\\]\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 8\\\\) is not a solution. Let's try \\\\(y = 9\\\\):\\n\\\\[2(9)z + 10(9) + 7z = 86,\\\\]\\n\\\\[18z + 90 + 7z = 86,\\\\]\\n\\\\[25z + 90 = 86,\\\\]\\n\\\\[25z = -4,\\\\]\\n\\\\[z = -\\\\frac{4}{25}.\\\\]\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 9\\\\) is not a solution. Let's try \\\\(y = 10\\\\):\\n\\\\[2(10)z + 10(10) + 7z = 86,\\\\]\\n\\\\[20z + 100 + 7z = 86,\\\\]\\n\\\\[27z + 100 = 86,\\\\]\\n\\\\[27z = -14,\\\\]\\n\\\\[z = -\\\\frac{14}{27}.\\\\]\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 10\\\\) is not a solution. Let's try \\\\(y = 11\\\\):\\n\\\\[2(11)z + 10(11) + 7z = 86,\\\\]\\n\\\\[22z + 110 + 7z = 86,\\\\]\\n\\\\[29z + 110 = 86,\\\\]\\n\\\\[29z = -24,\\\\]\\n\\\\[z = -\\\\frac{24}{29}.\\\\]\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 11\\\\) is not a solution. Let's try \\\\(y = 12\\\\):\\n\\\\[2(12)z + 10(12) + 7z = 86,\\\\]\\n\\\\[24z + 120 + 7z = 86,\\\\]\\n\\\\[31z + 120 = 86,\\\\]\\n\\\\[31z = -34,\\\\]\\n\\\\[z = -\\\\frac{34}{31}.\\\\]\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 12\\\\) is not a solution. Let's try \\\\(y = 13\\\\):\\n\\\\[2(13)z + 10(13) + 7z = 86,\\\\]\\n\\\\[26z + 130 + 7z = 86,\\\\]\\n\\\\[33z + 130 = 86,\\\\]\\n\\\\[33z = -44,\\\\]\\n\\\\[z = -\\\\frac{44}{33}.\\\\]\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 13\\\\) is not a solution. Let's try \\\\(y = 14\\\\):\\n\\\\[2(14)z + 10(14) + 7z = 86,\\\\]\\n\\\\[28z + 140 + 7z = 86,\\\\]\\n\\\\[35z + 140 = 86,\\\\]\\n\\\\[35z = -54,\\\\]\\n\\\\[z = -\\\\frac{54}{35}.\\\\]\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 14\\\\) is not a solution. Let's try \\\\(y = 15\\\\):\\n\\\\[2(15)z + 10(15) + 7z = 86,\\\\]\\n\\\\[30z + 150 + 7z = 86,\\\\]\\n\\\\[37z + 150 = 86,\\\\]\\n\\\\[37z = -64,\\\\]\\n\\\\[z = -\\\\frac{64}{37}.\\\\]\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 15\\\\) is\", \"To solve the equation \\\\(6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = 812\\\\) for positive integers \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\), we start by factoring the left-hand side of the equation.\\n\\nFirst, let's rewrite the equation:\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = 812.\\\\]\\n\\nWe can factor by grouping terms involving common factors:\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = (6xyz + 30xy + 21xz) + (2yz + 105x + 10y + 7z).\\\\]\\n\\nNotice that we can factor out common terms from each group:\\n\\\\[6xyz + 30xy + 21xz = 3x(2yz + 10y + 7z),\\\\]\\n\\\\[2yz + 105x + 10y + 7z = 2yz + 7z + 105x + 10y = z(2y + 7) + 10(10.5x + y).\\\\]\\n\\nHowever, a more straightforward approach is to try specific values for \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\) and see if they satisfy the equation. Let's start with small values and check.\\n\\nAssume \\\\(x = 1\\\\):\\n\\\\[6(1)yz + 30(1)y + 21(1)z + 2yz + 105(1) + 10y + 7z = 812,\\\\]\\n\\\\[6yz + 30y + 21z + 2yz + 105 + 10y + 7z = 812,\\\\]\\n\\\\[8yz + 40y + 28z + 105 = 812,\\\\]\\n\\\\[8yz + 40y + 28z = 707.\\\\]\\n\\nNow, assume \\\\(y = 1\\\\):\\n\\\\[8(1)z + 40(1) + 28z = 707,\\\\]\\n\\\\[8z + 40 + 28z = 707,\\\\]\\n\\\\[36z + 40 = 707,\\\\]\\n\\\\[36z = 667,\\\\]\\n\\\\[z = \\\\frac{667}{36}.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 1\\\\) does not work. Let's try \\\\(y = 2\\\\):\\n\\\\[8(2)z + 40(2) + 28z = 707,\\\\]\\n\\\\[16z + 80 + 28z = 707,\\\\]\\n\\\\[44z + 80 = 707,\\\\]\\n\\\\[44z = 627,\\\\]\\n\\\\[z = \\\\frac{627}{44}.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 2\\\\) does not work. Let's try \\\\(y = 3\\\\):\\n\\\\[8(3)z + 40(3) + 28z = 707,\\\\]\\n\\\\[24z + 120 + 28z = 707,\\\\]\\n\\\\[52z + 120 = 707,\\\\]\\n\\\\[52z = 587,\\\\]\\n\\\\[z = \\\\frac{587}{52}.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 3\\\\) does not work. Let's try \\\\(y = 4\\\\):\\n\\\\[8(4)z + 40(4) + 28z = 707,\\\\]\\n\\\\[32z + 160 + 28z = 707,\\\\]\\n\\\\[60z + 160 = 707,\\\\]\\n\\\\[60z = 547,\\\\]\\n\\\\[z = \\\\frac{547}{60}.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 4\\\\) does not work. Let's try \\\\(y = 5\\\\):\\n\\\\[8(5)z + 40(5) + 28z = 707,\\\\]\\n\\\\[40z + 200 + 28z = 707,\\\\]\\n\\\\[68z + 200 = 707,\\\\]\\n\\\\[68z = 507,\\\\]\\n\\\\[z = \\\\frac{507}{68}.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 5\\\\) does not work. Let's try \\\\(y = 6\\\\):\\n\\\\[8(6)z + 40(6) + 28z = 707,\\\\]\\n\\\\[48z + 240 + 28z = 707,\\\\]\\n\\\\[76z + 240 = 707,\\\\]\\n\\\\[76z = 467,\\\\]\\n\\\\[z = \\\\frac{467}{76}.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 6\\\\) does not work. Let's try \\\\(y = 7\\\\):\\n\\\\[8(7)z + 40(7) + 28z = 707,\\\\]\\n\\\\[56z + 280 + 28z = 707,\\\\]\\n\\\\[84z + 280 = 707,\\\\]\\n\\\\[84z = 427,\\\\]\\n\\\\[z = \\\\frac{427}{84}.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 7\\\\) does not work. Let's try \\\\(y = 8\\\\):\\n\\\\[8(8)z + 40(8) + 28z = 707,\\\\]\\n\\\\[64z + 320 + 28z = 707,\\\\]\\n\\\\[92z + 320 = 707,\\\\]\\n\\\\[92z = 387,\\\\]\\n\\\\[z = \\\\frac{387}{92}.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 8\\\\) does not work. Let's try \\\\(y = 9\\\\):\\n\\\\[8(9)z + 40(9) + 28z = 707,\\\\]\\n\\\\[72z + 360 + 28z = 707,\\\\]\\n\\\\[100z + 360 = 707,\\\\]\\n\\\\[100z = 347,\\\\]\\n\\\\[z = \\\\frac{347}{100}.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 9\\\\) does not work. Let's try \\\\(y = 10\\\\):\\n\\\\[8(10)z + 40(10) + 28z = 707,\\\\]\\n\\\\[80z + 400 + 28z = 707,\\\\]\\n\\\\[108z + 400 = 707,\\\\]\\n\\\\[108z = 307,\\\\]\\n\\\\[z = \\\\frac{307}{108}.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 10\\\\) does not work. Let's try \\\\(y = 11\\\\):\\n\\\\[8(11)z + 40(11) + 28z = 707,\\\\]\\n\\\\[88z + 440 + 28z = 707,\\\\]\\n\\\\[116z + 440 = 707,\\\\]\\n\\\\[116z = 267,\\\\]\\n\\\\[z = \\\\frac{267}{116}.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 11\\\\) does not work. Let's try \\\\(y = 12\\\\):\\n\\\\[8(12)z + 40(12) + 28z = 707,\\\\]\\n\\\\[96z + 480 + 28z = 707,\\\\]\\n\\\\[124z + 480 = 707,\\\\]\\n\\\\[124z = 227,\\\\]\\n\\\\[z = \\\\frac{227}{124}.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 12\\\\) does not work. Let's try \\\\(y = 13\\\\):\\n\\\\[8(13)z + 40(13) + 28z = 707,\\\\]\\n\\\\[104z + 520 + 28z = 707,\\\\]\\n\\\\[132z + 520 = 707,\\\\]\\n\\\\[132z = 187,\\\\]\\n\\\\[z = \\\\frac{187}{132}.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 13\\\\) does not work. Let's try \\\\(y = 14\\\\):\\n\\\\[8(14)z\", \"To solve the equation \\\\(6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = 812\\\\) for positive integers \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\), we start by factoring the left-hand side of the equation.\\n\\nFirst, let's group the terms in a way that might help us factor them:\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = 812.\\\\]\\n\\nWe can rewrite the equation as:\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = 812.\\\\]\\n\\nNotice that we can factor out common terms from groups of terms:\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = (6xyz + 30xy + 21xz) + (2yz + 105x + 10y + 7z).\\\\]\\n\\nHowever, a more effective approach is to look for a simpler factorization. Let's try to factor by grouping or by looking for a pattern. We can add and subtract the same term to facilitate factoring:\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z + 105 - 105 = 812.\\\\]\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z + 105 = 817.\\\\]\\n\\nNow, we can rewrite the equation as:\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z + 105 = 817.\\\\]\\n\\nWe notice that:\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z + 105 = (2x + 7)(3y + 15)(z + 15).\\\\]\\n\\nSo, we have:\\n\\\\[(2x + 7)(3y + 15)(z + 15) = 817.\\\\]\\n\\nNext, we factorize 817:\\n\\\\[817 = 19 \\\\times 43.\\\\]\\n\\nSince \\\\(2x + 7\\\\), \\\\(3y + 15\\\\), and \\\\(z + 15\\\\) are all positive integers, we need to assign the factors 19 and 43 to these expressions. The possible assignments are:\\n\\\\[2x + 7 = 19, \\\\quad 3y + 15 = 43, \\\\quad z + 15 = 1,\\\\]\\nor\\n\\\\[2x + 7 = 1, \\\\quad 3y + 15 = 19, \\\\quad z + 15 = 43.\\\\]\\n\\nThe first assignment gives:\\n\\\\[2x + 7 = 19 \\\\implies 2x = 12 \\\\implies x = 6,\\\\]\\n\\\\[3y + 15 = 43 \\\\implies 3y = 28 \\\\implies y = \\\\frac{28}{3} \\\\text{ (not an integer)},\\\\]\\nso this is not a valid solution.\\n\\nThe second assignment gives:\\n\\\\[2x + 7 = 1 \\\\implies 2x = -6 \\\\text{ (not a positive integer)},\\\\]\\nso this is also not a valid solution.\\n\\nThe correct assignment is:\\n\\\\[2x + 7 = 19, \\\\quad 3y + 15 = 1, \\\\quad z + 15 = 43.\\\\]\\n\\nThis gives:\\n\\\\[2x + 7 = 19 \\\\implies 2x = 12 \\\\implies x = 6,\\\\]\\n\\\\[3y + 15 = 1 \\\\implies 3y = -14 \\\\text{ (not a positive integer)},\\\\]\\nso this is not a valid solution either. Instead, we should try:\\n\\\\[2x + 7 = 19, \\\\quad 3y + 15 = 43, \\\\quad z + 15 = 1.\\\\]\\n\\nThis gives:\\n\\\\[2x + 7 = 19 \\\\implies 2x = 12 \\\\implies x = 6,\\\\]\\n\\\\[3y + 15 = 43 \\\\implies 3y = 28 \\\\implies y = \\\\frac{28}{3} \\\\text{ (not an integer)},\\\\]\\nso this is not a valid solution. Instead, we should try:\\n\\\\[2x + 7 = 1, \\\\quad 3y + 15 = 43, \\\\quad z + 15 = 19.\\\\]\\n\\nThis gives:\\n\\\\[2x + 7 = 19 \\\\implies 2x = 12 \\\\implies x = 6,\\\\]\\n\\\\[3y + 15 = 43 \\\\implies 3y = 28 \\\\implies y = \\\\frac{28}{3} \\\\text{ (not an integer)},\\\\]\\nso this is not a valid solution. Instead, we should try:\\n\\\\[2x + 7 = 19, \\\\quad 3y + 15 = 43, \\\\quad z + 15 = 1.\\\\]\\n\\nThis gives:\\n\\\\[2x + 7 = 19 \\\\implies 2x = 12 \\\\implies x = 6,\\\\]\\n\\\\[3y + 15 = 43 \\\\implies 3y = 28 \\\\implies y = \\\\frac{28}{3} \\\\text{ (not an integer)},\\\\]\\nso this is not a valid solution. Instead, we should try:\\n\\\\[2x + 7 = 19, \\\\quad 3y + 15 = 43, \\\\quad z + 15 = 1.\\\\]\\n\\nThis gives:\\n\\\\[2x + 7 = 19 \\\\implies 2x = 12 \\\\implies x = 6,\\\\]\\n\\\\[3y + 15 = 43 \\\\implies 3y = 28 \\\\implies y = \\\\frac{28}{3} \\\\text{ (not an integer)},\\\\]\\nso this is not a valid solution. Instead, we should try:\\n\\\\[2x + 7 = 19, \\\\quad 3y + 15 = 43, \\\\quad z + 15 = 1.\\\\]\\n\\nThis gives:\\n\\\\[2x + 7 = 19 \\\\implies 2x = 12 \\\\implies x = 6,\\\\]\\n\\\\[3y + 15 = 43 \\\\implies 3y = 28 \\\\implies y = \\\\frac{28}{3} \\\\text{ (not an integer)},\\\\]\\nso this is not a valid solution. Instead, we should try:\\n\\\\[2x + 7 = 19, \\\\quad 3y + 15 = 43, \\\\quad z + 15 = 1.\\\\]\\n\\nThis gives:\\n\\\\[2x + 7 = 19 \\\\implies 2x = 12 \\\\implies x = 6,\\\\]\\n\\\\[3y + 15 = 43 \\\\implies 3y = 28 \\\\implies y = \\\\frac{28}{3} \\\\text{ (not an integer)},\\\\]\\nso this is not a valid solution. Instead, we should try:\\n\\\\[2x + 7 = 19, \\\\quad 3y + 15 = 43, \\\\quad z + 15 = 1.\\\\]\\n\\nThis gives:\\n\\\\[2x + 7 = 19 \\\\implies 2x = 12 \\\\implies x = 6,\\\\]\\n\\\\[3y + 15 = 43 \\\\implies 3y = 28 \\\\implies y = \\\\frac{28}{3} \\\\text{ (not an integer)},\\\\]\\nso this is not a valid solution. Instead, we should try:\\n\\\\[2x + 7 = 19, \\\\quad 3y + 15 = 43, \\\\quad z + 15 = 1.\\\\]\\n\\nThis gives:\\n\\\\[2x + 7 = 19 \\\\implies 2x = 12 \\\\implies x = 6,\\\\]\\n\\\\[3y + 15 = 43 \\\\implies 3y = 28 \\\\implies y = \\\\frac{28}{3} \\\\text{ (not an integer)},\\\\]\\nso this is not a valid solution. Instead, we should try:\\n\\\\[2x + 7 = 19, \\\\quad 3y + 15 = 43, \\\\quad z + 15 = 1.\\\\]\\n\\nThis gives:\\n\\\\[2x + 7 = 19 \\\\implies 2x = 12 \\\\implies x = 6,\\\\]\\n\\\\[3y + 15 = 43 \\\\implies 3y = 28 \\\\\"], 'sequence_outputs': [\"Let's carefully re-examine the problem and solve it step-by-step.\\n\\nGiven the equation:\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = 812.\\\\]\\n\\nWe will attempt to factor the left-hand side. Notice that the expression can be grouped and factored as follows:\\n\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z + 105 - 105 = 812.\\\\]\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z + 105 = 817.\\\\]\\n\\nRewriting the equation:\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z + 105 = 817.\\\\]\\n\\nWe recognize that:\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z + 105 = (2x + 7)(3y + 15)(z + 15).\\\\]\\n\\nThus, we have:\\n\\\\[(2x + 7)(3y + 15)(z + 15) = 817.\\\\]\\n\\nNext, we factorize 817:\\n\\\\[817 = 19 \\\\times 43.\\\\]\\n\\nWe need to assign the factors 19 and 43 to the expressions \\\\(2x + 7\\\\), \\\\(3y + 15\\\\), and \\\\(z + 15\\\\). The possible assignments are:\\n\\\\[2x + 7 = 19, \\\\quad 3y + 15 = 43, \\\\quad z + 15 = 1,\\\\]\\nor\\n\\\\[2x + 7 = 1, \\\\quad 3y + 15 = 19, \\\\quad z + 15 = 43.\\\\]\\n\\nLet's check the first assignment:\\n\\\\[2x + 7 = 19 \\\\implies 2x = 12 \\\\implies x = 6,\\\\]\\n\\\\[3y + 15 = 43 \\\\implies 3y = 28 \\\\implies y = \\\\frac{28}{3} \\\\text{ (not an integer)}.\\\\]\\n\\nThis is not a valid solution. Now, let's check the second assignment:\\n\\\\[2x + 7 = 1 \\\\implies 2x = -6 \\\\text{ (not a positive integer)},\\\\]\\nso this is not a valid solution either.\\n\\nThe correct assignment is:\\n\\\\[2x + 7 = 19, \\\\quad 3y + 15 = 1, \\\\quad z + 15 = 43.\\\\]\\n\\nThis gives:\\n\\\\[2x + 7 = 19 \\\\implies 2x = 12 \\\\implies x = 6,\\\\]\\n\\\\[3y + 15 = 1 \\\\implies 3y = -14 \\\\text{ (not a positive integer)},\\\\]\\nso this is not a valid solution. Instead, we should try:\\n\\\\[2x + 7 = 19, \\\\quad 3y + 15 = 43, \\\\quad z + 15 = 1.\\\\]\\n\\nThis gives:\\n\\\\[2x + 7 = 19 \\\\implies 2x = 12 \\\\implies x = 6,\\\\]\\n\\\\[3y + 15 = 43 \\\\implies 3y = 28 \\\\implies y = \\\\frac{28}{3} \\\\text{ (not an integer)},\\\\]\\nso this is not a valid solution. Instead, we should try:\\n\\\\[2x + 7 = 19, \\\\quad 3y + 15 = 43, \\\\quad z + 15 = 1.\\\\]\\n\\nThis gives:\\n\\\\[2x + 7 = 19 \\\\implies 2x = 12 \\\\implies x = 6,\\\\]\\n\\\\[3y + 15 = 43 \\\\implies 3y = 28 \\\\implies y = \\\\frac{28}{3} \\\\text{ (not an integer)},\\\\]\\nso this is not a valid solution. Instead, we should try:\\n\\\\[2x + 7 = 19, \\\\quad 3y + 15 = 43, \\\\quad z + 15 = 1.\\\\]\\n\\nThis gives:\\n\\\\[2x + 7 = 19 \\\\implies 2x = 12 \\\\implies x = 6,\\\\]\\n\\\\[3y + 15 = 43 \\\\implies 3y = 28 \\\\implies y = \\\\frac{28}{3} \\\\text{ (not an integer)},\\\\]\\nso this is not a valid solution. Instead, we should try:\\n\\\\[2x + 7 = 19, \\\\quad 3y + 15 = 43, \\\\quad z + 15 = 1.\\\\]\\n\\nThis gives:\\n\\\\[2x + 7 = 19 \\\\implies 2x = 12 \\\\implies x = 6,\\\\]\\n\\\\[3y + 15 = 43 \\\\implies 3y = 28 \\\\implies y = \\\\frac{28}{3} \\\\text{ (not an integer)},\\\\]\\nso this is not a valid solution. Instead, we should try:\\n\\\\[2x + 7 = 19, \\\\quad 3y + 15 = 43, \\\\quad z + 15 = 1.\\\\]\\n\\nThis gives:\\n\\\\[2x + 7 = 19 \\\\implies 2x = 12 \\\\implies x = 6,\\\\]\\n\\\\[3y + 15 = 43 \\\\implies 3y = 28 \\\\implies y = \\\\frac{28}{3} \\\\text{ (not an integer)},\\\\]\\nso this is not a valid solution. Instead, we should try:\\n\\\\[2x + 7 = 19, \\\\quad 3y + 15 = 43, \\\\quad z + 15 = 1.\\\\]\\n\\nThis gives:\\n\\\\[2x + 7 = 19 \\\\implies 2x = 12 \\\\implies x = 6,\\\\]\\n\\\\[3y + 15 = 43 \\\\implies 3y = 28 \\\\implies y = \\\\frac{28}{3} \\\\text{ (not an integer)},\\\\]\\nso this is not a valid solution. Instead, we should try:\\n\\\\[2x + 7 = 19, \\\\quad 3y + 15 = 43, \\\\quad z + 15 = 1.\\\\]\\n\\nThis gives:\\n\\\\[2x + 7 = 19 \\\\implies 2x = 12 \\\\implies x = 6,\\\\]\\n\\\\[3y + 15 = 43 \\\\implies 3y = 28 \\\\implies y = \\\\frac{28}{3} \\\\text{ (not an integer)},\\\\]\\nso this is not a valid solution. Instead, we should try:\\n\\\\[2x + 7 = 19, \\\\quad 3y + 15 = 43, \\\\quad z + 15 = 1.\\\\]\\n\\nThis gives:\\n\\\\[2x + 7 = 19 \\\\implies 2x = 12 \\\\implies x = 6,\\\\]\\n\\\\[3y + 15 = 43 \\\\implies 3y = 28 \\\\implies y = \\\\frac{28}{3} \\\\text{ (not an integer)},\\\\]\\nso this is not a valid solution. Instead, we should try:\\n\\\\[2x + 7 = 19, \\\\quad 3y + 15 = 43, \\\\quad z + 15 = 1.\\\\]\\n\\nThis gives:\\n\\\\[2x + 7 = 19 \\\\implies 2x = 12 \\\\implies x = 6,\\\\]\\n\\\\[3y + 15 = 43 \\\\implies 3y = 28 \\\\implies y = \\\\frac{28}{3} \\\\text{ (not an integer)},\\\\]\\nso this is not a valid solution. Instead, we should try:\\n\\\\[2x + 7 = 19, \\\\quad 3y + 15 = 43, \\\\quad z + 15 = 1.\\\\]\\n\\nThis gives:\\n\\\\[2x + 7 = 19 \\\\implies 2x = 12 \\\\implies x = 6,\\\\]\\n\\\\[3y + 15 = 43 \\\\implies 3y = 28 \\\\implies y = \\\\frac{28}{3} \\\\text{ (not an integer)},\\\\]\\nso this is not a valid solution. Instead, we should try:\\n\\\\[2x + 7 = 19, \\\\quad 3y + 15 = 43, \\\\quad z + 15 = 1.\\\\]\\n\\nThis gives:\\n\\\\[2x + 7 = 19 \\\\implies 2x = \", \"To solve the equation \\\\(6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = 812\\\\) for positive integers \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\), we start by testing small values for \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\).\\n\\nLet's first try \\\\(x = 1\\\\):\\n\\\\[6(1)yz + 30(1)y + 21(1)z + 2yz + 105(1) + 10y + 7z = 812,\\\\]\\n\\\\[6yz + 30y + 21z + 2yz + 105 + 10y + 7z = 812,\\\\]\\n\\\\[8yz + 40y + 28z + 105 = 812,\\\\]\\n\\\\[8yz + 40y + 28z = 707.\\\\]\\n\\nNext, we test \\\\(y = 7\\\\):\\n\\\\[8(7)z + 40(7) + 28z = 707,\\\\]\\n\\\\[56z + 280 + 28z = 707,\\\\]\\n\\\\[84z + 280 = 707,\\\\]\\n\\\\[84z = 427,\\\\]\\n\\\\[z = \\\\frac{427}{84} \\\\approx 5.0952.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 7\\\\) does not work. Now, let's try \\\\(y = 6\\\\):\\n\\\\[8(6)z + 40(6) + 28z = 707,\\\\]\\n\\\\[48z + 240 + 28z = 707,\\\\]\\n\\\\[76z + 240 = 707,\\\\]\\n\\\\[76z = 467,\\\\]\\n\\\\[z = \\\\frac{467}{76} \\\\approx 6.1447.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 6\\\\) does not work. Next, let's try \\\\(y = 5\\\\):\\n\\\\[8(5)z + 40(5) + 28z = 707,\\\\]\\n\\\\[40z + 200 + 28z = 707,\\\\]\\n\\\\[68z + 200 = 707,\\\\]\\n\\\\[68z = 507,\\\\]\\n\\\\[z = \\\\frac{507}{68} \\\\approx 7.4412.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 5\\\\) does not work. Now, let's try \\\\(y = 4\\\\):\\n\\\\[8(4)z + 40(4) + 28z = 707,\\\\]\\n\\\\[32z + 160 + 28z = 707,\\\\]\\n\\\\[60z + 160 = 707,\\\\]\\n\\\\[60z = 547,\\\\]\\n\\\\[z = \\\\frac{547}{60} \\\\approx 9.1167.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 4\\\\) does not work. Next, let's try \\\\(y = 3\\\\):\\n\\\\[8(3)z + 40(3) + 28z = 707,\\\\]\\n\\\\[24z + 120 + 28z = 707,\\\\]\\n\\\\[52z + 120 = 707,\\\\]\\n\\\\[52z = 587,\\\\]\\n\\\\[z = \\\\frac{587}{52} \\\\approx 11.2885.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 3\\\\) does not work. Now, let's try \\\\(y = 2\\\\):\\n\\\\[8(2)z + 40(2) + 28z = 707,\\\\]\\n\\\\[16z + 80 + 28z = 707,\\\\]\\n\\\\[44z + 80 = 707,\\\\]\\n\\\\[44z = 627,\\\\]\\n\\\\[z = \\\\frac{627}{44} \\\\approx 14.25.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 2\\\\) does not work. Finally, let's try \\\\(y = 1\\\\):\\n\\\\[8(1)z + 40(1) + 28z = 707,\\\\]\\n\\\\[8z + 40 + 28z = 707,\\\\]\\n\\\\[36z + 40 = 707,\\\\]\\n\\\\[36z = 667,\\\\]\\n\\\\[z = \\\\frac{667}{36} \\\\approx 18.5278.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 1\\\\) does not work. Now, let's try \\\\(x = 2\\\\):\\n\\\\[6(2)yz + 30(2)y + 21(2)z + 2yz + 105(2) + 10y + 7z = 812,\\\\]\\n\\\\[12yz + 60y + 42z + 2yz + 210 + 10y + 7z = 812,\\\\]\\n\\\\[14yz + 70y + 49z + 210 = 812,\\\\]\\n\\\\[14yz + 70y + 49z = 602.\\\\]\\n\\nNext, let's try \\\\(y = 7\\\\):\\n\\\\[14(7)z + 70(7) + 49z = 602,\\\\]\\n\\\\[98z + 490 + 49z = 602,\\\\]\\n\\\\[147z + 490 = 602,\\\\]\\n\\\\[147z = 112,\\\\]\\n\\\\[z = \\\\frac{112}{147} \\\\approx 0.7619.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 7\\\\) does not work. Now, let's try \\\\(y = 6\\\\):\\n\\\\[14(6)z + 70(6) + 49z = 602,\\\\]\\n\\\\[84z + 420 + 49z = 602,\\\\]\\n\\\\[133z + 420 = 602,\\\\]\\n\\\\[133z = 182,\\\\]\\n\\\\[z = \\\\frac{182}{133} = 1.3671.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 6\\\\) does not work. Next, let's try \\\\(y = 5\\\\):\\n\\\\[14(5)z + 70(5) + 49z = 602,\\\\]\\n\\\\[70z + 350 + 49z = 602,\\\\]\\n\\\\[119z + 350 = 602,\\\\]\\n\\\\[119z = 252,\\\\]\\n\\\\[z = \\\\frac{252}{119} = 2.11.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 5\\\\) does not work. Now, let's try \\\\(y = 4\\\\):\\n\\\\[14(4)z + 70(4) + 49z = 602,\\\\]\\n\\\\[56z + 280 + 49z = 602,\\\\]\\n\\\\[105z + 280 = 602,\\\\]\\n\\\\[105z = 322,\\\\]\\n\\\\[z = \\\\frac{322}{105} = 3.0671.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 4\\\\) does not work. Next, let's try \\\\(y = 3\\\\):\\n\\\\[14(3)z + 70(3) + 49z = 602,\\\\]\\n\\\\[42z + 210 + 49z = 602,\\\\]\\n\\\\[91z + 210 = 602,\\\\]\\n\\\\[91z = 392,\\\\]\\n\\\\[z = \\\\frac{392}{91} = 4.31.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(y = 3\\\\) does not work. Now, let's try \\\\(y = 2\\\\):\\n\\\\[14(2)z + 70(2) + 49z = 602,\\\\]\\n\\\\[28z + 140 + 49z = 602,\\\\]\\n\\\\[77z + 140 = 602,\\\\]\\n\\\\[77z = 462,\\\\]\\n\\\\[z = \\\\frac{462}{77} = 6.\\\\]\\n\\nSince \\\\(z\\\\) is an integer, we have \\\\(z = 6\\\\). Substituting \\\\(y = 2\\\\) and \\\\(z = 6\\\\) back into the\", \"To solve the equation \\\\(6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = 812\\\\) for positive integers \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\), we will use a systematic approach by testing small values for \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\).\\n\\nFirst, let's start with \\\\(x = 1\\\\):\\n\\n\\\\[6(1)yz + 30(1)y + 21(1)z + 2yz + 105(1) + 10y + 7z = 812,\\\\]\\n\\\\[6yz + 30y + 21z + 2yz + 105 + 10y + 7z = 812,\\\\]\\n\\\\[8yz + 40y + 28z + 105 = 812,\\\\]\\n\\\\[8yz + 40y + 28z = 707.\\\\]\\n\\nNow, let's try \\\\(y = 7\\\\):\\n\\n\\\\[8(7)z + 40(7) + 28z = 707,\\\\]\\n\\\\[56z + 280 + 28z = 707,\\\\]\\n\\\\[84z + 280 = 707,\\\\]\\n\\\\[84z = 427.\\\\]\\n\\nSince 427 is not divisible by 84, \\\\(y = 7\\\\) does not work. Let's try \\\\(y = 6\\\\):\\n\\n\\\\[8(6)z + 40(6) + 28z = 707,\\\\]\\n\\\\[48z + 240 + 28z = 707,\\\\]\\n\\\\[76z + 240 = 707,\\\\]\\n\\\\[76z = 467.\\\\]\\n\\nSince 467 is not divisible by 76, \\\\(y = 6\\\\) does not work. Let's try \\\\(y = 5\\\\):\\n\\n\\\\[8(5)z + 40(5) + 28z = 707,\\\\]\\n\\\\[40z + 200 + 28z = 707,\\\\]\\n\\\\[68z + 200 = 707,\\\\]\\n\\\\[68z = 507.\\\\]\\n\\nSince 507 is not divisible by 68, \\\\(y = 5\\\\) does not work. Let's try \\\\(y = 4\\\\):\\n\\n\\\\[8(4)z + 40(4) + 28z = 707,\\\\]\\n\\\\[32z + 160 + 28z = 707,\\\\]\\n\\\\[60z + 160 = 707,\\\\]\\n\\\\[60z = 547.\\\\]\\n\\nSince 547 is not divisible by 60, \\\\(y = 4\\\\) does not work. Let's try \\\\(y = 3\\\\):\\n\\n\\\\[8(3)z + 40(3) + 28z = 707,\\\\]\\n\\\\[24z + 120 + 28z = 707,\\\\]\\n\\\\[52z + 120 = 707,\\\\]\\n\\\\[52z = 587.\\\\]\\n\\nSince 587 is not divisible by 52, \\\\(y = 3\\\\) does not work. Let's try \\\\(y = 2\\\\):\\n\\n\\\\[8(2)z + 40(2) + 28z = 707,\\\\]\\n\\\\[16z + 80 + 28z = 707,\\\\]\\n\\\\[44z + 80 = 707,\\\\]\\n\\\\[44z = 627.\\\\]\\n\\nSince 627 is not divisible by 44, \\\\(y = 2\\\\) does not work. Let's try \\\\(y = 1\\\\):\\n\\n\\\\[8(1)z + 40(1) + 28z = 707,\\\\]\\n\\\\[8z + 40 + 28z = 707,\\\\]\\n\\\\[36z + 40 = 707,\\\\]\\n\\\\[36z = 667.\\\\]\\n\\nSince 667 is not divisible by 36, \\\\(y = 1\\\\) does not work. Let's try \\\\(x = 2\\\\):\\n\\n\\\\[6(2)yz + 30(2)y + 21(2)z + 2yz + 105(2) + 10y + 7z = 812,\\\\]\\n\\\\[12yz + 60y + 42z + 2yz + 210 + 10y + 7z = 812,\\\\]\\n\\\\[14yz + 70y + 49z + 210 = 812,\\\\]\\n\\\\[14yz + 70y + 49z = 602.\\\\]\\n\\nNow, let's try \\\\(y = 7\\\\):\\n\\n\\\\[14(7)z + 70(7) + 49z = 602,\\\\]\\n\\\\[98z + 490 + 49z = 602,\\\\]\\n\\\\[147z + 490 = 602,\\\\]\\n\\\\[147z = 112.\\\\]\\n\\nSince 112 is not divisible by 147, \\\\(y = 7\\\\) does not work. Let's try \\\\(y = 6\\\\):\\n\\n\\\\[14(6)z + 70(6) + 49z = 602,\\\\]\\n\\\\[84z + 420 + 49z = 602,\\\\]\\n\\\\[133z + 420 = 602,\\\\]\\n\\\\[133z = 182.\\\\]\\n\\nSince 182 is divisible by 133, \\\\(z = 1\\\\):\\n\\n\\\\[133(1) = 182.\\\\]\\n\\nThus, \\\\(z = 1\\\\). Therefore, the solution is \\\\(x = 2\\\\), \\\\(y = 6\\\\), and \\\\(z = 1\\\\).\\n\\nFinally, we calculate \\\\(x + y + z\\\\):\\n\\n\\\\[x + y + z = 2 + 6 + 1 = 9.\\\\]\\n\\nThe final answer is \\\\(\\\\boxed{9}\\\\).\", \"Let's re-evaluate the problem step-by-step to ensure we find the correct solution for \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\).\\n\\nGiven the equation:\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = 812.\\\\]\\n\\nWe start by factoring the left-hand side. Notice that:\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = (6xyz + 30xy + 21xz) + (2yz + 105x + 10y + 7z).\\\\]\\n\\nGrouping and factoring:\\n\\\\[6xyz + 30xy + 21xz = 3x(2yz + 10y + 7z),\\\\]\\n\\\\[2yz + 105x + 10y + 7z = 2yz + 7z + 105x + 10y = z(2y + 7) + 105x + 10y.\\\\]\\n\\nThus, the equation becomes:\\n\\\\[3x(2yz + 10y + 7z) + z(2y + 7) + 105x + 10y = 812.\\\\]\\n\\nWe will test small values for \\\\(x\\\\), starting with \\\\(x = 1\\\\):\\n\\\\[6yz + 30y + 21z + 2yz + 10y + 7z + 105 + 10 + 7 = 812,\\\\]\\n\\\\[8yz + 40y + 28z + 122 = 812,\\\\]\\n\\\\[8yz + 40y + 28z = 690.\\\\]\\nDivide by 2:\\n\\\\[4yz + 20y + 14z = 345.\\\\]\\n\\nNow, test \\\\(y = 5\\\\):\\n\\\\[4z + 100 + 14z = 345,\\\\]\\n\\\\[18z + 100 = 345,\\\\]\\n\\\\[18z = 245,\\\\]\\n\\\\[z = \\\\frac{245}{18},\\\\]\\nwhich is not an integer.\\n\\nTest \\\\(y = 6\\\\):\\n\\\\[4z + 120 + 14z = 345,\\\\]\\n\\\\[18z + 120 = 345,\\\\]\\n\\\\[18z = 225,\\\\]\\n\\\\[z = \\\\frac{225}{18} = 12.5,\\\\]\\nwhich is not an integer.\\n\\nTest \\\\(y = 7\\\\):\\n\\\\[4z + 140 + 14z = 345,\\\\]\\n\\\\[18z + 140 = 345,\\\\]\\n\\\\[18z = 205,\\\\]\\n\\\\[z = \\\\frac{205}{18},\\\\]\\nwhich is not an integer.\\n\\nTest \\\\(y = 8\\\\):\\n\\\\[4z + 160 + 14z = 345,\\\\]\\n\\\\[18z + 160 = 345,\\\\]\\n\\\\[18z = 185,\\\\]\\n\\\\[z = \\\\frac{185}{18},\\\\]\\nwhich is not an integer.\\n\\nTest \\\\(y = 9\\\\):\\n\\\\[4z + 180 + 14z = 345,\\\\]\\n\\\\[18z + 180 = 345,\\\\]\\n\\\\[18z = 165,\\\\]\\n\\\\[z = \\\\frac{165}{18} = 9.1667,\\\\]\\nwhich is not an integer.\\n\\nTest \\\\(y = 10\\\\):\\n\\\\[4z + 200 + 14z = 345,\\\\]\\n\\\\[18z + 200 = 345,\\\\]\\n\\\\[18z = 145,\\\\]\\n\\\\[z = \\\\frac{145}{18},\\\\]\\nwhich is not an integer.\\n\\nTest \\\\(y = 11\\\\):\\n\\\\[4z + 220 + 14z = 345,\\\\]\\n\\\\[18z + 220 = 345,\\\\]\\n\\\\[18z = 125,\\\\]\\n\\\\[z = \\\\frac{125}{18},\\\\]\\nwhich is not an integer.\\n\\nTest \\\\(y = 12\\\\):\\n\\\\[4z + 240 + 14z = 345,\\\\]\\n\\\\[18z + 240 = 345,\\\\]\\n\\\\[18z = 105,\\\\]\\n\\\\[z = \\\\frac{105}{18} = 5.8333,\\\\]\\nwhich is not an integer.\\n\\nTest \\\\(y = 13\\\\):\\n\\\\[4z + 260 + 14z = 345,\\\\]\\n\\\\[18z + 260 = 345,\\\\]\\n\\\\[18z = 85,\\\\]\\n\\\\[z = \\\\frac{85}{18},\\\\]\\nwhich is not an integer.\\n\\nTest \\\\(y = 14\\\\):\\n\\\\[4z + 280 + 14z = 345,\\\\]\\n\\\\[18z + 280 = 345,\\\\]\\n\\\\[18z = 65,\\\\]\\n\\\\[z = \\\\frac{65}{18},\\\\]\\nwhich is not an integer.\\n\\nTest \\\\(y = 15\\\\):\\n\\\\[4z + 300 + 14z = 345,\\\\]\\n\\\\[18z + 300 = 345,\\\\]\\n\\\\[18z = 45,\\\\]\\n\\\\[z = \\\\frac{45}{18} = 2.5,\\\\]\\nwhich is not an integer.\\n\\nTest \\\\(y = 16\\\\):\\n\\\\[4z + 320 + 14z = 345,\\\\]\\n\\\\[18z + 320 = 345,\\\\]\\n\\\\[18z = 25,\\\\]\\n\\\\[z = \\\\frac{25}{18},\\\\]\\nwhich is not an integer.\\n\\nTest \\\\(y = 17\\\\):\\n\\\\[4z + 340 + 14z = 345,\\\\]\\n\\\\[18z + 340 = 345,\\\\]\\n\\\\[18z = 5,\\\\]\\n\\\\[z = \\\\frac{5}{18},\\\\]\\nwhich is not an integer.\\n\\nFinally, test \\\\(y = 10\\\\):\\n\\\\[4z + 200 + 14z = 345,\\\\]\\n\\\\[18z + 200 = 345,\\\\]\\n\\\\[18z = 145,\\\\]\\n\\\\[z = \\\\frac{145}{18} = 8,\\\\]\\nwhich is an integer.\\n\\nThus, \\\\(x = 1\\\\), \\\\(y = 10\\\\), and \\\\(z = 8\\\\). Therefore, \\\\(x + y + z = 1 + 10 + 8 = 19\\\\).\\n\\nThe final answer is:\\n\\\\[\\n\\\\boxed{19}\\n\\\\]\", \"Let's re-evaluate the problem step-by-step to ensure we find the correct solution for \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\).\\n\\nGiven the equation:\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = 812.\\\\]\\n\\nFirst, let's try \\\\(x = 1\\\\):\\n\\\\[6(1)yz + 30(1)y + 21(1)z + 2yz + 105(1) + 10y + 7z = 812,\\\\]\\n\\\\[6yz + 30y + 21z + 2yz + 105 + 10y + 7z = 812,\\\\]\\n\\\\[8yz + 40y + 28z + 105 = 812,\\\\]\\n\\\\[8yz + 40y + 28z = 707.\\\\]\\n\\nNow, let's test \\\\(y = 7\\\\):\\n\\\\[8(7)z + 40(7) + 28z = 707,\\\\]\\n\\\\[56z + 280 + 28z = 707,\\\\]\\n\\\\[84z + 280 = 707,\\\\]\\n\\\\[84z = 427,\\\\]\\n\\\\[z = \\\\frac{427}{84}.\\\\]\\n\\nSince \\\\(z\\\\) is not an integer, \\\\(y = 7\\\\) is not a solution. Let's try \\\\(y = 6\\\\):\\n\\\\[8(6)z + 40(6) + 28z = 707,\\\\]\\n\\\\[48z + 240 + 28z = 707,\\\\]\\n\\\\[76z + 240 = 707,\\\\]\\n\\\\[76z = 467,\\\\]\\n\\\\[z = \\\\frac{467}{76}.\\\\]\\n\\nSince \\\\(z\\\\) is not an integer, \\\\(y = 6\\\\) is not a solution. Let's try \\\\(y = 5\\\\):\\n\\\\[8(5)z + 40(5) + 28z = 707,\\\\]\\n\\\\[40z + 200 + 28z = 707,\\\\]\\n\\\\[68z + 200 = 707,\\\\]\\n\\\\[68z = 507,\\\\]\\n\\\\[z = \\\\frac{507}{68}.\\\\]\\n\\nSince \\\\(z\\\\) is not an integer, \\\\(y = 5\\\\) is not a solution. Let's try \\\\(y = 4\\\\):\\n\\\\[8(4)z + 40(4) + 28z = 707,\\\\]\\n\\\\[32z + 160 + 28z = 707,\\\\]\\n\\\\[60z + 160 = 707,\\\\]\\n\\\\[60z = 547,\\\\]\\n\\\\[z = \\\\frac{547}{60}.\\\\]\\n\\nSince \\\\(z\\\\) is not an integer, \\\\(y = 4\\\\) is not a solution. Let's try \\\\(y = 3\\\\):\\n\\\\[8(3)z + 40(3) + 28z = 707,\\\\]\\n\\\\[24z + 120 + 28z = 707,\\\\]\\n\\\\[52z + 120 = 707,\\\\]\\n\\\\[52z = 587,\\\\]\\n\\\\[z = \\\\frac{587}{52}.\\\\]\\n\\nSince \\\\(z\\\\) is not an integer, \\\\(y = 3\\\\) is not a solution. Let's try \\\\(y = 2\\\\):\\n\\\\[8(2)z + 40(2) + 28z = 707,\\\\]\\n\\\\[16z + 80 + 28z = 707,\\\\]\\n\\\\[44z + 80 = 707,\\\\]\\n\\\\[44z = 627,\\\\]\\n\\\\[z = \\\\frac{627}{44}.\\\\]\\n\\nSince \\\\(z\\\\) is not an integer, \\\\(y = 2\\\\) is not a solution. Let's try \\\\(y = 1\\\\):\\n\\\\[8(1)z + 40(1) + 28z = 707,\\\\]\\n\\\\[8z + 40 + 28z = 707,\\\\]\\n\\\\[36z + 40 = 707,\\\\]\\n\\\\[36z = 667,\\\\]\\n\\\\[z = \\\\frac{667}{36}.\\\\]\\n\\nSince \\\\(z\\\\) is not an integer, \\\\(y = 1\\\\) is not a solution. Now, let's try \\\\(x = 2\\\\):\\n\\\\[6(2)yz + 30(2)y + 21(2)z + 2yz + 105(2) + 10y + 7z = 812,\\\\]\\n\\\\[12yz + 60y + 42z + 2yz + 210 + 10y + 7z = 812,\\\\]\\n\\\\[14yz + 70y + 49z + 210 = 812,\\\\]\\n\\\\[14yz + 70y + 49z = 602.\\\\]\\n\\nNow, let's test \\\\(y = 7\\\\):\\n\\\\[14(7)z + 70(7) + 49z = 602,\\\\]\\n\\\\[98z + 490 + 49z = 602,\\\\]\\n\\\\[147z + 490 = 602,\\\\]\\n\\\\[147z = 112,\\\\]\\n\\\\[z = \\\\frac{112}{147}.\\\\]\\n\\nSince \\\\(z\\\\) is not an integer, \\\\(y = 7\\\\) is not a solution. Let's try \\\\(y = 6\\\\):\\n\\\\[14(6)z + 70(6) + 49z = 602,\\\\]\\n\\\\[84z + 420 + 49z = 602,\\\\]\\n\\\\[133z + 420 = 602,\\\\]\\n\\\\[133z = 182,\\\\]\\n\\\\[z = \\\\frac{182}{133}.\\\\]\\n\\nSince \\\\(z\\\\) is not an integer, \\\\(y = 6\\\\) is not a solution. Let's try \\\\(y = 5\\\\):\\n\\\\[14(5)z + 70(5) + 49z = 602,\\\\]\\n\\\\[70z + 350 + 49z = 602,\\\\]\\n\\\\[119z + 350 = 602,\\\\]\\n\\\\[119z = 252,\\\\]\\n\\\\[z = \\\\frac{252}{119}.\\\\]\\n\\nSince \\\\(z\\\\) is not an integer, \\\\(y = 5\\\\) is not a solution. Let's try \\\\(y = 4\\\\):\\n\\\\[14(4)z + 70(4) + 49z = 602,\\\\]\\n\\\\[56z + 280 + 49z = 602,\\\\]\\n\\\\[105z + 280 = 602,\\\\]\\n\\\\[105z = 322,\\\\]\\n\\\\[z = \\\\frac{322}{105}.\\\\]\\n\\nSince \\\\(z\\\\) is not an integer, \\\\(y = 4\\\\) is not a solution. Let's try \\\\(y = 3\\\\):\\n\\\\[14(3)z + 70(3) + 49z = 602,\\\\]\\n\\\\[42z + 210 + 49z = 602,\\\\]\\n\\\\[91z + 210 = 602,\\\\]\\n\\\\[91z = 392,\\\\]\\n\\\\[z = 4.\\\\]\\n\\nSo, \\\\(x = 2\\\\), \\\\(y = 3\\\\), and \\\\(z = 4\\\\) is a solution. Therefore, \\\\(x + y + z = 2 + 3 + 4 = 9\\\\).\\n\\nThe final answer is:\\n\\\\[\\n\\\\boxed{9}\\n\\\\]\", \"Let's re-evaluate the problem step-by-step to ensure accuracy.\\n\\nGiven the equation:\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = 812\\\\]\\n\\nFirst, we factorize the left-hand side:\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = 3x(2yz + 10y + 7z) + 2yz + 105x + 10y + 7z = 812.\\\\]\\n\\nLet's simplify it:\\n\\\\[3x(2yz + 10y + 7z) + 2yz + 105x + 10y + 7z = 812.\\\\]\\n\\\\[3x(2yz + 10y + 7z) + (2yz + 105x + 10y + 7z) = 812.\\\\]\\n\\nWe will test small values for \\\\(x\\\\), starting with \\\\(x = 1\\\\):\\n\\\\[3(2yz + 10y + 7z) + (2yz + 105 + 10y + 7z) = 812.\\\\]\\n\\\\[5(2yz + 10y + 7z) + 105 + 10y = 812.\\\\]\\n\\\\[5(2yz + 10y + 7z) + 10y = 707.\\\\]\\n\\nNow, test \\\\(y = 4\\\\):\\n\\\\[5(2(4)z + 10(4) + 7z) + 10(4) = 707.\\\\]\\n\\\\[5(8z + 40 + 7z) + 40 = 707.\\\\]\\n\\\\[5(15z + 40) + 40 = 707.\\\\]\\n\\\\[75z + 200 + 40 = 707.\\\\]\\n\\\\[75z + 240 = 707.\\\\]\\n\\\\[75z = 467.\\\\]\\n\\\\[z = \\\\frac{467}{75}.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(z = 467/75\\\\) is not an integer. Next, test \\\\(y = 3\\\\):\\n\\\\[5(2(3)z + 10(3) + 7z) + 10(3) = 707.\\\\]\\n\\\\[5(6z + 30 + 7z) + 30 = 707.\\\\]\\n\\\\[5(13z + 30) + 30 = 707.\\\\]\\n\\\\[65z + 150 + 30 = 707.\\\\]\\n\\\\[65z + 180 = 707.\\\\]\\n\\\\[65z = 527.\\\\]\\n\\\\[z = \\\\frac{527}{65}.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(z = 527/65\\\\) is not an integer. Next, test \\\\(y = 2\\\\):\\n\\\\[5(2(2)z + 10(2) + 7z) + 10(2) = 707.\\\\]\\n\\\\[5(4z + 20 + 7z) + 20 = 707.\\\\]\\n\\\\[5(11z + 20) + 20 = 707.\\\\]\\n\\\\[55z + 100 + 20 = 707.\\\\]\\n\\\\[55z + 120 = 707.\\\\]\\n\\\\[55z = 587.\\\\]\\n\\\\[z = \\\\frac{587}{55}.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(z = 587/55\\\\) is not an integer. Next, test \\\\(y = 1\\\\):\\n\\\\[5(2(1)z + 10(1) + 7z) + 10(1) = 707.\\\\]\\n\\\\[5(2z + 10 + 7z) + 10 = 707.\\\\]\\n\\\\[5(9z + 10) + 10 = 707.\\\\]\\n\\\\[45z + 50 + 10 = 707.\\\\]\\n\\\\[45z + 60 = 707.\\\\]\\n\\\\[45z = 647.\\\\]\\n\\\\[z = \\\\frac{647}{45}.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(z = 647/45\\\\) is not an integer. Now, test \\\\(x = 2\\\\):\\n\\\\[12(2yz + 10y + 7z) + 2yz + 210 + 10y + 7z = 812.\\\\]\\n\\\\[24yz + 120y + 84z + 2yz + 210 + 10y + 7z = 812.\\\\]\\n\\\\[26yz + 130y + 91z + 210 = 812.\\\\]\\n\\\\[26yz + 130y + 91z = 602.\\\\]\\n\\nNow, test \\\\(y = 2\\\\):\\n\\\\[26(2)z + 130(2) + 91z = 602.\\\\]\\n\\\\[52z + 260 + 91z = 602.\\\\]\\n\\\\[143z + 260 = 602.\\\\]\\n\\\\[143z = 342.\\\\]\\n\\\\[z = \\\\frac{342}{143}.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(z = 342/143\\\\) is not an integer. Now, test \\\\(y = 1\\\\):\\n\\\\[26z + 130 + 91z = 602.\\\\]\\n\\\\[117z + 130 = 602.\\\\]\\n\\\\[117z = 472.\\\\]\\n\\\\[z = \\\\frac{472}{117}.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(z = 472/117\\\\) is not an integer. Now, test \\\\(x = 3\\\\):\\n\\\\[18(2yz + 10y + 7z) + 2yz + 315 + 10y + 7z = 812.\\\\]\\n\\\\[36yz + 180y + 126z + 2yz + 315 + 10y + 7z = 812.\\\\]\\n\\\\[38yz + 190y + 133z + 315 = 812.\\\\]\\n\\\\[38yz + 190y + 133z = 497.\\\\]\\n\\nNow, test \\\\(y = 1\\\\):\\n\\\\[38z + 190 + 133z = 497.\\\\]\\n\\\\[171z + 190 = 497.\\\\]\\n\\\\[171z = 307.\\\\]\\n\\\\[z = \\\\frac{307}{171}.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(z = 307/171\\\\) is not an integer. Now, test \\\\(y = 2\\\\):\\n\\\\[38(2)z + 190(2) + 133z = 497.\\\\]\\n\\\\[76z + 380 + 133z = 497.\\\\]\\n\\\\[209z + 380 = 497.\\\\]\\n\\\\[209z = 117.\\\\]\\n\\\\[z = \\\\frac{117}{209}.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(z = 117/209\\\\) is not an integer. Finally, test \\\\(y = 3\\\\):\\n\\\\[38(3)z + 190(3) + 133z = 497.\\\\]\\n\\\\[114z + 570 + 133z = 497.\\\\]\\n\\\\[247z + 570 = 497.\\\\]\\n\\\\[247z = -73.\\\\]\\n\\nSince \\\\(z\\\\) must be an integer, \\\\(z = -73/247\\\\) is not an integer. The correct values are \\\\(x = 2\\\\), \\\\(y = 3\\\\), and \\\\(z = 4\\\\).\\n\\nThus, the sum \\\\(x + y + z = 2 + 3 + 4 = 9\\\\).\\n\\nThe final answer is:\\n\\\\[\\n\\\\boxed{9}\\n\\\\]\", \"Let's re-evaluate the problem step-by-step to ensure accuracy and clarity.\\n\\nGiven the equation:\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = 812\\\\]\\n\\nWe start by testing small values for \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\). Let's begin with \\\\(x = 1\\\\):\\n\\n\\\\[6(1)yz + 30(1)y + 21(1)z + 2yz + 105(1) + 10y + 7z = 812\\\\]\\n\\\\[6yz + 30y + 21z + 2yz + 105 + 10y + 7z = 812\\\\]\\n\\\\[8yz + 40y + 28z + 105 = 812\\\\]\\n\\\\[8yz + 40y + 28z = 707\\\\]\\n\\nNext, we test \\\\(y = 7\\\\):\\n\\n\\\\[8(7)z + 40(7) + 28z = 707\\\\]\\n\\\\[56z + 280 + 28z = 707\\\\]\\n\\\\[84z + 280 = 707\\\\]\\n\\\\[84z = 427\\\\]\\n\\\\[z = \\\\frac{427}{84}\\\\]\\n\\nSince \\\\(z\\\\) is not an integer, \\\\(y = 7\\\\) does not work. We continue testing other values for \\\\(y\\\\).\\n\\nNext, let's try \\\\(y = 6\\\\):\\n\\n\\\\[8(6)z + 40(6) + 28z = 707\\\\]\\n\\\\[48z + 240 + 28z = 707\\\\]\\n\\\\[76z + 240 = 707\\\\]\\n\\\\[76z = 467\\\\]\\n\\\\[z = \\\\frac{467}{76}\\\\]\\n\\nSince \\\\(z\\\\) is not an integer, \\\\(y = 6\\\\) does not work. We continue testing other values for \\\\(y\\\\).\\n\\nNext, let's try \\\\(y = 5\\\\):\\n\\n\\\\[8(5)z + 40(5) + 28z = 707\\\\]\\n\\\\[40z + 200 + 28z = 707\\\\]\\n\\\\[68z + 200 = 707\\\\]\\n\\\\[68z = 507\\\\]\\n\\\\[z = \\\\frac{507}{68}\\\\]\\n\\nSince \\\\(z\\\\) is not an integer, \\\\(y = 5\\\\) does not work. We continue testing other values for \\\\(y\\\\).\\n\\nNext, let's try \\\\(y = 4\\\\):\\n\\n\\\\[8(4)z + 40(4) + 28z = 707\\\\]\\n\\\\[32z + 160 + 28z = 707\\\\]\\n\\\\[60z + 160 = 707\\\\]\\n\\\\[60z = 547\\\\]\\n\\\\[z = \\\\frac{547}{60}\\\\]\\n\\nSince \\\\(z\\\\) is not an integer, \\\\(y = 4\\\\) does not work. We continue testing other values for \\\\(y\\\\).\\n\\nNext, let's try \\\\(y = 3\\\\):\\n\\n\\\\[8(3)z + 40(3) + 28z = 707\\\\]\\n\\\\[24z + 120 + 28z = 707\\\\]\\n\\\\[52z + 120 = 707\\\\]\\n\\\\[52z = 587\\\\]\\n\\\\[z = \\\\frac{587}{52}\\\\]\\n\\nSince \\\\(z\\\\) is not an integer, \\\\(y = 3\\\\) does not work. We continue testing other values for \\\\(y\\\\).\\n\\nNext, let's try \\\\(y = 2\\\\):\\n\\n\\\\[8(2)z + 40(2) + 28z = 707\\\\]\\n\\\\[16z + 80 + 28z = 707\\\\]\\n\\\\[44z + 80 = 707\\\\]\\n\\\\[44z = 627\\\\]\\n\\\\[z = \\\\frac{627}{44}\\\\]\\n\\nSince \\\\(z\\\\) is not an integer, \\\\(y = 2\\\\) does not work. We continue testing other values for \\\\(y\\\\).\\n\\nNext, let's try \\\\(y = 1\\\\):\\n\\n\\\\[8(1)z + 40(1) + 28z = 707\\\\]\\n\\\\[8z + 40 + 28z = 707\\\\]\\n\\\\[36z + 40 = 707\\\\]\\n\\\\[36z = 667\\\\]\\n\\\\[z = \\\\frac{667}{36}\\\\]\\n\\nSince \\\\(z\\\\) is not an integer, \\\\(y = 1\\\\) does not work.\\n\\nFinally, let's try \\\\(x = 2\\\\):\\n\\n\\\\[6(2)yz + 30(2)y + 21(2)z + 2yz + 105(2) + 10y + 7z = 812\\\\]\\n\\\\[12yz + 60y + 42z + 2yz + 210 + 10y + 7z = 812\\\\]\\n\\\\[14yz + 70y + 49z + 210 = 812\\\\]\\n\\\\[14yz + 70y + 49z = 602\\\\]\\n\\nNext, let's try \\\\(y = 7\\\\):\\n\\n\\\\[14(7)z + 70(7) + 49z = 602\\\\]\\n\\\\[98z + 490 + 49z = 602\\\\]\\n\\\\[147z + 490 = 602\\\\]\\n\\\\[147z = 112\\\\]\\n\\\\[z = \\\\frac{112}{147}\\\\]\\n\\nSince \\\\(z\\\\) is not an integer, \\\\(y = 7\\\\) does not work. We continue testing other values for \\\\(y\\\\).\\n\\nFinally, let's try \\\\(x = 1\\\\), \\\\(y = 7\\\\), and \\\\(z = 10\\\\):\\n\\n\\\\[6(1)(7)(10) + 30(1)(7) + 21(1)(10) + 2(7)(10) + 105(1) + 10(7) + 7(10) = 420 + 210 + 210 + 140 + 105 + 70 + 70 = 1025 - 213 = 812\\\\]\\n\\nSo, \\\\(x + y + z = 1 + 7 + 10 = 18\\\\).\\n\\nThe correct answer is \\\\(\\\\boxed{18}\\\\).\", \"Let's carefully re-evaluate the given equation \\\\(6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = 812\\\\) for positive integers \\\\(x\\\\), \\\\(y\\\\), and \\\\(z\\\\).\\n\\nFirst, we'll try to factor the left-hand side of the equation. We can rewrite it as:\\n\\\\[6xyz + 30xy + 21xz + 2yz + 105x + 10y + 7z = (6xyz + 30xy + 21xz) + (2yz + 105x + 10y + 7z).\\\\]\\n\\nWe notice that:\\n\\\\[6xyz + 30xy + 21xz = 3x(2yz + 10y + 7z),\\\\]\\nand the remaining part is:\\n\\\\[2yz + 105x + 10y + 7z.\\\\]\\n\\nWe need to find a way to factor the entire expression. Let's test small values for \\\\(x\\\\).\\n\\nIf \\\\(x = 1\\\\):\\n\\\\[6(1)yz + 30(1)y + 21(1)z + 2yz + 105(1) + 10y + 7z = 812,\\\\]\\n\\\\[6yz + 30y + 21z + 2yz + 105 + 10y + 7z = 812,\\\\]\\n\\\\[8yz + 40y + 28z + 105 = 812,\\\\]\\n\\\\[8yz + 40y + 28z = 707.\\\\]\\nDividing the entire equation by 7:\\n\\\\[ \\\\frac{8yz + 40y + 28z}{7} = \\\\frac{707}{7},\\\\]\\n\\\\[ \\\\frac{8yz}{7} + \\\\frac{40y}{7} + 4z = 101.\\\\]\\nSince \\\\(y\\\\) and \\\\(z\\\\) are integers, \\\\(8yz\\\\) must be divisible by 7. The smallest possible value for \\\\(y\\\\) and \\\\(z\\\\) that satisfies this is \\\\(y = 7\\\\) and \\\\(z = 7\\\\):\\n\\\\[8(7)(7) + 40(7) + 28(7) = 392 + 280 + 196 = 868 - 61 = 707.\\\\]\\nSo, \\\\(y = 7\\\\) and \\\\(z = 7\\\\) works. Therefore, \\\\(x + y + z = 1 + 7 + 7 = 15\\\\).\\n\\nThus, the answer is \\\\(\\\\boxed{15}\\\\).\\n\\nUpon re-evaluation, there are no apparent mistakes or unclear reasoning in the steps provided. The solution is consistent and logically sound.\"], 'extracted_answers': [\"[z, 'z']\", \"[10, '10']\", \"[60, '60']\", \"[10, '10']\", \"[10, '10']\", \"[18, '18']\", \"[10, '10']\", \"[12, '12']\", \"[Eq(y, 15), 'y = 15']\", \"[Eq(z, 6), 'z = 6']\", \"[5, 'z = \\\\\\\\frac{5}{82},']\", \"[10, '10']\", \"[15, '15']\", \"[Eq(y, 15), 'y = 15']\", \"[Eq(y, 14), 'y = 14']\", \"[28, '28']\"], 'retrieved_indices': [574, 376, 249, 344, 631], 'retrieved_similarities': [0.7997391223907471, 0.7924380302429199, 0.7538705468177795, 0.7497026920318604, 0.7354580163955688], 'llm_rank_response': [5, 1, 3, 4, 2, 0], 'retrieved_data_info': [{'shuffled_idx': 574, 'original_idx': 1204, 'similarity': 0.7997391223907471, 'problem': 'Determine the largest positive integer $n$ such that there exist positive integers $x, y, z$ so that \\\\[\\nn^2 = x^2+y^2+z^2+2xy+2yz+2zx+3x+3y+3z-6\\n\\\\]', 'correct_sum': 15, 'llm_rank_result': 5}, {'shuffled_idx': 376, 'original_idx': 361, 'similarity': 0.7924380302429199, 'problem': 'If $x$, $y$, and $z$ are positive numbers satisfying \\\\[\\nx+\\\\frac{1}{y}=4,\\\\ \\\\ \\\\ y+\\\\frac{1}{z}=1,\\\\text{ and }z+\\\\frac{1}{x}=\\\\frac{7}{3},\\n\\\\]find the value of $xyz$.', 'correct_sum': 15, 'llm_rank_result': 1}, {'shuffled_idx': 249, 'original_idx': 1501, 'similarity': 0.7538705468177795, 'problem': 'Let the ordered triples $(x,y,z)$ of complex numbers that satisfy\\n\\\\begin{align*}\\nx + yz &= 7, \\\\\\\\\\ny + xz &= 10, \\\\\\\\\\nz + xy &= 10.\\n\\\\end{align*}be $(x_1,y_1,z_1),$ $(x_2,y_2,z_2),$ $\\\\dots,$ $(x_n,y_n,z_n).$  Find $x_1 + x_2 + \\\\dots + x_n.$', 'correct_sum': 1, 'llm_rank_result': 4}, {'shuffled_idx': 344, 'original_idx': 263, 'similarity': 0.7497026920318604, 'problem': 'Given the system of equations \\\\begin{align*}\\nxy &= 6 - 2x - 3y,\\\\\\\\\\nyz &= 6 - 4y - 2z,\\\\\\\\\\nxz &= 30 - 4x - 3z,\\n\\\\end{align*}find the positive solution of $x$.', 'correct_sum': 14, 'llm_rank_result': 2}, {'shuffled_idx': 631, 'original_idx': 1348, 'similarity': 0.7354580163955688, 'problem': 'Let $x,$ $y,$ and $z$ be positive real numbers such that $x + y + z = 1.$  Find the maximum value of $x^3 y^2 z.$', 'correct_sum': 4, 'llm_rank_result': 3}]}\n"
     ]
    }
   ],
   "source": [
    "import json\n",
    "\n",
    "merged_data_path=\"E:/copy/tts_schedule_730/batch_infer/src/memory_bank/llm_rank/results/retrieval_results_1000_20250806_145707.jsonl\"\n",
    "data_list=[]\n",
    "with open(merged_data_path, 'r') as f:\n",
    "    for line in f:\n",
    "        data = json.loads(line)\n",
    "        data_list.append(data)\n",
    "\n",
    "print(data_list[100])"
   ]
  }
 ],
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