20221025 afternoon
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"cells": [
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"cells": [
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{
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{
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"cell_type": "code",
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"cell_type": "code",
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"execution_count": 6,
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"execution_count": 2,
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"metadata": {},
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"metadata": {},
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"outputs": [
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"outputs": [
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{
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{
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"0"
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"0"
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]
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]
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},
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},
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"execution_count": 6,
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"execution_count": 2,
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"metadata": {},
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"metadata": {},
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"output_type": "execute_result"
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"output_type": "execute_result"
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}
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}
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@ -21,8 +21,7 @@
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"\n",
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"\n",
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"\"\"\"---设置关键字, 同一field下不同选项为or关系, 同一字典中不同字段间为and关系, 不同字典间为or关系, _not表示列表中的关键字都不含, 同一字典中的数字用来供应同一字段不同的条件之间的and---\"\"\"\n",
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"\"\"\"---设置关键字, 同一field下不同选项为or关系, 同一字典中不同字段间为and关系, 不同字典间为or关系, _not表示列表中的关键字都不含, 同一字典中的数字用来供应同一字段不同的条件之间的and---\"\"\"\n",
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"keywords_dict_table = [\n",
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"keywords_dict_table = [\n",
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" {\"tags\":[\"六\"]},\n",
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" {\"origin\":[\"测验\",\"考\"],\"tags\":[r\"[一二三五六]\"]}\n",
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" {\"tags\":[\"五\"],\"content\":[\"mathrm\",\"z\"]}\n",
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"]\n",
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"]\n",
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"\"\"\"---关键字设置完毕---\"\"\"\n",
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"\"\"\"---关键字设置完毕---\"\"\"\n",
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"# 示例： keywords_dict_table = [\n",
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"# 示例： keywords_dict_table = [\n",
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@ -86,7 +85,7 @@
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],
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],
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"metadata": {
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"metadata": {
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"kernelspec": {
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"kernelspec": {
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"display_name": "Python 3.8.8 ('base')",
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"display_name": "Python 3.9.7 ('base')",
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"language": "python",
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"language": "python",
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"name": "python3"
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"name": "python3"
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},
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},
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@ -100,12 +99,12 @@
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"name": "python",
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"name": "python",
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"nbconvert_exporter": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"pygments_lexer": "ipython3",
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"version": "3.8.8"
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"version": "3.9.7"
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},
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},
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"orig_nbformat": 4,
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"orig_nbformat": 4,
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"vscode": {
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"vscode": {
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"interpreter": {
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"interpreter": {
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"hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac"
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"hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba"
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}
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}
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}
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}
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},
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},
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"cells": [
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"cells": [
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{
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{
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"cell_type": "code",
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"cell_type": "code",
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"execution_count": 2,
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"execution_count": 3,
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"metadata": {},
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"metadata": {},
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"outputs": [
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"outputs": [
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{
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{
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"name": "stdout",
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"name": "stdout",
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"output_type": "stream",
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"output_type": "stream",
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"text": [
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"text": [
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"首行题目数量: 1650\n",
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"首行题目数量: 488\n",
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"剩余题目数量: 1448\n"
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"剩余题目数量: 421\n"
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]
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]
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}
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}
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],
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],
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@ -22,7 +22,7 @@
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"\"\"\"---设置题号列表文件结束---\"\"\"\n",
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"\"\"\"---设置题号列表文件结束---\"\"\"\n",
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"\n",
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"\n",
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"\"\"\"---设置要排除的题号所在的绝对路径---\"\"\"\n",
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"\"\"\"---设置要排除的题号所在的绝对路径---\"\"\"\n",
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"mainpath = r\"C:/Users/Weiye/Documents/wwy sync/23届/\"\n",
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"mainpath = r\"C:/Users/wang Weiye/Documents/wwy sync/23届/\"\n",
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"\n",
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"\n",
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"used_path_list = [\n",
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"used_path_list = [\n",
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"mainpath + \"第一轮复习讲义/\",\n",
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"mainpath + \"第一轮复习讲义/\",\n",
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],
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],
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"metadata": {
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"metadata": {
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"kernelspec": {
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"kernelspec": {
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"display_name": "Python 3.8.8 ('base')",
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"display_name": "Python 3.9.7 ('base')",
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"language": "python",
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"language": "python",
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"name": "python3"
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"name": "python3"
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},
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},
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"name": "python",
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"name": "python",
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"nbconvert_exporter": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"pygments_lexer": "ipython3",
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"version": "3.8.8"
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"version": "3.9.7"
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},
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},
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"orig_nbformat": 4,
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"orig_nbformat": 4,
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"vscode": {
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"vscode": {
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"interpreter": {
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"interpreter": {
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"hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac"
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"hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba"
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}
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}
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}
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}
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},
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},
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"cells": [
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"cells": [
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{
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{
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"cell_type": "code",
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"cell_type": "code",
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"execution_count": 2,
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"execution_count": 4,
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"metadata": {},
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"metadata": {},
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"outputs": [],
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"outputs": [],
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"source": [
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"source": [
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"import os,re,json,time\n",
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"import os,re,json,time\n",
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"\n",
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"\n",
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"\"\"\"---设置原题目id与新题目id---\"\"\"\n",
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"\"\"\"---设置原题目id与新题目id---\"\"\"\n",
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"old_id = \"9754\"\n",
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"old_id = \"10518\"\n",
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"new_id = \"30277\"\n",
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"new_id = \"30280\"\n",
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"\"\"\"---设置完毕---\"\"\"\n",
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"\"\"\"---设置完毕---\"\"\"\n",
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"\n",
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"\n",
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"old_id = old_id.zfill(6)\n",
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"old_id = old_id.zfill(6)\n",
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],
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],
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"metadata": {
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"metadata": {
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"kernelspec": {
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"kernelspec": {
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"display_name": "Python 3.8.8 ('base')",
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"display_name": "Python 3.9.7 ('base')",
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"language": "python",
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"language": "python",
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"name": "python3"
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"name": "python3"
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},
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},
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"name": "python",
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"name": "python",
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"nbconvert_exporter": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"pygments_lexer": "ipython3",
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"version": "3.8.8"
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"version": "3.9.7"
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},
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},
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"orig_nbformat": 4,
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"orig_nbformat": 4,
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"vscode": {
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"vscode": {
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"interpreter": {
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"interpreter": {
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"hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac"
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"hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba"
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}
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}
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}
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}
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},
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},
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"cells": [
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"cells": [
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{
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{
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"cell_type": "code",
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"cell_type": "code",
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"execution_count": 2,
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"execution_count": 4,
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"metadata": {},
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"metadata": {},
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"outputs": [
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"outputs": [
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{
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{
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"题块 1 处理完毕.\n",
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"题块 1 处理完毕.\n",
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"正在处理题块 2 .\n",
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"正在处理题块 2 .\n",
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"题块 2 处理完毕.\n",
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"题块 2 处理完毕.\n",
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||||||
"开始编译教师版本pdf文件: 临时文件/26_大数定律及独立性_教师_20221024.tex\n",
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"正在处理题块 3 .\n",
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"题块 3 处理完毕.\n",
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||||||
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"开始编译教师版本pdf文件: 临时文件/周末卷06_教师_20221025.tex\n",
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"0\n",
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"0\n",
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||||||
"开始编译学生版本pdf文件: 临时文件/26_大数定律及独立性_学生_20221024.tex\n",
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"开始编译学生版本pdf文件: 临时文件/周末卷06_学生_20221025.tex\n",
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"0\n"
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"0\n"
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]
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]
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}
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}
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"\"\"\"---设置模式结束---\"\"\"\n",
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"\"\"\"---设置模式结束---\"\"\"\n",
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"\n",
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"\n",
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"\"\"\"---设置模板文件名---\"\"\"\n",
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"\"\"\"---设置模板文件名---\"\"\"\n",
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"template_file = \"模板文件/第一轮复习讲义模板.tex\"\n",
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"# template_file = \"模板文件/第一轮复习讲义模板.tex\"\n",
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"# template_file = \"模板文件/测验周末卷模板.tex\"\n",
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"template_file = \"模板文件/测验周末卷模板.tex\"\n",
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"# template_file = \"模板文件/日常选题讲义模板.tex\"\n",
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"# template_file = \"模板文件/日常选题讲义模板.tex\"\n",
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"\"\"\"---设置模板文件名结束---\"\"\"\n",
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"\"\"\"---设置模板文件名结束---\"\"\"\n",
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"\n",
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"\n",
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"\"\"\"---设置其他预处理替换命令---\"\"\"\n",
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"\"\"\"---设置其他预处理替换命令---\"\"\"\n",
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"#2023届第一轮讲义更换标题\n",
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"#2023届第一轮讲义更换标题\n",
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"exec_list = [(\"标题数字待处理\",\"26\"),(\"标题文字待处理\",\"大数定律及独立性\")] \n",
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"# exec_list = [(\"标题数字待处理\",\"26\"),(\"标题文字待处理\",\"大数定律及独立性\")] \n",
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"enumi_mode = 0\n",
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"# enumi_mode = 0\n",
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"\n",
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"\n",
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"#2023届测验卷与周末卷\n",
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"#2023届测验卷与周末卷\n",
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"# exec_list = [(\"标题替换\",\"周末卷05\")]\n",
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"exec_list = [(\"标题替换\",\"周末卷06\")]\n",
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"# enumi_mode = 1\n",
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"enumi_mode = 1\n",
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"\n",
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"\n",
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"# 日常选题讲义\n",
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"# 日常选题讲义\n",
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"# exec_list = [(\"标题文字待处理\",\"2022年国庆卷(易错题订正)\")] \n",
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"# exec_list = [(\"标题文字待处理\",\"2022年国庆卷(易错题订正)\")] \n",
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"\"\"\"---其他预处理替换命令结束---\"\"\"\n",
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"\"\"\"---其他预处理替换命令结束---\"\"\"\n",
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"\n",
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"\n",
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"\"\"\"---设置目标文件名---\"\"\"\n",
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"\"\"\"---设置目标文件名---\"\"\"\n",
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"destination_file = \"临时文件/26_大数定律及独立性\"\n",
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"destination_file = \"临时文件/周末卷06\"\n",
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"\"\"\"---设置目标文件名结束---\"\"\"\n",
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"\"\"\"---设置目标文件名结束---\"\"\"\n",
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"\n",
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"\n",
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"\n",
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"\n",
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"\"\"\"---设置题号数据---\"\"\"\n",
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"\"\"\"---设置题号数据---\"\"\"\n",
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"problems = [\n",
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"problems = [\n",
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"\"30193,695,4150,9751,30188,10557,30189,224,230,9357,10554,226,10555,30194,30277,30191\",\n",
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"\"010497,010501,001726,30279,30280,001724,001668,030278,001631\",\n",
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"\"685,704,30186,30187,4324,30190,9749,10553,10558,9752,9753\"\n",
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"\"001676,010487,009998,010491\",\n",
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"\"010470,10533,010508,010000\"\n",
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"]\n",
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"]\n",
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"\"\"\"---设置题号数据结束---\"\"\"\n",
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"\"\"\"---设置题号数据结束---\"\"\"\n",
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"\n",
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"\n",
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],
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],
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"metadata": {
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"metadata": {
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"kernelspec": {
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"kernelspec": {
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"display_name": "Python 3.8.8 ('base')",
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"display_name": "Python 3.9.7 ('base')",
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"language": "python",
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"language": "python",
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"name": "python3"
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"name": "python3"
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},
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},
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"name": "python",
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"name": "python",
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"nbconvert_exporter": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"pygments_lexer": "ipython3",
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"version": "3.8.8"
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"version": "3.9.7"
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},
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},
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"orig_nbformat": 4,
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"orig_nbformat": 4,
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"vscode": {
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"vscode": {
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"interpreter": {
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"interpreter": {
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"hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac"
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"hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba"
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}
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}
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}
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}
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},
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"cells": [
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"cells": [
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{
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"cell_type": "code",
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"cell_type": "code",
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"execution_count": 8,
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"execution_count": 29,
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"metadata": {},
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"metadata": {},
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"outputs": [
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"outputs": [
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{
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{
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"name": "stdout",
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"name": "stdout",
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"output_type": "stream",
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"output_type": "stream",
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"text": [
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"text": [
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"开始编译教师版本pdf文件: 临时文件/test_教师用_20221022.tex\n",
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"开始编译教师版本pdf文件: 临时文件/test_教师用_20221025.tex\n",
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"0\n",
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"0\n",
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"开始编译学生版本pdf文件: 临时文件/test_学生用_20221022.tex\n",
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"开始编译学生版本pdf文件: 临时文件/test_学生用_20221025.tex\n",
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"0\n"
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"0\n"
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]
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]
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}
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}
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"\"\"\"---设置题目列表---\"\"\"\n",
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"\"\"\"---设置题目列表---\"\"\"\n",
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"#留空为编译全题库, a为读取临时文件中的题号筛选.txt文件生成题库\n",
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"#留空为编译全题库, a为读取临时文件中的题号筛选.txt文件生成题库\n",
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"problems = r\"\"\"\n",
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"problems = r\"\"\"\n",
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"a\n",
|
"003589,003590,003592,003593,003597,003601,003603,003604,003605,003607,003609,003610,003612,003613,003620,003622,003624,003625,003626,003628,003631,003632,003633,003636,003637,003642,003644,003646,003647,003649,003655,003656,003658,003665,003667,003668,003669,003673,003675,003676,003677,003679,003680,003681,003683,003689,003690,003693,003694,003695,003697,003698,003699,003700,004059,004061,004066,004067,004069,004070,004072,004074,004075,004076,004079,004081,004086,004088,004089,004090,004093,004094,004096,004097,004101,004102,004112,004113,004115,004117,004118,004119,004123,004124,004126,004130,004132,004133,004135,004136,004137,004138,004139,004143,004144,004145,004149,004151,004153,004154,004155,004159,004160,004162,004165,004168,004171,004172,004174,004175,004176,004177,004185,004186,004190,004191,004194,004198,004199,004200,004201,004202,004203,004205,004206,004208,004209,004214,004215,004217,004218,004219,004220,004221,004222,004223,004227,004228,004229,004230,004233,004234,004235,004236,004238,004241,004243,004244,004249,004253,004256,004258,004259,004261,004264,004266,004269,004270,004271,004272,004273,004274,004277,004278,004279,004284,004285,004286,004287,004289,004290,004291,004292,004293,004295,004301,004302,004305,004306,004307,004308,004311,004313,004314,004315,004316,004319,004323,004325,004326,004327,004329,004332,004333,004335,004336,004337,004339,004344,004345,004347,004348,004349,004350,004353,004354,004355,004357,004358,004360,004362,004364,004365,004366,004367,004368,004369,004371,004373,004374,004375,004376,004377,004378,004379,004380,004381,004382,004383,004384,004386,004387,004388,004389,004390,004391,004392,004393,004395,004396,004397,004398,004399,004401,004403,004404,004405,004406,004407,004408,004410,004411,004413,004415,004416,004417,004418,004419,004420,004421,004422,004423,004425,004426,004427,004429,004431,004432,004433,004434,004435,004436,004437,004438,004441,004442,004443,004445,004446,004447,004448,004449,004452,004454,004455,004456,004457,004458,004460,004461,004462,004463,004464,004465,004466,004468,004469,004470,004471,004477,004479,004481,004482,004483,004484,004485,004486,004489,004490,004493,004496,004498,004499,004500,004502,004503,004505,004506,004510,004512,004515,004516,004518,004520,004522,004523,004525,004526,004527,004530,004531,004532,004533,004540,004541,004542,004543,004544,004545,004546,004547,004549,004552,004554,004555,004556,004559,004562,004563,004564,004565,004567,004569,004571,004619,004620,004621,004623,004630,004631,004634,004635,004637,004640,004641,004645,004646,004649,004650,004652,004655,004656,004657,004658,004661,004662,004664,004665,004666,004667,004668,004669,004671,004673,004674,004675,004676,004677,004679,004681,004703,004704,004706,004707,004708,004714,004715,004719,004721,004745,004754,004755,004756,004757,004759,004760,004761,004762,004763,009984,009986,009988,009991,009994,009995,009996,009997,009998,010000,010001,010002\n",
|
||||||
|
"\n",
|
||||||
"\n",
|
"\n",
|
||||||
"\"\"\"\n",
|
"\"\"\"\n",
|
||||||
"\"\"\"---设置题目列表结束---\"\"\"\n",
|
"\"\"\"---设置题目列表结束---\"\"\"\n",
|
||||||
|
|
@ -174,7 +175,7 @@
|
||||||
],
|
],
|
||||||
"metadata": {
|
"metadata": {
|
||||||
"kernelspec": {
|
"kernelspec": {
|
||||||
"display_name": "Python 3.8.8 ('base')",
|
"display_name": "Python 3.9.7 ('base')",
|
||||||
"language": "python",
|
"language": "python",
|
||||||
"name": "python3"
|
"name": "python3"
|
||||||
},
|
},
|
||||||
|
|
@ -188,12 +189,12 @@
|
||||||
"name": "python",
|
"name": "python",
|
||||||
"nbconvert_exporter": "python",
|
"nbconvert_exporter": "python",
|
||||||
"pygments_lexer": "ipython3",
|
"pygments_lexer": "ipython3",
|
||||||
"version": "3.8.8"
|
"version": "3.9.7"
|
||||||
},
|
},
|
||||||
"orig_nbformat": 4,
|
"orig_nbformat": 4,
|
||||||
"vscode": {
|
"vscode": {
|
||||||
"interpreter": {
|
"interpreter": {
|
||||||
"hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac"
|
"hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba"
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
},
|
},
|
||||||
|
|
|
||||||
|
|
@ -42850,7 +42850,7 @@
|
||||||
},
|
},
|
||||||
"001631": {
|
"001631": {
|
||||||
"id": "001631",
|
"id": "001631",
|
||||||
"content": "直角$\\triangle ABC$所在平面外一点$P$到直角顶点$C$的距离为$5$, 到两直角边的距离均为$4$,则$PC$与平面$ABC$所成的角的正弦为\\blank{50}.",
|
"content": "直角$\\triangle ABC$所在平面外一点$P$到直角顶点$C$的距离为$5$, 到两直角边的距离均为$4$,则$PC$与平面$ABC$所成的角的正弦值为\\blank{50}.",
|
||||||
"objs": [],
|
"objs": [],
|
||||||
"tags": [
|
"tags": [
|
||||||
"第六单元"
|
"第六单元"
|
||||||
|
|
@ -42892,7 +42892,9 @@
|
||||||
"20220625\t王伟叶"
|
"20220625\t王伟叶"
|
||||||
],
|
],
|
||||||
"same": [],
|
"same": [],
|
||||||
"related": [],
|
"related": [
|
||||||
|
"030278"
|
||||||
|
],
|
||||||
"remark": "",
|
"remark": "",
|
||||||
"space": ""
|
"space": ""
|
||||||
},
|
},
|
||||||
|
|
@ -45198,7 +45200,7 @@
|
||||||
},
|
},
|
||||||
"001726": {
|
"001726": {
|
||||||
"id": "001726",
|
"id": "001726",
|
||||||
"content": "[选做]\n圆台上底面的面积为$4\\pi$, 下底面的面积为$16\\pi$, 其体积为$28\\pi$. 该圆台的母线和下底面所成角的大小为\\blank{80}.",
|
"content": "圆台上底面的面积为$4\\pi$, 下底面的面积为$16\\pi$, 其体积为$28\\pi$. 该圆台的母线和下底面所成角的大小为\\blank{80}.",
|
||||||
"objs": [],
|
"objs": [],
|
||||||
"tags": [
|
"tags": [
|
||||||
"第六单元"
|
"第六单元"
|
||||||
|
|
@ -113013,7 +113015,7 @@
|
||||||
},
|
},
|
||||||
"004462": {
|
"004462": {
|
||||||
"id": "004462",
|
"id": "004462",
|
||||||
"content": "在正三棱柱$ABC-A_1B_1C_1$中, $E,F$分别为棱$A_1B_1,A_1C_1$的中点, 去掉三棱锥$A_1-AEF$得到一个多面体$ABC-B_1C_1FE$. 已知$AB=6$, $BB_1=4$.\n\\begin{center}\n \\begin{tikzpicture}\n \\draw (0,0) node [left] {$A$} coordinate (A) -- (3,0) node [right] {$B$} coordinate (B) (A) ++ (1.5,0) ++ (45:{sqrt(3)*3/4}) node [above right] {$C$} coordinate (C);\n \\draw (A) ++ (0,2) node [left] {$A_1$} coordinate (A1);\n \\draw (B) ++ (0,2) node [right] {$B_1$} coordinate (B1);\n \\draw [dashed] (C) --++ (0,2) node [above] {$C_1$} coordinate (C1);\n \\draw (B) -- (B1) -- (C1);\n \\draw [dashed] (A) -- (C) -- (B);\n \\draw ($(A1)!0.5!(B1)$) node [above] {$E$} coordinate (E) ($(A1)!0.5!(C1)$) node [above] {$F$} coordinate (F);\n \\draw [dotted] (A1) -- (F) (A1) -- (E) (A) -- (A1);\n \\draw (A) -- (E) -- (B1) (E) -- (F) (A) -- (F) -- (C1);\n \\end{tikzpicture}\n\\end{center}\n(1) 求多面体$ABC-EFC_1B_1$的体积;\\\\\n(2) 求意面直线$AE$与$BC$所成角的大小.",
|
"content": "在正三棱柱$ABC-A_1B_1C_1$中, $E,F$分别为棱$A_1B_1,A_1C_1$的中点, 去掉三棱锥$A_1-AEF$得到一个多面体$ABC-B_1C_1FE$. 已知$AB=6$, $BB_1=4$.\n\\begin{center}\n \\begin{tikzpicture}\n \\draw (0,0) node [left] {$A$} coordinate (A) -- (3,0) node [right] {$B$} coordinate (B) (A) ++ (1.5,0) ++ (45:{sqrt(3)*3/4}) node [above right] {$C$} coordinate (C);\n \\draw (A) ++ (0,2) node [left] {$A_1$} coordinate (A1);\n \\draw (B) ++ (0,2) node [right] {$B_1$} coordinate (B1);\n \\draw [dashed] (C) --++ (0,2) node [above] {$C_1$} coordinate (C1);\n \\draw (B) -- (B1) -- (C1);\n \\draw [dashed] (A) -- (C) -- (B);\n \\draw ($(A1)!0.5!(B1)$) node [above] {$E$} coordinate (E) ($(A1)!0.5!(C1)$) node [above] {$F$} coordinate (F);\n \\draw [dotted] (A1) -- (F) (A1) -- (E) (A) -- (A1);\n \\draw (A) -- (E) -- (B1) (E) -- (F) (A) -- (F) -- (C1);\n \\end{tikzpicture}\n\\end{center}\n(1) 求多面体$ABC-EFC_1B_1$的体积;\\\\\n(2) 求异面直线$AE$与$BC$所成角的大小.",
|
||||||
"objs": [],
|
"objs": [],
|
||||||
"tags": [
|
"tags": [
|
||||||
"第六单元"
|
"第六单元"
|
||||||
|
|
@ -113089,7 +113091,7 @@
|
||||||
},
|
},
|
||||||
"004465": {
|
"004465": {
|
||||||
"id": "004465",
|
"id": "004465",
|
||||||
"content": "如图是函数$f(x)=A\\sin (\\omega x+\\varphi)$($A>0$, $\\omega>0$, $0\\le \\varphi\\le \\pi$)一个周期内的图像. 将$f(x)$图像上所有点的很顾总表伸长为原来的$2$倍, 纵坐标不变, 再把所得图像向右平移$\\dfrac\\pi 2$个单位长度, 得到函数$g(x)$的图像.\n\\begin{center}\n \\begin{tikzpicture}[>=latex]\n \\draw [->] (-1,0) -- (3,0) node [below] {$x$};\n \\draw [->] (0,-2.5) -- (0,2.5) node [left] {$y$};\n \\draw (0,0) node [below left] {$O$};\n \\draw [domain = -45:135, samples = 200] plot ({\\x/180*pi},{2*sin(2*\\x+90)});\n \\filldraw ({-pi/4},0) circle (0.03) node [above left] {$-\\frac\\pi 4$} ({pi/4},0) circle (0.03) node [above right] {$\\frac\\pi 4$};\n \\draw (0,2) node [above left] {$2$};\n \\draw [dashed] (0,-2) node [left] {$-2$} -- ({pi/2},-2) -- ({pi/2},0);\n \\end{tikzpicture}\n\\end{center}\n(1) 求函数$f(x)$和$g(x)$的解析式;\\\\\n(2) 若$f(x_0)=g(x_0)$, 求$\\sin (x_0\\dfrac\\pi 3)$的所有可能的值;\\\\\n(3) 求函数$F(x)=f(x)+ag(x)$($a$为正常数)在区间$(0,19\\pi)$内的所有零点之和.",
|
"content": "如图是函数$f(x)=A\\sin (\\omega x+\\varphi)$($A>0$, $\\omega>0$, $0\\le \\varphi\\le \\pi$)一个周期内的图像. 将$f(x)$图像上所有点的横坐标伸长为原来的$2$倍, 纵坐标不变, 再把所得图像向右平移$\\dfrac\\pi 2$个单位长度, 得到函数$g(x)$的图像.\n\\begin{center}\n \\begin{tikzpicture}[>=latex]\n \\draw [->] (-1,0) -- (3,0) node [below] {$x$};\n \\draw [->] (0,-2.5) -- (0,2.5) node [left] {$y$};\n \\draw (0,0) node [below left] {$O$};\n \\draw [domain = -45:135, samples = 200] plot ({\\x/180*pi},{2*sin(2*\\x+90)});\n \\filldraw ({-pi/4},0) circle (0.03) node [above left] {$-\\frac\\pi 4$} ({pi/4},0) circle (0.03) node [above right] {$\\frac\\pi 4$};\n \\draw (0,2) node [above left] {$2$};\n \\draw [dashed] (0,-2) node [left] {$-2$} -- ({pi/2},-2) -- ({pi/2},0);\n \\end{tikzpicture}\n\\end{center}\n(1) 求函数$f(x)$和$g(x)$的解析式;\\\\\n(2) 若$f(x_0)=g(x_0)$, 求$\\sin (x_0\\dfrac\\pi 3)$的所有可能的值;\\\\\n(3) 求函数$F(x)=f(x)+ag(x)$($a$为正常数)在区间$(0,19\\pi)$内的所有零点之和.",
|
||||||
"objs": [],
|
"objs": [],
|
||||||
"tags": [
|
"tags": [
|
||||||
"第三单元"
|
"第三单元"
|
||||||
|
|
@ -233518,7 +233520,7 @@
|
||||||
},
|
},
|
||||||
"009736": {
|
"009736": {
|
||||||
"id": "009736",
|
"id": "009736",
|
||||||
"content": "掷一颗骰子, 写出样本空间及与下列事件相对应的基本事件子集:\\\\\n(1) $1$没有出现;\\\\\n(2) 出现奇数;\\\\\n(3) 点数超过$2$.",
|
"content": "掷一颗骰子, 写出样本空间及与下列事件相对应的基本事件子集:\\\\\n\\textcircled{1} $1$没有出现;\\\\\n\\textcircled{2} 出现奇数;\\\\\n\\textcircled{3} 点数超过$2$.",
|
||||||
"objs": [
|
"objs": [
|
||||||
"K0802003B",
|
"K0802003B",
|
||||||
"K0802004B"
|
"K0802004B"
|
||||||
|
|
@ -251070,7 +251072,9 @@
|
||||||
"20220806\t王伟叶"
|
"20220806\t王伟叶"
|
||||||
],
|
],
|
||||||
"same": [],
|
"same": [],
|
||||||
"related": [],
|
"related": [
|
||||||
|
"030279"
|
||||||
|
],
|
||||||
"remark": "",
|
"remark": "",
|
||||||
"space": "12ex"
|
"space": "12ex"
|
||||||
},
|
},
|
||||||
|
|
@ -251235,7 +251239,9 @@
|
||||||
"20220806\t王伟叶"
|
"20220806\t王伟叶"
|
||||||
],
|
],
|
||||||
"same": [],
|
"same": [],
|
||||||
"related": [],
|
"related": [
|
||||||
|
"030280"
|
||||||
|
],
|
||||||
"remark": "",
|
"remark": "",
|
||||||
"space": "12ex"
|
"space": "12ex"
|
||||||
},
|
},
|
||||||
|
|
@ -251613,7 +251619,7 @@
|
||||||
},
|
},
|
||||||
"010535": {
|
"010535": {
|
||||||
"id": "010535",
|
"id": "010535",
|
||||||
"content": "抛掷$100$枚同一类型且质地均匀的硬币, 下面的陈述哪些是正确的, 哪些是错误的?\\\\\n(1) 全部出现正面向上是不可能的;\\\\\n(2) 至少有$1$枚出现正面向上是必然的;\\\\\n(3) 出现$50$枚正面向上、$50$枚正面向下是不确定的.",
|
"content": "抛掷$100$枚同一类型且质地均匀的硬币, 下面的陈述哪些是正确的, 哪些是错误的?\\\\\n\\textcircled{1} 全部出现正面向上是不可能的;\\\\\n\\textcircled{2} 至少有$1$枚出现正面向上是必然的;\\\\\n\\textcircled{3} 出现$50$枚正面向上、$50$枚正面向下是不确定的.",
|
||||||
"objs": [
|
"objs": [
|
||||||
"K0802005B"
|
"K0802005B"
|
||||||
],
|
],
|
||||||
|
|
@ -251705,7 +251711,7 @@
|
||||||
},
|
},
|
||||||
"010539": {
|
"010539": {
|
||||||
"id": "010539",
|
"id": "010539",
|
||||||
"content": "一个口袋中有大小与质地相同的$1$个白球、$2$个黑球、$3$个红球, 从中任取$2$个球, 观察球的颜色. 写出样本空间及与下列事件相应的基本事件子集:\\\\\n(1) 含有白球;\\\\\n(2) 至少含有$1$个黑球.",
|
"content": "一个口袋中有大小与质地相同的$1$个白球、$2$个黑球、$3$个红球, 从中任取$2$个球, 观察球的颜色. 写出样本空间及与下列事件相应的基本事件子集:\\\\\n\\textcircled{1} 含有白球;\\\\\n\\textcircled{2} 至少含有$1$个黑球.",
|
||||||
"objs": [
|
"objs": [
|
||||||
"K0802003B",
|
"K0802003B",
|
||||||
"K0802004B"
|
"K0802004B"
|
||||||
|
|
@ -296508,5 +296514,82 @@
|
||||||
],
|
],
|
||||||
"remark": "",
|
"remark": "",
|
||||||
"space": "12ex"
|
"space": "12ex"
|
||||||
|
},
|
||||||
|
"030278": {
|
||||||
|
"id": "030278",
|
||||||
|
"content": "$P$为$\\triangle ABC$所在平面$\\alpha$外一点, 且$PA=PB=PC=10$, $AB=6$, $BC=8$, $CA=10$, 则$P$到平面$ABC$的距离为\\blank{50}.",
|
||||||
|
"objs": [],
|
||||||
|
"tags": [
|
||||||
|
"第六单元"
|
||||||
|
],
|
||||||
|
"genre": "填空题",
|
||||||
|
"ans": "",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "2016届创新班作业\t2209-直线与平面所成的角[1]-20221025修改",
|
||||||
|
"edit": [
|
||||||
|
"20220625\t王伟叶",
|
||||||
|
"20221025\t王伟叶"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [
|
||||||
|
"001632"
|
||||||
|
],
|
||||||
|
"remark": "",
|
||||||
|
"space": ""
|
||||||
|
},
|
||||||
|
"030279": {
|
||||||
|
"id": "030279",
|
||||||
|
"content": "若圆锥的底面半径为$1$, 高为$\\sqrt 3$, 则圆锥的表面积为\\blank{50}.",
|
||||||
|
"objs": [
|
||||||
|
"K0620004B"
|
||||||
|
],
|
||||||
|
"tags": [
|
||||||
|
"第六单元"
|
||||||
|
],
|
||||||
|
"genre": "填空题",
|
||||||
|
"ans": "",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "新教材必修第三册习题-20221025修改",
|
||||||
|
"edit": [
|
||||||
|
"20220806\t王伟叶",
|
||||||
|
"20221025\t朱敏慧"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [
|
||||||
|
"010511"
|
||||||
|
],
|
||||||
|
"remark": "",
|
||||||
|
"space": ""
|
||||||
|
},
|
||||||
|
"030280": {
|
||||||
|
"id": "030280",
|
||||||
|
"content": "设圆台的母线长为$l$, 上、下底面的半径分别为$r'$、$r$. 用$r'$、$r$和$l$表示圆台的侧面积, 所得结果为\\blank{50}.",
|
||||||
|
"objs": [
|
||||||
|
"K0618007B",
|
||||||
|
"K0620004B"
|
||||||
|
],
|
||||||
|
"tags": [
|
||||||
|
"第六单元"
|
||||||
|
],
|
||||||
|
"genre": "填空题",
|
||||||
|
"ans": "",
|
||||||
|
"solution": "",
|
||||||
|
"duration": -1,
|
||||||
|
"usages": [],
|
||||||
|
"origin": "新教材必修第三册习题-20221025修改",
|
||||||
|
"edit": [
|
||||||
|
"20220806\t王伟叶",
|
||||||
|
"20221025\t朱敏慧"
|
||||||
|
],
|
||||||
|
"same": [],
|
||||||
|
"related": [
|
||||||
|
"010518"
|
||||||
|
],
|
||||||
|
"remark": "",
|
||||||
|
"space": ""
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
Reference in New Issue