收录高二寒假作业1新题
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20240131-164456
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024412,030659,000737,024413:024414,011267,024415:024417,017631
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20240203-220459 高二寒假作业1
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024418:024422,017769,024423:024424
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],
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"000341",
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"020919"
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"024421"
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"20220730\t王伟叶"
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"20220806\t王伟叶"
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],
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"related": [
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"same": [
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"009147"
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"related": [],
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"024421"
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@ -661594,6 +661603,155 @@
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"space": "",
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"unrelated": []
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},
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"024418": {
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"id": "024418",
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"content": "一条直线与直线外四点, 它们最多可确定\\blank{50}个平面, 最少可确定\\blank{50}个平面.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20240203\t杨懿荔"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"024419": {
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"id": "024419",
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"content": "正方体 $ABCD-A_1B_1C_1D_1$ 的棱长为 $a$, 那么:\\\\\n(1) 哪些棱所在直线与直线 $BA_1$ 成异面直线?\\blank{50}.\\\\\n(2) 直线 $BA_1$ 与 $CC_1$ 所成角的大小为\\blank{50}.\\\\\n(3) 直线 $BA_1$ 与 $B_1C$ 所成角的大小为\\blank{50}.\\\\\n(4) 异面直线 $BC$ 与 $AA_1$ 的距离为\\blank{50}.\\\\\n(5) 异面直线 $BA_1$ 与 $CC_1$ 的距离是\\blank{50}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20240203\t杨懿荔"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"024420": {
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"id": "024420",
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"content": "在空间四边形 $ABCD$ 中, $E$、$F$、$G$、$H$ 分别是边 $AB$、$BC$、$CD$、$DA$ 的中点.\\\\\n(1) 若 $AC=BD$, 则 $EFGH$ 是\\blank{50};\\\\\n(2) 若 $AC \\perp BD$, 则 $EFGH$ 是\\blank{50}形;\\\\\n(3) 若 $AC=BD$ 且 $AC \\perp BD$, 则 $EFGH$ 是\\blank{50}形.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20240203\t杨懿荔"
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],
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"same": [],
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"related": [
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"010455"
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"024421": {
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"id": "024421",
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"content": "设正方体 $ABCD-A_1B_1C_1D_1$ 的棱长为 $\\mathbf{1}$, 那么,\\\\\n(1) $A$ 点到 $CD_1$ 的距离为\\blank{50}.\\\\\n(2) $A$ 点到 $BD_1$ 的距离为\\blank{50}.\\\\\n(3) $A$ 点到面 $BDD_1B_1$ 的距离为\\blank{50}.\\\\\n(4) $A$ 点到面 $A_1BD$ 的距离为\\blank{50}.\\\\\n(5) $AA_1$ 与面 $BDD_1B_1$ 的距离为\\blank{50}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20240203\t杨懿荔"
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],
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"same": [],
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"related": [
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"009147",
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"020919",
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"009698"
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],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"024422": {
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"id": "024422",
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"content": "长方体 $AC_1$ 中, 对角线 $BD_1$ 与棱 $BA$、$BC$ 所成的角分别为 $60^{\\circ}$、$45^{\\circ}$, 则对角线 $BD_1$ 与 $BB_1$ 所成的角的大小为\\blank{50}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20240203\t杨懿荔"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"024423": {
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"id": "024423",
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"content": "在长方体 $ABCD-A_1B_1C_1D_1$ 中, $AB=BC=2$, $AA_1=1$, 则 $BC_1$ 与平面 $BB_1D_1D$ 所成角的大小为\\blank{50}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20240203\t杨懿荔"
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],
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"same": [],
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"related": [
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"003488",
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"031552"
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],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"024424": {
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"id": "024424",
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"content": "$A$、$B$ 两点相距 $4 \\mathrm{cm}$, 且 $A$、$B$ 与平面 $\\alpha$ 的距离分别为 $3 \\mathrm{cm}$ 和 $1 \\mathrm{cm}$, 则 $AB$ 与平面 $\\alpha$ 所成的角的大小是\\bracket{20}.\n\\fourch{$30^{\\circ}$}{$90^{\\circ}$}{$30^{\\circ}$ 或 $90^{\\circ}$}{$30^{\\circ}$ 或 $90^{\\circ}$ 或 $150^{\\circ}$}",
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"objs": [],
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"tags": [],
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"genre": "选择题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20240203\t杨懿荔"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"030001": {
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"id": "030001",
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"content": "若$x,y,z$都是实数, 则:(填写``\\textcircled{1} 充分非必要、\\textcircled{2} 必要非充分、\\textcircled{3} 充要、\\textcircled{4} 既非充分又非必要''之一)\\\\\n(1) ``$xy=0$''是``$x=0$''的\\blank{50}条件;\\\\\n(2) ``$x\\cdot y=y\\cdot z$''是``$x=z$''的\\blank{50}条件;\\\\\n(3) ``$\\dfrac xy=\\dfrac yz$''是``$xz=y^2$''的\\blank{50}条件;\\\\\n(4) ``$|x |>| y|$''是``$x>y>0$''的\\blank{50}条件;\\\\\n(5) ``$x^2>4$''是``$x>2$'' 的\\blank{50}条件;\\\\\n(6) ``$x=-3$''是``$x^2+x-6=0$'' 的\\blank{50}条件;\\\\\n(7) ``$|x+y|<2$''是``$|x|<1$且$|y|<1$'' 的\\blank{50}条件;\\\\\n(8) ``$|x|<3$''是``$x^2<9$'' 的\\blank{50}条件;\\\\\n(9) ``$x^2+y^2>0$''是``$x\\ne 0$'' 的\\blank{50}条件;\\\\\n(10) ``$\\dfrac{x^2+x+1}{3x+2}<0$''是``$3x+2<0$'' 的\\blank{50}条件;\\\\\n(11) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",
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"20230730\t王伟叶"
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],
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"same": [],
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"related": [],
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"related": [
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"024423"
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],
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"remark": "",
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"space": "",
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"unrelated": []
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