论坛 › 开心茶馆 › 蹬高游戏

王守恩 发表于 2019-4-12 11:00:02

蹬高游戏

蹬高台阶共35级，每次可以蹬 2 级或 3 级，
个位数是 4 的不能蹬，个位数是 8 的必须蹬，问有多少种蹬法？

倪举鹏 发表于 2019-4-12 11:56:42

母函数加排除法

zeroieme 发表于 2019-4-12 12:29:26

你们真的觉得论坛里爬楼梯的题目不够多吗

逢8必蹬，于是中间段是$x^n$，前后段生成函数计算，相乘。

markfang2050 发表于 2019-4-12 17:03:29

真的觉得论坛里爬楼梯的题目不够多吗

markfang2050 发表于 2019-4-12 18:51:09

倪举鹏 发表于 2019-4-12 11:56
母函数加排除法

期待大佬写程序

王守恩 发表于 2019-4-13 06:40:23

本帖最后由 王守恩 于 2019-4-13 06:41 编辑

markfang2050 发表于 2019-4-12 18:51
期待大佬写程序

谢谢 zeroieme ！   逢\(\ \ 8\ \ \)必蹬！于是中间段是\(\ \ x^n\)，前后段生成函数计算，相乘。
前段：第 1 级到第 8 级有 3 种蹬法，
中间段：分2节，8——18——28，每节有 5 种蹬法，
后段：第 28 级到第 35 级有 3 种蹬法，
合计：3×5^2×3=225 种蹬法。

markfang2050 发表于 2019-4-13 16:27:05

程序计算得
-------------------
225

markfang2050 发表于 2019-4-13 17:02:22

{{2, 5, 8, 10, 12, 15, 18, 20, 22, 25, 28, 30, 32, 35}, {2, 5, 8, 10,
12, 15, 18, 20, 22, 25, 28, 30, 33, 35}, {2, 5, 8, 10, 12, 15, 18,
20, 22, 25, 28, 31, 33, 35}, {2, 5, 8, 10, 12, 15, 18, 20, 23, 25,
28, 30, 32, 35}, {2, 5, 8, 10, 12, 15, 18, 20, 23, 25, 28, 30, 33,
35}, {2, 5, 8, 10, 12, 15, 18, 20, 23, 25, 28, 31, 33, 35}, {2, 5,
8, 10, 12, 15, 18, 20, 23, 26, 28, 30, 32, 35}, {2, 5, 8, 10, 12,
15, 18, 20, 23, 26, 28, 30, 33, 35}, {2, 5, 8, 10, 12, 15, 18, 20,
23, 26, 28, 31, 33, 35}, {2, 5, 8, 10, 12, 15, 18, 21, 23, 25, 28,
30, 32, 35}, {2, 5, 8, 10, 12, 15, 18, 21, 23, 25, 28, 30, 33,
35}, {2, 5, 8, 10, 12, 15, 18, 21, 23, 25, 28, 31, 33, 35}, {2, 5,
8, 10, 12, 15, 18, 21, 23, 26, 28, 30, 32, 35}, {2, 5, 8, 10, 12,
15, 18, 21, 23, 26, 28, 30, 33, 35}, {2, 5, 8, 10, 12, 15, 18, 21,
23, 26, 28, 31, 33, 35}, {2, 5, 8, 10, 13, 15, 18, 20, 22, 25, 28,
30, 32, 35}, {2, 5, 8, 10, 13, 15, 18, 20, 22, 25, 28, 30, 33,
35}, {2, 5, 8, 10, 13, 15, 18, 20, 22, 25, 28, 31, 33, 35}, {2, 5,
8, 10, 13, 15, 18, 20, 23, 25, 28, 30, 32, 35}, {2, 5, 8, 10, 13,
15, 18, 20, 23, 25, 28, 30, 33, 35}, {2, 5, 8, 10, 13, 15, 18, 20,
23, 25, 28, 31, 33, 35}, {2, 5, 8, 10, 13, 15, 18, 20, 23, 26, 28,
30, 32, 35}, {2, 5, 8, 10, 13, 15, 18, 20, 23, 26, 28, 30, 33,
35}, {2, 5, 8, 10, 13, 15, 18, 20, 23, 26, 28, 31, 33, 35}, {2, 5,
8, 10, 13, 15, 18, 21, 23, 25, 28, 30, 32, 35}, {2, 5, 8, 10, 13,
15, 18, 21, 23, 25, 28, 30, 33, 35}, {2, 5, 8, 10, 13, 15, 18, 21,
23, 25, 28, 31, 33, 35}, {2, 5, 8, 10, 13, 15, 18, 21, 23, 26, 28,
30, 32, 35}, {2, 5, 8, 10, 13, 15, 18, 21, 23, 26, 28, 30, 33,
35}, {2, 5, 8, 10, 13, 15, 18, 21, 23, 26, 28, 31, 33, 35}, {2, 5,
8, 10, 13, 16, 18, 20, 22, 25, 28, 30, 32, 35}, {2, 5, 8, 10, 13,
16, 18, 20, 22, 25, 28, 30, 33, 35}, {2, 5, 8, 10, 13, 16, 18, 20,
22, 25, 28, 31, 33, 35}, {2, 5, 8, 10, 13, 16, 18, 20, 23, 25, 28,
30, 32, 35}, {2, 5, 8, 10, 13, 16, 18, 20, 23, 25, 28, 30, 33,
35}, {2, 5, 8, 10, 13, 16, 18, 20, 23, 25, 28, 31, 33, 35}, {2, 5,
8, 10, 13, 16, 18, 20, 23, 26, 28, 30, 32, 35}, {2, 5, 8, 10, 13,
16, 18, 20, 23, 26, 28, 30, 33, 35}, {2, 5, 8, 10, 13, 16, 18, 20,
23, 26, 28, 31, 33, 35}, {2, 5, 8, 10, 13, 16, 18, 21, 23, 25, 28,
30, 32, 35}, {2, 5, 8, 10, 13, 16, 18, 21, 23, 25, 28, 30, 33,
35}, {2, 5, 8, 10, 13, 16, 18, 21, 23, 25, 28, 31, 33, 35}, {2, 5,
8, 10, 13, 16, 18, 21, 23, 26, 28, 30, 32, 35}, {2, 5, 8, 10, 13,
16, 18, 21, 23, 26, 28, 30, 33, 35}, {2, 5, 8, 10, 13, 16, 18, 21,
23, 26, 28, 31, 33, 35}, {2, 5, 8, 11, 13, 15, 18, 20, 22, 25, 28,
30, 32, 35}, {2, 5, 8, 11, 13, 15, 18, 20, 22, 25, 28, 30, 33,
35}, {2, 5, 8, 11, 13, 15, 18, 20, 22, 25, 28, 31, 33, 35}, {2, 5,
8, 11, 13, 15, 18, 20, 23, 25, 28, 30, 32, 35}, {2, 5, 8, 11, 13,
15, 18, 20, 23, 25, 28, 30, 33, 35}, {2, 5, 8, 11, 13, 15, 18, 20,
23, 25, 28, 31, 33, 35}, {2, 5, 8, 11, 13, 15, 18, 20, 23, 26, 28,
30, 32, 35}, {2, 5, 8, 11, 13, 15, 18, 20, 23, 26, 28, 30, 33,
35}, {2, 5, 8, 11, 13, 15, 18, 20, 23, 26, 28, 31, 33, 35}, {2, 5,
8, 11, 13, 15, 18, 21, 23, 25, 28, 30, 32, 35}, {2, 5, 8, 11, 13,
15, 18, 21, 23, 25, 28, 30, 33, 35}, {2, 5, 8, 11, 13, 15, 18, 21,
23, 25, 28, 31, 33, 35}, {2, 5, 8, 11, 13, 15, 18, 21, 23, 26, 28,
30, 32, 35}, {2, 5, 8, 11, 13, 15, 18, 21, 23, 26, 28, 30, 33,
35}, {2, 5, 8, 11, 13, 15, 18, 21, 23, 26, 28, 31, 33, 35}, {2, 5,
8, 11, 13, 16, 18, 20, 22, 25, 28, 30, 32, 35}, {2, 5, 8, 11, 13,
16, 18, 20, 22, 25, 28, 30, 33, 35}, {2, 5, 8, 11, 13, 16, 18, 20,
22, 25, 28, 31, 33, 35}, {2, 5, 8, 11, 13, 16, 18, 20, 23, 25, 28,
30, 32, 35}, {2, 5, 8, 11, 13, 16, 18, 20, 23, 25, 28, 30, 33,
35}, {2, 5, 8, 11, 13, 16, 18, 20, 23, 25, 28, 31, 33, 35}, {2, 5,
8, 11, 13, 16, 18, 20, 23, 26, 28, 30, 32, 35}, {2, 5, 8, 11, 13,
16, 18, 20, 23, 26, 28, 30, 33, 35}, {2, 5, 8, 11, 13, 16, 18, 20,
23, 26, 28, 31, 33, 35}, {2, 5, 8, 11, 13, 16, 18, 21, 23, 25, 28,
30, 32, 35}, {2, 5, 8, 11, 13, 16, 18, 21, 23, 25, 28, 30, 33,
35}, {2, 5, 8, 11, 13, 16, 18, 21, 23, 25, 28, 31, 33, 35}, {2, 5,
8, 11, 13, 16, 18, 21, 23, 26, 28, 30, 32, 35}, {2, 5, 8, 11, 13,
16, 18, 21, 23, 26, 28, 30, 33, 35}, {2, 5, 8, 11, 13, 16, 18, 21,
23, 26, 28, 31, 33, 35}, {3, 5, 8, 10, 12, 15, 18, 20, 22, 25, 28,
30, 32, 35}, {3, 5, 8, 10, 12, 15, 18, 20, 22, 25, 28, 30, 33,
35}, {3, 5, 8, 10, 12, 15, 18, 20, 22, 25, 28, 31, 33, 35}, {3, 5,
8, 10, 12, 15, 18, 20, 23, 25, 28, 30, 32, 35}, {3, 5, 8, 10, 12,
15, 18, 20, 23, 25, 28, 30, 33, 35}, {3, 5, 8, 10, 12, 15, 18, 20,
23, 25, 28, 31, 33, 35}, {3, 5, 8, 10, 12, 15, 18, 20, 23, 26, 28,
30, 32, 35}, {3, 5, 8, 10, 12, 15, 18, 20, 23, 26, 28, 30, 33,
35}, {3, 5, 8, 10, 12, 15, 18, 20, 23, 26, 28, 31, 33, 35}, {3, 5,
8, 10, 12, 15, 18, 21, 23, 25, 28, 30, 32, 35}, {3, 5, 8, 10, 12,
15, 18, 21, 23, 25, 28, 30, 33, 35}, {3, 5, 8, 10, 12, 15, 18, 21,
23, 25, 28, 31, 33, 35}, {3, 5, 8, 10, 12, 15, 18, 21, 23, 26, 28,
30, 32, 35}, {3, 5, 8, 10, 12, 15, 18, 21, 23, 26, 28, 30, 33,
35}, {3, 5, 8, 10, 12, 15, 18, 21, 23, 26, 28, 31, 33, 35}, {3, 5,
8, 10, 13, 15, 18, 20, 22, 25, 28, 30, 32, 35}, {3, 5, 8, 10, 13,
15, 18, 20, 22, 25, 28, 30, 33, 35}, {3, 5, 8, 10, 13, 15, 18, 20,
22, 25, 28, 31, 33, 35}, {3, 5, 8, 10, 13, 15, 18, 20, 23, 25, 28,
30, 32, 35}, {3, 5, 8, 10, 13, 15, 18, 20, 23, 25, 28, 30, 33,
35}, {3, 5, 8, 10, 13, 15, 18, 20, 23, 25, 28, 31, 33, 35}, {3, 5,
8, 10, 13, 15, 18, 20, 23, 26, 28, 30, 32, 35}, {3, 5, 8, 10, 13,
15, 18, 20, 23, 26, 28, 30, 33, 35}, {3, 5, 8, 10, 13, 15, 18, 20,
23, 26, 28, 31, 33, 35}, {3, 5, 8, 10, 13, 15, 18, 21, 23, 25, 28,
30, 32, 35}, {3, 5, 8, 10, 13, 15, 18, 21, 23, 25, 28, 30, 33,
35}, {3, 5, 8, 10, 13, 15, 18, 21, 23, 25, 28, 31, 33, 35}, {3, 5,
8, 10, 13, 15, 18, 21, 23, 26, 28, 30, 32, 35}, {3, 5, 8, 10, 13,
15, 18, 21, 23, 26, 28, 30, 33, 35}, {3, 5, 8, 10, 13, 15, 18, 21,
23, 26, 28, 31, 33, 35}, {3, 5, 8, 10, 13, 16, 18, 20, 22, 25, 28,
30, 32, 35}, {3, 5, 8, 10, 13, 16, 18, 20, 22, 25, 28, 30, 33,
35}, {3, 5, 8, 10, 13, 16, 18, 20, 22, 25, 28, 31, 33, 35}, {3, 5,
8, 10, 13, 16, 18, 20, 23, 25, 28, 30, 32, 35}, {3, 5, 8, 10, 13,
16, 18, 20, 23, 25, 28, 30, 33, 35}, {3, 5, 8, 10, 13, 16, 18, 20,
23, 25, 28, 31, 33, 35}, {3, 5, 8, 10, 13, 16, 18, 20, 23, 26, 28,
30, 32, 35}, {3, 5, 8, 10, 13, 16, 18, 20, 23, 26, 28, 30, 33,
35}, {3, 5, 8, 10, 13, 16, 18, 20, 23, 26, 28, 31, 33, 35}, {3, 5,
8, 10, 13, 16, 18, 21, 23, 25, 28, 30, 32, 35}, {3, 5, 8, 10, 13,
16, 18, 21, 23, 25, 28, 30, 33, 35}, {3, 5, 8, 10, 13, 16, 18, 21,
23, 25, 28, 31, 33, 35}, {3, 5, 8, 10, 13, 16, 18, 21, 23, 26, 28,
30, 32, 35}, {3, 5, 8, 10, 13, 16, 18, 21, 23, 26, 28, 30, 33,
35}, {3, 5, 8, 10, 13, 16, 18, 21, 23, 26, 28, 31, 33, 35}, {3, 5,
8, 11, 13, 15, 18, 20, 22, 25, 28, 30, 32, 35}, {3, 5, 8, 11, 13,
15, 18, 20, 22, 25, 28, 30, 33, 35}, {3, 5, 8, 11, 13, 15, 18, 20,
22, 25, 28, 31, 33, 35}, {3, 5, 8, 11, 13, 15, 18, 20, 23, 25, 28,
30, 32, 35}, {3, 5, 8, 11, 13, 15, 18, 20, 23, 25, 28, 30, 33,
35}, {3, 5, 8, 11, 13, 15, 18, 20, 23, 25, 28, 31, 33, 35}, {3, 5,
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15, 18, 20, 23, 26, 28, 30, 33, 35}, {3, 5, 8, 11, 13, 15, 18, 20,
23, 26, 28, 31, 33, 35}, {3, 5, 8, 11, 13, 15, 18, 21, 23, 25, 28,
30, 32, 35}, {3, 5, 8, 11, 13, 15, 18, 21, 23, 25, 28, 30, 33,
35}, {3, 5, 8, 11, 13, 15, 18, 21, 23, 25, 28, 31, 33, 35}, {3, 5,
8, 11, 13, 15, 18, 21, 23, 26, 28, 30, 32, 35}, {3, 5, 8, 11, 13,
15, 18, 21, 23, 26, 28, 30, 33, 35}, {3, 5, 8, 11, 13, 15, 18, 21,
23, 26, 28, 31, 33, 35}, {3, 5, 8, 11, 13, 16, 18, 20, 22, 25, 28,
30, 32, 35}, {3, 5, 8, 11, 13, 16, 18, 20, 22, 25, 28, 30, 33,
35}, {3, 5, 8, 11, 13, 16, 18, 20, 22, 25, 28, 31, 33, 35}, {3, 5,
8, 11, 13, 16, 18, 20, 23, 25, 28, 30, 32, 35}, {3, 5, 8, 11, 13,
16, 18, 20, 23, 25, 28, 30, 33, 35}, {3, 5, 8, 11, 13, 16, 18, 20,
23, 25, 28, 31, 33, 35}, {3, 5, 8, 11, 13, 16, 18, 20, 23, 26, 28,
30, 32, 35}, {3, 5, 8, 11, 13, 16, 18, 20, 23, 26, 28, 30, 33,
35}, {3, 5, 8, 11, 13, 16, 18, 20, 23, 26, 28, 31, 33, 35}, {3, 5,
8, 11, 13, 16, 18, 21, 23, 25, 28, 30, 32, 35}, {3, 5, 8, 11, 13,
16, 18, 21, 23, 25, 28, 30, 33, 35}, {3, 5, 8, 11, 13, 16, 18, 21,
23, 25, 28, 31, 33, 35}, {3, 5, 8, 11, 13, 16, 18, 21, 23, 26, 28,
30, 32, 35}, {3, 5, 8, 11, 13, 16, 18, 21, 23, 26, 28, 30, 33,
35}, {3, 5, 8, 11, 13, 16, 18, 21, 23, 26, 28, 31, 33, 35}, {3, 6,
8, 10, 12, 15, 18, 20, 22, 25, 28, 30, 32, 35}, {3, 6, 8, 10, 12,
15, 18, 20, 22, 25, 28, 30, 33, 35}, {3, 6, 8, 10, 12, 15, 18, 20,
22, 25, 28, 31, 33, 35}, {3, 6, 8, 10, 12, 15, 18, 20, 23, 25, 28,
30, 32, 35}, {3, 6, 8, 10, 12, 15, 18, 20, 23, 25, 28, 30, 33,
35}, {3, 6, 8, 10, 12, 15, 18, 20, 23, 25, 28, 31, 33, 35}, {3, 6,
8, 10, 12, 15, 18, 20, 23, 26, 28, 30, 32, 35}, {3, 6, 8, 10, 12,
15, 18, 20, 23, 26, 28, 30, 33, 35}, {3, 6, 8, 10, 12, 15, 18, 20,
23, 26, 28, 31, 33, 35}, {3, 6, 8, 10, 12, 15, 18, 21, 23, 25, 28,
30, 32, 35}, {3, 6, 8, 10, 12, 15, 18, 21, 23, 25, 28, 30, 33,
35}, {3, 6, 8, 10, 12, 15, 18, 21, 23, 25, 28, 31, 33, 35}, {3, 6,
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15, 18, 21, 23, 26, 28, 30, 33, 35}, {3, 6, 8, 10, 12, 15, 18, 21,
23, 26, 28, 31, 33, 35}, {3, 6, 8, 10, 13, 15, 18, 20, 22, 25, 28,
30, 32, 35}, {3, 6, 8, 10, 13, 15, 18, 20, 22, 25, 28, 30, 33,
35}, {3, 6, 8, 10, 13, 15, 18, 20, 22, 25, 28, 31, 33, 35}, {3, 6,
8, 10, 13, 15, 18, 20, 23, 25, 28, 30, 32, 35}, {3, 6, 8, 10, 13,
15, 18, 20, 23, 25, 28, 30, 33, 35}, {3, 6, 8, 10, 13, 15, 18, 20,
23, 25, 28, 31, 33, 35}, {3, 6, 8, 10, 13, 15, 18, 20, 23, 26, 28,
30, 32, 35}, {3, 6, 8, 10, 13, 15, 18, 20, 23, 26, 28, 30, 33,
35}, {3, 6, 8, 10, 13, 15, 18, 20, 23, 26, 28, 31, 33, 35}, {3, 6,
8, 10, 13, 15, 18, 21, 23, 25, 28, 30, 32, 35}, {3, 6, 8, 10, 13,
15, 18, 21, 23, 25, 28, 30, 33, 35}, {3, 6, 8, 10, 13, 15, 18, 21,
23, 25, 28, 31, 33, 35}, {3, 6, 8, 10, 13, 15, 18, 21, 23, 26, 28,
30, 32, 35}, {3, 6, 8, 10, 13, 15, 18, 21, 23, 26, 28, 30, 33,
35}, {3, 6, 8, 10, 13, 15, 18, 21, 23, 26, 28, 31, 33, 35}, {3, 6,
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16, 18, 20, 22, 25, 28, 30, 33, 35}, {3, 6, 8, 10, 13, 16, 18, 20,
22, 25, 28, 31, 33, 35}, {3, 6, 8, 10, 13, 16, 18, 20, 23, 25, 28,
30, 32, 35}, {3, 6, 8, 10, 13, 16, 18, 20, 23, 25, 28, 30, 33,
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16, 18, 20, 23, 26, 28, 30, 33, 35}, {3, 6, 8, 10, 13, 16, 18, 20,
23, 26, 28, 31, 33, 35}, {3, 6, 8, 10, 13, 16, 18, 21, 23, 25, 28,
30, 32, 35}, {3, 6, 8, 10, 13, 16, 18, 21, 23, 25, 28, 30, 33,
35}, {3, 6, 8, 10, 13, 16, 18, 21, 23, 25, 28, 31, 33, 35}, {3, 6,
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16, 18, 21, 23, 26, 28, 30, 33, 35}, {3, 6, 8, 10, 13, 16, 18, 21,
23, 26, 28, 31, 33, 35}, {3, 6, 8, 11, 13, 15, 18, 20, 22, 25, 28,
30, 32, 35}, {3, 6, 8, 11, 13, 15, 18, 20, 22, 25, 28, 30, 33,
35}, {3, 6, 8, 11, 13, 15, 18, 20, 22, 25, 28, 31, 33, 35}, {3, 6,
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15, 18, 20, 23, 25, 28, 30, 33, 35}, {3, 6, 8, 11, 13, 15, 18, 20,
23, 25, 28, 31, 33, 35}, {3, 6, 8, 11, 13, 15, 18, 20, 23, 26, 28,
30, 32, 35}, {3, 6, 8, 11, 13, 15, 18, 20, 23, 26, 28, 30, 33,
35}, {3, 6, 8, 11, 13, 15, 18, 20, 23, 26, 28, 31, 33, 35}, {3, 6,
8, 11, 13, 15, 18, 21, 23, 25, 28, 30, 32, 35}, {3, 6, 8, 11, 13,
15, 18, 21, 23, 25, 28, 30, 33, 35}, {3, 6, 8, 11, 13, 15, 18, 21,
23, 25, 28, 31, 33, 35}, {3, 6, 8, 11, 13, 15, 18, 21, 23, 26, 28,
30, 32, 35}, {3, 6, 8, 11, 13, 15, 18, 21, 23, 26, 28, 30, 33,
35}, {3, 6, 8, 11, 13, 15, 18, 21, 23, 26, 28, 31, 33, 35}, {3, 6,
8, 11, 13, 16, 18, 20, 22, 25, 28, 30, 32, 35}, {3, 6, 8, 11, 13,
16, 18, 20, 22, 25, 28, 30, 33, 35}, {3, 6, 8, 11, 13, 16, 18, 20,
22, 25, 28, 31, 33, 35}, {3, 6, 8, 11, 13, 16, 18, 20, 23, 25, 28,
30, 32, 35}, {3, 6, 8, 11, 13, 16, 18, 20, 23, 25, 28, 30, 33,
35}, {3, 6, 8, 11, 13, 16, 18, 20, 23, 25, 28, 31, 33, 35}, {3, 6,
8, 11, 13, 16, 18, 20, 23, 26, 28, 30, 32, 35}, {3, 6, 8, 11, 13,
16, 18, 20, 23, 26, 28, 30, 33, 35}, {3, 6, 8, 11, 13, 16, 18, 20,
23, 26, 28, 31, 33, 35}, {3, 6, 8, 11, 13, 16, 18, 21, 23, 25, 28,
30, 32, 35}, {3, 6, 8, 11, 13, 16, 18, 21, 23, 25, 28, 30, 33,
35}, {3, 6, 8, 11, 13, 16, 18, 21, 23, 25, 28, 31, 33, 35}, {3, 6,
8, 11, 13, 16, 18, 21, 23, 26, 28, 30, 32, 35}, {3, 6, 8, 11, 13,
16, 18, 21, 23, 26, 28, 30, 33, 35}, {3, 6, 8, 11, 13, 16, 18, 21,
23, 26, 28, 31, 33, 35}}
225种登高方案。@守恩王:lol

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