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Time Limit: 1 s Memory Limit: 256 MB Total points: 100

#4789. Infinite Pattern Matching

统计

考虑由所有正整数的二进制表示按递增顺序连接而成的无限二进制字符串 $I$:$I = \text{“}11011100 \dots \text{”}$。

给定一个二进制字符串 $A$。你的任务是找到最小的整数 $L$,使得 $A$ 是 $I[1 \dots L]$ 的后缀。

输入格式

输入仅一行,包含二进制字符串 $A$,满足 $1 \le |A| \le 55$。

输出格式

输出一行,包含一个整数:数字 $L$。

样例

样例输入 1

11

样例输出 1

2

样例输入 2

011011

样例输出 2

42

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