隐藏的数字 - 题目

#15527. 隐藏的数字

统计

AI Translation — This statement was translated using AI and may contain inaccuracies. Please refer to the original statement if in doubt.

有一个长度为 $N$ ($1 \le N \le 18$) 的隐藏数字字符串（由数字 0 到 9 组成）。你想知道在这个隐藏的数字中，是否存在任意长度的子串，其代表的数值能被 3 整除。

你最多可以进行 2 次如下格式的询问：? i，它会告诉你所请求的下标 $i$ ($1 \le i \le N$) 处的数字。

输入格式

第一行包含一个整数 $N$，表示隐藏字符串的长度。

交互

你最多可以进行 2 次如下格式的询问：? i

在进行一次询问后，你将收到单行一个 0 到 9 的数字，表示隐藏字符串中下标 $i$ 处的数字。

给出答案时，如果存在能被 3 整除的子串，请输出单行 ! 1；否则输出 ! 0。

样例

输入 1

2
6
8

输出 1

? 1
? 2
! 1

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