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Time Limit: 6.5 s Memory Limit: 256 MB Total points: 100 Hackable ✓

#9244. 计数字符串

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给定一个长度为 $n$ 的字符串 $s$。

我们称字符串 $t$ 在 $s$ 中被提及,当且仅当存在整数 $l, r$,满足 $1 \le l \le r \le n$,$\gcd(l, r) = 1$ 且 $s[l, r] = t$。

其中,$s[l, r]$ 定义为由 $s_l, s_{l+1}, \dots, s_r$ 连接而成的字符串,$\gcd(l, r)$ 表示 $l$ 和 $r$ 的最大公约数。

你需要计算所有不同的非空字符串中,在 $s$ 中被提及的字符串的长度之和。

输入格式

第一行包含一个整数 $n$ ($1 \le n \le 100000$)。

第二行包含字符串 $s$,仅由小写英文字母组成。

输出格式

在一行中输出所有不同的非空且在 $s$ 中被提及的字符串的长度之和。

样例

输入 1

4
abca

输出 1

14

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