Score : $300$ points

Problem Statement

You are given a string $S$ of length $N$. For each $1\leq i\leq N$, let $S_i$ denote the string obtained by deleting the $i$-th character from $S$.

Find the number of pairs of integers $(i,j)$ that satisfy both of the conditions below.

• $1\leq i < j\leq N$
• $S_i = S_j$

Constraints

• $2\leq N\leq 3\times 10^5$
• $S$ is a string of length $N$ consisting of lowercase English letters.

Input

Input is given from Standard Input in the following format:

$N$

$S$

Output

Print the answer.

7
abbbcca

4

Here are the strings $S_i$ in order: bbbcca, abbcca, abbcca, abbcca, abbbca, abbbca, abbbcc.

The following $4$ pairs $(i,j)$ satisfy the conditions.

• $(i,j) = (2,3)$
• $(i,j) = (2,4)$
• $(i,j) = (3,4)$
• $(i,j) = (5,6)$

4
xxxx

6

2
pp

1

2
st

0