Score : $400$ points

Problem Statement

We have a string $S$ of length $N$ consisting of A, T, C, and G.

Strings $T_1$ and $T_2$ of the same length are said to be complementary when, for every $i$ ($1 \leq i \leq l$), the $i$-th character of $T_1$ and the $i$-th character of $T_2$ are complementary. Here, A and T are complementary to each other, and so are C and G.

Find the number of non-empty contiguous substrings $T$ of $S$ that satisfies the following condition:

• There exists a string that is a permutation of $T$ and is complementary to $T$.

Here, we distinguish strings that originate from different positions in $S$, even if the contents are the same.

Constraints

• $1 \leq N \leq 5000$
• $S$ consists of A, T, C, and G.

Input

Input is given from Standard Input in the following format:

$N$ $S$

Output

Print the number of non-empty contiguous substrings $T$ of $S$ that satisfies the condition.

4 AGCT

2

The following two substrings satisfy the condition:

• GC (the $2$-nd through $3$-rd characters) is complementary to CG, which is a permutation of GC.
• AGCT (the $1$-st through $4$-th characters) is complementary to TCGA, which is a permutation of AGCT.

4 ATAT

4

The following four substrings satisfy the condition:

• AT (the $1$-st through $2$-nd characters) is complementary to TA, which is a permutation of AT.
• TA (the $2$-st through $3$-rd characters) is complementary to AT, which is a permutation of TA.
• AT (the $3$-rd through $4$-th characters) is complementary to TA, which is a permutation of AT.
• ATAT (the $1$-st through $4$-th characters) is complementary to TATA, which is a permutation of ATAT.

10 AAATACCGCG

6