Problem Statement

This year's AtCoder mayoral election has two candidates, A and B, and $N$ voters have cast their votes. The voters are assigned numbers from $1$ to $N$, and voter $i$ $(1 \leq i \leq N)$ voted for candidate $c_i$.

Now, the votes will be counted. As each vote is counted, the provisional result will be announced as one of the following three outcomes:

• Result A: Currently, candidate A has more votes.
• Result B: Currently, candidate B has more votes.
• Result C: Currently, candidates A and B have the same number of votes.

There is a rule regarding the order of vote counting: votes from all voters except voter $1$ must be counted in ascending order of their voter numbers. (The vote from voter $1$ may be counted at any time.)

How many different sequences of provisional results could be announced?

What is a sequence of provisional results?Let $s_i$ be the result (A, B, or C) reported when the $i$-th vote $(1 \leq i \leq N)$ is counted. The sequence of provisional results refers to the string $s_1 s_2 \dots s_N$.

Constraints

• $N$ is an integer such that $2 \leq N \leq 1000000$.
• Each of $c_1, c_2, \dots, c_N$ is A or B.

Input

The input is given from Standard Input in the following format:

N
c_1 c_2 \cdots c_N

Output

Print the answer.