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 $s_1 s_2 \dots s_N$.

Input

The input is given from Standard Input in the following format:
N
$c_1 c_2 \cdots c_N$

Output

Print the answer.

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.

Sample Input 1

4
AABB

Sample Output 1

3

In this sample input, there are four possible orders in which the votes may be counted:

• The votes are counted in the order of voter $1 \to$ $2 \to$ $3 \to$ 4.
• The votes are counted in the order of voter $2 \to$ $1 \to$ $3 \to$ 4.
• The votes are counted in the order of voter $2 \to$ $3 \to$ $1 \to$ 4.
• The votes are counted in the order of voter $2 \to$ $3 \to$ $4 \to$ 1.

The sequences of preliminary results for these will be AAAC, AAAC, ACAC, ACBC from top to bottom, so there are three possible sequences of preliminary results.

Sample Input 2

4
AAAA

Sample Output 2

1

No matter the order of counting, the sequence of preliminary results will be AAAA.

Sample Input 3

10
BBBAAABBAA

Sample Output 3

5

Sample Input 4

172
AABAAAAAABBABAABBBBAABBAAABBABBABABABBAAABAAABAABAABBBBABBBABBABBBBBBBBAAABAAABAAABABBBAABAAAABABBABBABBBBBABAABAABBBABABBAAAABAABABBBABAAAABBBBABBBABBBABAABBBAAAABAAABAAAB

Sample Output 4

24

见题面 Input 部分

见题面 Output 部分