Leaders

문제

Farmer John has $NN$ cows ($2\le N\le {10}^{5}2\; \backslash leq\; N\; \backslash leq\; 10^5$). Each cow has a breed that is either Guernsey or Holstein. As is often the case, the cows are standing in a line, numbered $1\dots N1\; \backslash ldots\; N$ in this order.

Over the course of the day, each cow writes down a list of cows. Specifically, cow $ii$'s list contains the range of cows starting with herself (cow $ii$) up to and including cow $E_{i}E\_i$ ($i\le E_i\le Ni\; \backslash leq\; E\_i\; \backslash leq\; N$).

FJ has recently discovered that each breed of cow has exactly one distinct leader. FJ does not know who the leaders are, but he knows that each leader must have a list that includes all the cows of their breed, or the other breed's leader (or both).

Help FJ count the number of pairs of cows that could be leaders. It is guaranteed that there is at least one possible pair.

입력

The first line contains $NN$.

The second line contains a string of length $NN$, with the $ii$th character denoting the breed of the $ii$th cow (G meaning Guernsey and H meaning Holstein). It is guaranteed that there is at least one Guernsey and one Holstein.

The third line contains $E_1\dots E_{N}E\_1\; \backslash dots\; E\_N$.

출력

Output the number of possible pairs of leaders.

4
GHHG
2 4 3 4

1

3
GGH
2 3 3

2