A7863 | Balance

Nick likes strings very much, he likes to rotate them, sort them, rearrange characters within a string... Once he wrote a random string of characters a, b, c on a piece of paper and began to perform the following operations:

- to take two adjacent characters and replace the second character with the first one,
- to take two adjacent characters and replace the first character with the second one

To understand these actions better, let's take a look at a string «abc». All of the following strings can be obtained by performing one of the described operations on «abc»: «bbc», «abb», «acc». Let's denote the frequency of a character for each of the characters a, b and c as the number of occurrences of this character in the string. For example, for string «abc»: | $a$ | = 1, | $b$ | = 1, | $c$ | = 1, and for string «bbc»: | $a$ | = 0, | $b$ | = 2, | $c$ | = 1.

While performing the described operations, Nick sometimes got balanced strings. Let's say that a string is balanced, if the frequencies of each character differ by at most 1. That is $-1<=|a|-|b|<=1$ , $-1<=|a|-|c|<=1$ и $-1<=|b|-|c|<=1$ .

Would you help Nick find the number of different balanced strings that can be obtained by performing the operations described above, perhaps multiple times, on the given string $s$ . This number should be calculated modulo $51123987$ .

The first line contains integer $n$ ( $1<=n<=150$ ) — the length of the given string $s$ . Next line contains the given string $s$ . The initial string can be balanced as well, in this case it should be counted too. The given string $s$ consists only of characters a, b and c.

Output the only number — the number of different balanced strings that can be obtained by performing the described operations, perhaps multiple times, on the given string $s$ , modulo $51123987$ .