CF17C 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

The first line contains integer $ n $ ( $ 1

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 $ .

In the first sample it is possible to get $ 51 $ different strings through the described operations, but only $ 7 $ of them are balanced: «abca», «bbca», «bcca», «bcaa», «abcc», «abbc», «aabc». In the second sample: «abbc», «aabc», «abcc». In the third sample there is only one balanced string — «ab» itself.