B'Given a list of distinct values, we denote with first minimum, second minimum, and third minimum the three smallest values (in increasing order). A permutation p_1, p_2, ... , p_n is good if the following statement holds for all pairs (l,r) with 1 <= l < l+2 <= r <= n . You are given an integer n and a string s of length m consisting of characters "<" and ">". Count the number of good permutations p_1, p_2, ... , p_n such that, for all 1 <= i <= m , The first line contains two integers n and m ( 2 <= n <= 2 cdot 10^5 , 1 <= q m <= q min(100, n-1) ). The second line contains a string s of length m , consisting of characters "<" and ">". Print a single integer: the number of good permutations satisfying the constraints described in the statement, modulo 998 ,244 ,353 . In the first test, there are 5 good permutations satisfying the constraints given by the string s : [4, 3, 2, 1, 5] , [5, 3, 2, 1, 4] , [5, 4, 2, 1, 3] , [5, 4, 3, 1, 2] , [5, 4, 3, 2, 1] . Each of them In the second test, there are 60 permutations such that p_1 < p_2 . Only 56 of them are good: the permutations [1, 4, 3, 5, 2] , [1, 5, 3, 4, 2] , [2, 4, 3, 5, 1] , [2, 5, 3, 4, 1] are not good because the required condition doesn 't hold for (l, r) = (1, 5) . For example, for the permutation [2, 4, 3, 5, 1] , In the third test, there are 23 good permutations satisfying the constraints given by the string s : [1, 2, 4, 3, 6, 5] , [1, 2, 5, 3, 6, 4] , [1, 2, 6, 3, 5, 4] , [1, 3, 4, 2, 6, 5] , [1, 3, 5, 2, 6, 4] , [1, 3, 6, 2, 5, 4] , [1, 4, 5, 2, 6, 3] , [1, 4, 6, 2, 5, 3] , [1, 5, 6, 2, 4, 3] , [2, 3, 4, 1, 6, 5] , [2, 3, 5, 1, 6, 4] , [2, 3, 6, 1, 5, 4] , [2, 4, 5, 1, 6, 3] , [2, 4, 6, 1, 5, 3] , [2, 5, 6, 1, 4, 3] , [3, 4, 5, '...