B'Monocarp has n numbers 1, 2, ... , n and a set (initially empty). He adds his numbers to this set n times in some order. During each step, he adds a new number (which has not been present in the set before). In other words, the sequence of added numbers is a permutation of length n . Every time Monocarp adds an element into the set except for the first time, he writes out a character: You are given a string s of n-1 characters, which represents the characters written out by Monocarp (in the order he wrote them out). You have to process m queries to the string. Each query has the following format: Both before processing the queries and after each query, you have to calculate the number of different ways to order the integers 1, 2, 3, ... , n such that, if Monocarp inserts the integers into the set in that order, he gets the string s . Since the answers might be large, print them modulo 998244353 . The first line contains two integers n and m ( 2 <= n <= 3 cdot 10^5 ; 1 <= m <= 3 cdot 10^5 ). The second line contains the string s , consisting of exactly n-1 characters <, > and/or ?. Then m lines follow. Each of them represents a query. Each line contains an integer i and a character c ( 1 <= i <= n-1 ; c is either <, >, or ?). Both before processing the queries and after each query, print one integer -- the number of ways to order the integers 1, 2, 3, ... , n such that, if Monocarp inserts the integers into the set in that order, he gets the string s . Since the answers might be large, print them modulo 998244353 . In the first example, there are three possible orderings before all queries: After the last query, there is only one possible ordering: '...