For a sequence of strings (t_1, t_2, \dots, t_m), let's define the function (f(t_1, t_2, \dots, t_m)) as the number of different strings ( including the empty string ) that are subsequences of at least one string (t_i). (f([]) = 0) (i. e. the number of such strings for an empty sequence is (0)). You are given a sequence of strings (s_1, s_2, \dots, s_n). Every string in this sequence consists of lowercase Latin letters and is sorted (i. e., each string begins with several (maybe zero) characters a , then several (maybe zero) characters b , ..., ends with several (maybe zero) characters z ). For each of (2^n) subsequences of (s_1, s_2, \dots, s_n), calculate the value of the function (f) modulo (998244353). The first line contains one integer (n) ((1 \le n \le 23)) — the number of strings. Then (n) lines follow. The (i)-th line contains the string (s_i) ((1 \le |s_i| \le 2 \cdot 10^4)), consisting of lowercase Latin letters. Each string (s_i) is sorted. Since printing up to (2^{23}) integers would be really slow, you should do the following: For each of the (2^n) subsequences (which we denote as (s_{i_1}, s_{i_2}, \dots, s_{i_k})), calculate (f(s_{i_1}, s_{i_2}, \dots, s_{i_k})), take it modulo (998244353), then multiply it by (k \cdot (i_1 + i_2 + \dots + i_k)). Print the XOR of all (2^n) integers you get. The indices (i_1, i_2, \dots, i_k) in the description of each subsequences are (1)-indexed (i. e. are from (1) to (n)).