C. Count Binary Stringstime limit per test2 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputYou are given an integer n. You have to calculate the number of binary (consisting of characters 0 and/or 1) strings s meeting the following constraints.For every pair of integers (i, j) such that 1 \le i \le j \le n, an integer a_{i,j} is given. It imposes the following constraint on the string s_i s_{i+1} s_{i+2} \dots s_j:  if a_{i,j} = 1, all characters in s_i s_{i+1} s_{i+2} \dots s_j should be the same;  if a_{i,j} = 2, there should be at least two different characters in s_i s_{i+1} s_{i+2} \dots s_j;  if a_{i,j} = 0, there are no additional constraints on the string s_i s_{i+1} s_{i+2} \dots s_j. Count the number of binary strings s of length n meeting the aforementioned constraints. Since the answer can be large, print it modulo 998244353.InputThe first line contains one integer n (2 \le n \le 100).Then n lines follow. The i-th of them contains n-i+1 integers a_{i,i}, a_{i,i+1}, a_{i,i+2}, \dots, a_{i,n} (0 \le a_{i,j} \le 2).OutputPrint one integer — the number of strings meeting the constraints, taken modulo 998244353.ExamplesInput
3
1 0 2
1 0
1
Output
6
Input
3
1 1 2
1 0
1
Output
2
Input
3
1 2 1
1 0
1
Output
0
Input
3
2 0 2
0 1
1
Output
0
NoteIn the first example, the strings meeting the constraints are 001, 010, 011, 100, 101, 110.In the second example, the strings meeting the constraints are 001, 110.
3
1 0 2
1 0
1

6 
['data structures', 'dp', '*2100']