#include<bits/stdc++.h>
#define int long long
using namespace std;
int n, m, f[35][35][45][45], sum[35][35][45][45]; //区间 （理论）最小可行 最大值
int b[35][45], c[35];
char cc;
const int mod = 998244353;
signed main() {
	ios::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);
	cin >> n >> m;
	for (int i = 1; i <= n; i++) {
		cin >> c[i];
	}
	for (int i = 1; i <= n; i++) {
		for (int j = 1; j <= m; j++) {
			cin >> cc;
			b[i][j] = cc - '0';
		}
	}
	for (int i = 1; i <= n; i++) {
		for (int j = 1; j <= m; j++) {
			for (int k = 1; k <= m; k++) {
				if (b[i][k] && (c[i] == 2 || ((k >= j) == c[i]))) {
					f[i][i][j][k] = 1;
				}
				sum[i][i][j][k] = sum[i][i][j][k - 1] + f[i][i][j][k];
			}
		}
	}
	int op;
	for (int len = 2; len <= n; len++) {
		for (int l = 1, r = len; r <= n; l++, r++) {
			for (int p = 1; p <= m; p++) {
				for (int q = 1; q <= m; q++) {
					for (int i = l; i <= r; i++) {
						if (b[i][q] && (c[i] == 2 || ((q >= p) == c[i]))) {
							op = 1;
							if (l <= i - 1) {
								op = op * sum[l][i - 1][max(p, q - ((i - 1) - l))][q - 1] % mod;
							}
							if (i + 1 <= r) {
								op = op * sum[i + 1][r][max(p, q - (r - (i + 1)))][q] % mod;
							}
							f[l][r][p][q] = (f[l][r][p][q] + op) % mod;
						}
					}
					sum[l][r][p][q] = (sum[l][r][p][q - 1] + f[l][r][p][q]) % mod;
				}
			}
		}
	}
	op = 0;
	cout << sum[1][n][1][m];
}