#include <bits/stdc++.h>
#define maxn 100086

using namespace std;

int n, k, l[10];
int ans;

char s[10][10];
inline int read(){
    int x = 0, f = 1;char ch = getchar();
    while(ch > '9' || ch < '0'){if(ch == '-') f = -1;ch = getchar();}
    while(ch >= '0' && ch <= '9'){x = x * 10 + ch -'0';ch = getchar();}
    return x * f;
}

bool vis[10][10];

bool check(){
	for(int i = 1; i <= n; i++){
		for(int j = 1; j <= n; j++){
			if(s[i][j] == '.') continue;
			if(s[i][j] == 'X' && vis[i][j]) return 0;
			if(s[i][j] == 'O' && !vis[i][j]) return 0;
		}
	}
	return 1;
}

bool check(int x1, int y1, int x2, int y2){
	int sum = 0;
	for(int i = x1; i <= x2; i++) for(int j = y1; j <= y2; j++) sum += vis[i][j];
	return sum > 0;
}

void fil(int x1, int y1, int x2, int y2, int x){
	for(int i = x1; i <= x2; i++) for(int j = y1; j <= y2; j++) vis[i][j] = x;
}

void dfs(int x){
	if(x == k + 1){
		ans += check();
		return ;
	}
	for(int i = 1; i <= n; i++){
		for(int j = 1; j <= n; j++){
			if(j + l[x] - 1 <= n && !check(i, j, i, j + l[x] - 1)){
				fil(i, j, i, j + l[x] - 1, 1);
				dfs(x + 1);
				fil(i, j, i, j + l[x] - 1, 0);
			}
			if(l[x] > 1 && i + l[x] - 1 <= n && !check(i, j, i + l[x] - 1, j)){
				fil(i, j, i + l[x] - 1, j, 1);
				dfs(x + 1);
				fil(i, j, i + l[x] - 1, j, 0);
			}
		}
	}
}

int main(){
	n = read(), k = read();
	for(int i = 1; i <= n; i++)
		scanf("%s", s[i] + 1);
	for(int i = 1; i <= k; i++) l[i] = read();
	dfs(1);
	printf("%d\n", ans);
}
/*


2 2
.O
..
1
1
*/