#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> pi;
typedef pair<ll, ll> pl;
typedef vector<int> vi;
typedef vector<ll> vl;
#define PB push_back
#define MP make_pair
#define A first
#define B second
#define SZ(x) int(x.size())
#define FR(i, a, b) for (int i = (a); i < (b); ++i)
#define FOR(i, n) FR(i, 0, n)
const int M = 1000000007;
mt19937_64 rnd(chrono::steady_clock::now().time_since_epoch().count());

int n, m;
vector<vi> a;
vi b;

int main() {
    ios::sync_with_stdio(0);
    cin.tie(0);
    cin >> n >> m;
    a.resize(n, vi(n, -1));
    b.resize(m);
    int yes = 0, no = 0;
    FOR(i, n) {
        string s;
        cin >> s;
        FOR(j, n) {
            if (s[j] == 'X') {
                a[i][j] = 0;
                no |= 1 << (i * n + j);
            }
            if (s[j] == 'O') {
                a[i][j] = 1;
                yes |= 1 << (i * n + j);
            }
        }
    }
    vi buc(6);
    FOR(i, m) {
        cin >> b[i];
        buc[b[i]]++;
    }
    int tot = 0;
    FOR(i, m) tot += b[i];
    int mx = 0, idx = 0;
    FOR(i, 6) {
        if (buc[i] > mx) {
            mx = buc[i];
            idx = i;
        }
    }
    FOR(i, m) {
        if (b[i] == idx) b[i] = -1;
    }
    mx = m - mx;

    sort(b.rbegin(), b.rend());
    FOR(i, m) {
        if (b[i] == -1) b[i] = idx;
    }
    int ans = 0;
    FOR(i, (1 << (n * n))) {
        if ((i & yes) != yes) continue;
        if (((~i) & no) != no) continue;
        int cnt = 0;
        FOR(j, n * n) {
            cnt += ((i >> j) & 1);
        }
        if (cnt != tot) continue;
        vector<vi> t(n, vi(n));
        FOR(j, n) {
            FOR(k, n) {
                if ((i >> (j * n + k)) & 1) t[j][k] = 1;
            }
        }
        function<int(int, int)> get = [&](int x, int num) {
            if (num == m) return 1;
            int nxt_len = b[num];
            int acc = 0;
            bool fin = false;
            FOR(i, n) {
                if (fin) break;
                FOR(j, n) {
                    if ((x >> (i * n + j)) & 1) {
                        if (num >= mx) fin = true;
                        int mask = 0;
                        if (j <= n - nxt_len) {
                            FOR(k, nxt_len) mask |= (1 << (i * n + j + k));
                            if ((x & mask) == mask) {
                                acc += get(x ^ mask, num + 1);
                            }
                        }
                        mask = 0;
                        if (nxt_len > 1) {
                            FOR(k, nxt_len) mask |= (1 << (i * n + j + k * n));
                            if ((x & mask) == mask) {
                                acc += get(x ^ mask, num + 1);
                            }
                        }

                    }
                    if (fin) break;
                }
            }
            return acc;
        };
        ans += get(i, 0);
    }
    FR(i, 1, m - mx + 1) ans *= i;
    cout << ans << '\n';

}