#include <bits/stdc++.h>

using namespace std;

#ifdef LOCAL
template <class... T> void dbg(T... x) { char e{}; ((cerr << e << x, e = ' '), ...); }
template <class T> void org(T l, T r) { while (l != r) cerr << ' ' << *l++; cerr << '\n'; }
#define debug(x...) dbg(#x, '=', x, '\n')
#define olist(x...) dbg(#x, '='), org(x)
#else
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#define debug(...) ((void)0)
#define olist(...) ((void)0)
#endif
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()
#define ff first
#define ss second

using u32 = unsigned int;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;
using Pt = pair<int, int>;

template <class T> inline constexpr T inf = numeric_limits<T>::max() / 2;
constexpr int mod = 998244353;

template<class T> bool chmin(T &a, T b) { return (b < a and (a = b, true)); }
template<class T> bool chmax(T &a, T b) { return (a < b and (a = b, true)); }
template<class... T> int add(T... x) { int t{}; return (((t += x) %= mod), ...), t; }
template<class... T> int mul(T... x) { i64 t{1}; return (((t *= x) %= mod), ...), t; }
    
void solve() {
    int n, m;
    cin >> n >> m;

    vector G(n, string{});
    for (auto &s : G) {
        cin >> s;
    }

    vector<int> shi(m);
    for (int &x : shi) cin >> x;

    int ans = 0;
    vector vis(n, vector<int>(n));

    function<void(int)> rec = [&](int x) -> void {
        if (x == m) {
            bool ok = true;
            for (int i = 0; i < n and ok; i++)
                for (int j = 0; j < n; j++) {
                    if (G[i][j] == 'O' and !vis[i][j]) {
                        ok = false;
                        break;
                    }
                    if (G[i][j] == 'X' and vis[i][j]) {
                        ok = false;
                        break;
                    }
                }
            if (ok) ans++;
            return;
        } 

        for (int i = 0; i < n; i++)
            for (int j = 0; j < n; j++) {
                if (j + shi[x] <= n) {
                    bool ok = true;
                    for (int t = 0; t < shi[x]; t++) {
                        if (vis[i][j + t]) ok = false;
                        vis[i][j + t]++;
                    }
                    if (ok) rec(x + 1);
                    for (int t = 0; t < shi[x]; t++) {
                        vis[i][j + t]--;
                    }
                }
                if (shi[x] != 1 and i + shi[x] <= n) {
                    bool ok = true;
                    for (int t = 0; t < shi[x]; t++) {
                        if (vis[i + t][j]) ok = false;
                        vis[i + t][j]++;
                    }
                    if (ok) rec(x + 1);
                    for (int t = 0; t < shi[x]; t++) {
                        vis[i + t][j]--;
                    }
                }
            }
    };
    rec(0);

    cout << ans << '\n';
}

signed main() {
    cin.tie(0)->sync_with_stdio(false);
    cin.exceptions(cin.failbit);
    int T = 1;
    // cin >> T;
    while (T--) {
        solve();
    }
    return 0;
}