#include "bits/extc++.h"

using namespace std;

template <typename T, typename... U>
void dbgh(const T& t, const U&... u) {
    cerr << t;
    ((cerr << " | " << u), ...);
    cerr << endl;
}

#ifdef DEBUG
#define dbg(...)                                              \
    cerr << "L" << __LINE__ << " [" << #__VA_ARGS__ << "]: "; \
    dbgh(__VA_ARGS__)
#else
#define dbg(...)
#define cerr   \
    if (false) \
    cerr
#endif

#define endl "\n"
#define long int64_t
#define sz(x) int(std::size(x))

constexpr int maxn = 10;

int n, m, ans, sizes[maxn];
string arr[maxn];
bool vis[maxn][maxn];

bool check() {
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            if (arr[i][j] == 'X') {
                if (vis[i][j]) {
                    return false;
                }
            } else if (arr[i][j] == 'O') {
                if (!vis[i][j]) {
                    return false;
                }
            }
        }
    }
    return true;
}

void dfs(int ind) {
    if (ind == m) {
        ans += check();
        return;
    }
    int x = sizes[ind];
    for (int i = 0; i < n; i++) {
        for (int j = 0; j + x <= n; j++) {
            bool b = false;
            for (int k = j; k < j + x; k++) {
                b |= vis[i][k];
            }
            if (b) {
                continue;
            }
            for (int k = j; k < j + x; k++) {
                vis[i][k] = true;
            }
            dfs(ind + 1);
            for (int k = j; k < j + x; k++) {
                vis[i][k] = false;
            }
        }
    }
    if (x == 1) {
        return;
    }
    for (int i = 0; i < n; i++) {
        for (int j = 0; j + x <= n; j++) {
            bool b = false;
            for (int k = j; k < j + x; k++) {
                b |= vis[k][i];
            }
            if (b) {
                continue;
            }
            for (int k = j; k < j + x; k++) {
                vis[k][i] = true;
            }
            dfs(ind + 1);
            for (int k = j; k < j + x; k++) {
                vis[k][i] = false;
            }
        }
        }
}

void solve() {
    cin >> n >> m;
    for (int i = 0; i < n; i++) {
        cin >> arr[i];
    }
    for (int i = 0; i < m; i++) {
        cin >> sizes[i];
    }
    dfs(0);
    cout << ans << endl;
}

int main() {
    cin.tie(nullptr);
    cin.exceptions(ios::failbit);
    ios_base::sync_with_stdio(false);
    solve();
}