// qdd on Jan 29, 2023

#ifdef qdd
#include <ringo>
#else
#include <bits/stdc++.h>
#define dbg(...)
#define dbgr(x, y)
#endif

using namespace std;

using ll = long long;

template <class T>
istream& operator>>(istream& is, vector<T>& v) {
  for (T& x : v) is >> x;
  return is;
}

template <class T>
ostream& operator<<(ostream& os, const vector<T>& v) {
  bool f = 0;
  for (const T& x : v) (f ? os << ' ' : os) << x, f = 1;
  return os;
}

void sol() {
  int n, m;
  cin >> n >> m;
  vector<string> a(n);
  cin >> a;
  vector<int> l(m);
  cin >> l;
  vector<string> g(n, string(n, ' '));
  auto chk = [&](int x, int y, int t, int len) {
    if (t == 1) {
      for (int j = y; j < y + len; j++) {
        if (j >= n) return false;
        if (g[x][j] != ' ') return false;
      }
    } else {
      for (int i = x; i < x + len; i++) {
        if (i >= n) return false;
        if (g[i][y] != ' ') return false;
      }
    }
    return true;
  };
  auto put = [&](int x, int y, int t, int len, char c = '#') {
    if (t == 1) {
      for (int j = y; j < y + len; j++) {
        g[x][j] = c;
      }
    } else {
      for (int i = x; i < x + len; i++) {
        g[i][y] = c;
      }
    }
  };
  auto valid = [&]() {
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < n; j++) {
        if (g[i][j] == '#' && a[i][j] == 'X') return false;
        if (g[i][j] == ' ' && a[i][j] == 'O') return false;
      }
    }
    return true;
  };
  int ans = 0;
  function<void(int)> dfs = [&](int idx) {
    if (idx == m) {
      if (valid()) {
        ans += 1;
      }
      return;
    }
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < n; j++) {
        if (chk(i, j, 0, l[idx])) {
          put(i, j, 0, l[idx]);
          dfs(idx + 1);
          put(i, j, 0, l[idx], ' ');
        }
        if (l[idx] > 1) {
          if (chk(i, j, 1, l[idx])) {
            put(i, j, 1, l[idx]);
            dfs(idx + 1);
            put(i, j, 1, l[idx], ' ');
          }
        }
      }
    }
  };
  dfs(0);
  cout << ans << '\n';
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  sol();
  return 0;
}