//Remember: (a mod m)/b IS NOT (a/b) mod m
//Checklist: multitest (!!), maxn, mod, constraints, NEGATIVE ANSWER
#include <iostream>
#include<map>
#include<set>
#include<vector>
#include<string>
#include<queue>
#include<random>
#include<stack>
#include<chrono>
#include<bitset>
using namespace std;

//#define labeltc
#define endl "\n"
#define uint unsigned int
#define ll long long
#define ull unsigned long long
#define db double
#define ld long double
#define MOD 1000000007
//#define MOD 998244353
#define INFLL 2000000000001000000LL
#define INFI 1001000000
#define PI ((ld)(M_PI))
#define pii pair<int,int>
#define piii tuple<int,int,int>
#define pll pair<ll,ll>
#define plll tuple<ll,ll,ll>
#define fi first
#define sc second
#define m_p make_pair
#define p_b emplace_back
#define l_b lower_bound
#define u_b upper_bound
#define vi vector<int>
#define vl vector<ll>
#define rand_num(x,y) uniform_int_distribution<ll>((ll)x,(ll)y)(rng)
#define lsb(x) (x&(-x))
#define dgt(x) (x-'0')
#define all(x) x.begin(),x.end()
#define pans(x) ((x)? "YES " : "NO ")
template<typename T> bool ckmin(T& a, const T& b) {return (a>b)? a = b, 1 : 0;}
template<typename T> bool ckmax(T& a, const T& b) {return (a<b)? a = b, 1 : 0;}

mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());

ll power(ll x, ll e, ll m){
    ll r = 1;
    while(e>0){
        if(e%2) r = (r*x)%m;
        x = (x*x)%m;
        e >>= 1;
    }
    return r;
}

template <typename T, typename U>
ostream& operator<<(ostream& os, const pair<T,U>& v){
    os << v.fi << " " << v.sc;
    return os;
}
template <typename T>
ostream& operator<<(ostream& os, const vector<T>& v){
    for (int i = 0; i < v.size(); ++i) {os << v[i] << " ";}
    return os;
}
template <typename T>
ostream& operator<<(ostream& os, const set<T>& v){
    for (auto it : v) {os << it << " ";}
    return os;
}
template <typename T, typename U>
ostream& operator<<(ostream& os, const map<T,U>& v){
    for (auto it : v) {os << it << "\n";}
    return os;
}
template <typename T, typename U, typename W>
ostream& operator<<(ostream& os, const tuple<T,U,W>& v){
    os << sp(get<0>(v)) << sp(get<1>(v)) << sp(get<2>(v));
    return os;
}

void setIO(string s) {
    freopen((s+".in").c_str(),"r",stdin);
    freopen((s+".out").c_str(),"w",stdout);
}


int n,k,x[6];
int ans,tot;
vector<bitset<25>> all[6];


void precomp(){
    for (int i=0; i<25; i++){
        bitset<25> z;
        z.set(i);
        all[1].push_back(z);
    }
    for (int len=1; len<=4; len++) {
        for (int i = 0; i < 5; i++) {
            for (int j = 0; j + len < 5; j++) {
                bitset<25> z, y;
                for (int l = 0; l <= len; l++) {
                    z.set(5 * i + j + l);
                    y.set(5 * j + i + 5 * l);
                }
                all[len + 1].push_back(z);
                all[len + 1].push_back(y);
            }
        }
    }
}

void solve(){
    cin >> n >> k;
    bitset<25> bad,good;
    for (int i=0; i<n; i++){
        string row; cin >> row;
        for (int j=0; j<n; j++){
            if(row[j] == 'O'){
                good.set(5*i+j);
            }
            else if(row[j] == 'X'){
                bad.set(5*i+j);
            }
        }
    }
    if(n<5){
        for (int i=n; i<5; i++){
            for (int j=0; j<5; j++){
                bad.set(5*i+j);
                bad.set(5*j+i);
            }
        }
    }
    for (int i=0; i<k; i++){
        cin >> x[i];
        tot += x[i];
    }
    bitset<25> emp;
    all[0].p_b(emp);
    for (auto c: all[x[0]]){
        for(bitset<25> y: all[x[1]]){
            for (bitset<25> z: all[x[2]]){
                for (bitset<25> a: all[x[3]]){
                    for (bitset<25> b: all[x[4]]){
                        bitset<25> cand;
                        cand |= c;
                        cand |= y;
                        cand |= z;
                        cand |= a;
                        cand |= b;
                        int cur = cand.count();
                        if(cur == tot){
                            cand |= good;
                            if(cand.count() == cur){
                                cand ^= bad;
                                if(cand.count()-bad.count() == cur){
                                    ans++;
                                }
                            }
                        }
                    }
                }
            }
        }
    }
    cout << ans << endl;
}

signed main(){
    //setIO();
    ios_base::sync_with_stdio(0);
    cin.tie(NULL);
    precomp();
    solve();
}