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#include <iostream>
#include <vector>
#include <map>
#include <unordered_map>
#include <queue>
using namespace std;
const short max_size = 1000;
short n;
vector<string> words;
unordered_map<string, short> mapa;
short cnt_words(const vector<string> & c) {
    short res = 0;
    unordered_map<string, short> cnt_map;
    for(short i = 0; i < n; i++) {
        string s = "";
        for(short j = 0; j < n; j++) {
            s += c[i][j];
        }
        cnt_map[s]++;
    }
    for(short j = 0; j < n; j++) {
        string s = "";
        for(short i = 0; i < n; i++) {
            s += c[i][j];
        }
        
        cnt_map[s]++;
    }
    for(pair<string, short> p : mapa) {
        res += min(p.second, cnt_map[p.first]);
    }
    return res;
}
int main()
{
    ios_base::sync_with_stdio(false);
    short k;
    cin >> n >> k;
    
    for(short i = 0; i < k; i++) {
        string s;
        cin >> s;
        words.push_back(s);
        mapa[s]++;
    }
    
    map<vector<string>, bool> map_visited;
    vector<string> v(n);
    string S = "";
    for(int i = 0; i < n; i++) {
        S += ".";
    }
    for(int i = 0; i < n; i++) {
        v[i] = S;
    }
    queue<vector<string>> q;
    queue<short> q_vis;
    q_vis.push(0);
    q.push(v);
    
    short res = 0;
    vector<string> tmp;
    while(!q.empty()) {
        vector<string> c = q.front();
        q.pop();
        short visited = q_vis.front();
        q_vis.pop();
        
        
        short cnt = 0;
        for(short i = 0; i < n; i++) {
            for(short j = 0; j < n; j++) {
                if(c[i][j] == '.') {
                    cnt++;
                    break;
                }
            }
            if(cnt > 0) {
                break;
            }
        }
        
        if(cnt == 0 and cnt_words(c) >= 2 * n) {
            res++;
//            for(short i = 0;i < n; i++) {
//                for(short j = 0; j < n; j++) {
//                    cout << c[i][j];
//                }
//                cout << endl;
//            }
//            cout << endl;
            continue;
        }
        if(cnt == 0) {
            continue;
        }
        
        for(short w = 0; w < k; w++) {
            if(!(visited & (1 << w))) {
                for(short i = 0; i < n; i++) {
                    bool check = true;

for(short j = 0; j < n; j++) {
                        if(c[i][j] != '.' and c[i][j] != words[w][j]) {
                            check = false;
                            break;
                        }
                    }
                    if(check) {
                         tmp = c;
                        for(short j = 0; j < n; j++) {
                            tmp[i][j] = words[w][j];
                        }
                        if(!map_visited[tmp]) {
                            q.push(tmp);
                            q_vis.push(visited | (1 << w));
                            map_visited[tmp] = true;
                        }
                    }
                }
                for(short j = 0; j < n; j++) {
                    bool check = true;
                    for(short i = 0; i < n; i++) {
                        if(c[i][j] != '.' and words[w][i] != c[i][j]) {
                            check = false;
                            break;
                        }
                    }
                    if(check) {
                         tmp = c;
                        for(short i = 0; i < n; i++) {
                            tmp[i][j] = words[w][i];
                        }
                        
                        if(!map_visited[tmp]) {
                            map_visited[tmp] = true;
                            q.push(tmp);
                            q_vis.push(visited | (1 << w));
                            
                        }
                    }
                    
                    
                }
            }
        }
        
        
    }
    cout << res << endl;
    return 0;

}