#include<bits/stdc++.h>
#include<atcoder/all>
using namespace std;
using namespace atcoder;
#define rep(i,n)for (int i = 0; i < int(n); ++i)
#define rrep(i,n)for (int i = int(n)-1; i >= 0; --i)
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
template<class T> void chmax(T& a, const T& b) {a = max(a, b);}
template<class T> void chmin(T& a, const T& b) {a = min(a, b);}
using ll = long long;
using P = pair<int,int>;
using VI = vector<int>;
using VVI = vector<VI>;
using VL = vector<ll>;
using VVL = vector<VL>;

int case_5[8][5][5] = {{
{0, 0, 0, 0, 0},
{0, 0, 0, 0, 0},
{1, 1, 1, 1, 1},
{0, 0, 0, 0, 0},
{0, 0, 0, 0, 0},
},{
{0, 0, 1, 0, 0},
{0, 0, 1, 0, 0},
{0, 0, 1, 0, 0},
{0, 0, 1, 0, 0},
{0, 0, 1, 0, 0},
},{
{0, 1, 1, 0, 1},
{1, 0, 0, 1, 0},
{0, 1, 1, 0, 1},
{0, 1, 1, 0, 1},
{1, 0, 0, 1, 0},
},{
{0, 1, 0, 0, 1},
{1, 0, 1, 1, 0},
{1, 0, 1, 1, 0},
{0, 1, 0, 0, 1},
{1, 0, 1, 1, 0},
},{
{1, 0, 1, 1, 0},
{0, 1, 0, 0, 1},
{1, 0, 1, 1, 0},
{1, 0, 1, 1, 0},
{0, 1, 0, 0, 1},
},{
{1, 0, 0, 1, 0},
{0, 1, 1, 0, 1},
{0, 1, 1, 0, 1},
{1, 0, 0, 1, 0},
{0, 1, 1, 0, 1},
},{
{1, 1, 0, 1, 1},
{1, 1, 0, 1, 1},
{0, 0, 1, 0, 0},
{1, 1, 0, 1, 1},
{1, 1, 0, 1, 1},
},{
{1, 1, 1, 1, 1},
{1, 1, 1, 1, 1},
{1, 1, 1, 1, 1},
{1, 1, 1, 1, 1},
{1, 1, 1, 1, 1},
}};

bool g[11][11];
bool s[11][11];

int solve5() {
    int m;
    cin >> m;
    vector<tuple<int, int, int>> xyz(m);
    rep(i, m) {
        int x, y, z;
        cin >> x >> y >> z;
        x--, y--;
        xyz[i] = {x, y, z};
    }
    int ans = 0;
    rep(i, 8) {
        bool ok = true;
        for(auto [x, y, z]: xyz) {
            if (case_5[i][x][y] != z) {
                ok = false;
                break;
            }
        }
        ans += ok;
    }
    cout << ans << endl;
    return 0;
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    int n;
    cin >> n;
    if (n == 5) return solve5();
    int m;
    cin >> m;
    vector<tuple<int, int, int>> xyz(m);
    rep(i, m) {
        int x, y, z;
        cin >> x >> y >> z;
        x--, y--;
        xyz[i] = {x, y, z};
    }
    if (n < 5) {
        int ans = 0;
        rep(bit, 1 << n * n) {
            int t = bit;
            rep(i, n) rep(j, n) g[i][j] = t & 1, t >>= 1;
            bool ok = true;
            rep(i, n) rep(j, n) s[i+1][j+1] = s[i+1][j] ^ s[i][j+1] ^ s[i][j] ^ g[i][j];
            rep(i, n) rep(j, n) for(int k = 2; i + k <= n && j + k <= n; k++) {
                if ((s[i][j] ^ s[i + k][j] ^ s[i][j + k] ^ s[i+k][j+k] ^ k) & 1) {
                    ok = false;
                    goto done;
                }
            }
            done:
            if (!ok) continue;
            // rep(i, n) rep(j, n) cout << int(g[i][j]) << " \n"[j + 1 == n];
            // cout << endl;
            for(auto [x, y, z]: xyz) {
                if (g[x][y] != z) {
                    ok = false;
                    break;
                }
            }
            ans += ok;
        }
        cout << ans << '\n';
        return 0;
    }
    bool ok = true;
    for(auto [x, y, z]: xyz) {
        if (z != 1) {
            ok = false;
            break;
        }
    }
    cout << int(ok) << '\n';
}