#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <cmath>
#include <vector>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <queue>
#include <ctime>
#include <cassert>
#include <complex>
#include <string>
#include <cstring>
#include <chrono>
#include <random>
#include <bitset>
#include <fstream>
#include <array>
using namespace std;
#define int long long
#define ii pair <int, int>
#define app push_back
#define all(a) a.begin(), a.end()
#define bp __builtin_popcountll
#define ll long long
#define mp make_pair
#define x first
#define y second
#define Time (double)clock()/CLOCKS_PER_SEC
#define debug(x) std::cerr << #x << ": " << x << '\n';

#define FORI(i,a,b) for (int i = (a); i < (b); ++i)
#define FOR(i,a) FORI(i,0,a)
#define ROFI(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define ROF(i,a) ROFI(i,0,a)
#define rep(a) FOR(_,a)
#define each(a,x) for (auto& a: x)
#define FORN(i, n) FORI(i, 1, n + 1)

using vi = vector<int>;
template <typename T>
std::istream& operator >>(std::istream& input, std::pair <T, T> & data)
{
    input >> data.x >> data.y;
    return input;
}
template <typename T>
std::istream& operator >>(std::istream& input, std::vector<T>& data)
{
    for (T& x : data)
        input >> x;
    return input;
}
template <typename T>
std::ostream& operator <<(std::ostream& output, const pair <T, T> & data)
{
    output << "(" << data.x << "," << data.y << ")";
    return output;
}
template <typename T>
std::ostream& operator <<(std::ostream& output, const std::vector<T>& data)
{
    for (const T& x : data)
        output << x << " ";
    return output;
}
std::ostream& operator <<(std::ostream& output, const __int128 &x)
{
    __int128 n = x;
    if (n == 0) {
        output << "0";
        return output;
    }
    if (n < 0) {
        n = -n;
        output << "-";
    }
    string s;
    while (n) {
        s += '0' + (n%10);
        n /= 10;
    }
    reverse(all(s));
    cout << s;
    return output;
}
ll div_up(ll a, ll b) { return a/b+((a^b)>0&&a%b); } // divide a by b rounded up
ll div_down(ll a, ll b) { return a/b-((a^b)<0&&a%b); } // divide a by b rounded down 
ll math_mod(ll a, ll b) { return a - b * div_down(a, b); }
#define tcT template<class T
#define tcTU tcT, class U
tcT> using V = vector<T>; 
tcT> bool ckmin(T& a, const T& b) {
    return b < a ? a = b, 1 : 0; 
} // set a = min(a,b)
tcT> bool ckmax(T& a, const T& b) {
    return a < b ? a = b, 1 : 0; 
}
ll gcd(ll a, ll b) {
    while (b) {
        tie(a, b) = mp(b, a % b);
    }
    return a;
}
int Bit(int mask, int bit) { return (mask >> bit) & 1; }

int a[10][10];
V <vi> want;
int ans = 0;

int n;
void gen(int ci, int cj) {

    for (int k = 2; k <= n; ++k) {
        FOR (i, n - k + 1) {
            FOR (j, n - k + 1) {

                int sum = 0;
                bool in = 1;
                FOR (x, k) {
                    FOR (y, k) {
                        in &= mp(i + x, j + y) < mp(ci, cj);
                        sum += a[i + x][j + y];
                    }
                }
                if (in && (sum&1)!=(k&1)) {
                    return;
                }

            }  
        }
    }

    if (ci == n) {
        bool ok = 1;
        each (e, want) {
            ok &= a[e[0]][e[1]] == e[2];
        }
        ans += ok;
        return;
    }

    a[ci][cj] = 0;
    if (cj == n - 1) {
        gen(ci + 1, 0);
    }
    else {
        gen(ci, cj + 1);
    }

    a[ci][cj] = 1;
    if (cj == n - 1) {
        gen(ci + 1, 0);
    }
    else {
        gen(ci, cj + 1);
    }

}

signed main() {
    #ifdef LOCAL
    #else
    #define endl '\n'
    ios_base::sync_with_stdio(0); cin.tie(0);
    #endif

    int q;
    cin >> n >> q;

    rep (q) {
        int x, y, w;
        cin >> x >> y >> w;
        x--; y--;
        want.app({x, y, w});
    }

    if (n <= 6) {
        gen(0, 0);
        cout << ans << endl;
    }
    else {
        each (e, want) {
            if (e[2] == 0) {
                cout << 0 << endl;
                exit(0);
            }
        }
        cout << 1 << endl;
    }

    /*
    FOR (mask, 1ll << (n * n)) {
        FOR (i, n) {
            FOR (j, n) {
                int num = i * n + j;
                a[i][j] = Bit(mask, num);
            }
        }

        bool ok = 1;
        for (int k = 2; k <= n; ++k) {
            FOR (i, n - k + 1) {
                FOR (j, n - k + 1) {

                    int sum = 0;
                    FOR (x, k) {
                        FOR (y, k) {
                            sum += a[i + x][j + y];
                        }
                    }
                    if ((sum&1)!=(k&1)) {
                        ok = 0;
                    }

                }  
            }
        }

        if (ok) {
            FOR (i, n) {
                FOR (j, n) {
                    cout << a[i][j] << ' ';
                }
                cout << endl;
            }
            cout << endl;
        }

    }
    */
}