#include <bits/stdc++.h>
using namespace std;
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
#endif
using ll = long long;
using ld = long double;
using ull = long long;
#define all(s) (s).begin(),(s).end()
#define rep2(i, m, n) for (int i = (m); i < (n); ++i)
#define rep(i, n) rep2(i, 0, n)
#define drep2(i, m, n) for (int i = (m)-1; i >= (n); --i)
#define drep(i, n) drep2(i, n, 0)
#define rever(vec) reverse(vec.begin(), vec.end())
#define sor(vec) sort(vec.begin(), vec.end())
#define fi first
#define se second
#define P pair<ll,ll>
#define REP(i, n) for (int i = 0; i < (n); ++i)
const ll mod = 998244353;
//const ll mod = 1000000007;
const ll inf = 2000000000000000000ll;
static const long double pi = 3.141592653589793;
template<class T>void vcin(vector<T> &n){for(int i=0;i<int(n.size());i++) cin>>n[i];}
template<class T>void vcout(vector<T> &n){for(int i=0;i<int(n.size());i++){cout<<n[i]<<" ";}cout<<endl;}
void YesNo(bool a){if(a){cout<<"Yes"<<endl;}else{cout<<"No"<<endl;}}
void YESNO(bool a){if(a){cout<<"YES"<<endl;}else{cout<<"NO"<<endl;}}
template<class T,class U> void chmax(T& t,const U& u){if(t<u) t=u;}
template<class T,class U> void chmin(T& t,const U& u){if(t>u) t=u;}
template<class T> void ifmin(T t,T u){if(t>u){cout<<-1<<endl;}else{cout<<t<<endl;}}
template<class T> void ifmax(T t,T u){if(t>u){cout<<-1<<endl;}else{cout<<t<<endl;}}
template<typename T,typename ...Args>auto make_vector(T x,int arg,Args ...args){if constexpr(sizeof...(args)==0)return vector<T>(arg,x);else return vector(arg,make_vector<T>(x,args...));}
ll modPow(ll a, ll n, ll mod) { ll ret = 1; ll p = a % mod; while (n) { if (n & 1) ret = ret * p % mod; p = p * p % mod; n >>= 1; } return ret; }

void gbjsmzmfuuvdf(){
  ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
  cout<< fixed << setprecision(20);
}
void solve(vector<vector<ll>> &ans){
  for(int i=1;i<ans.size();i++){
    for(int j=1;j<ans.size();j++){
      ans[i][j]=(ans[i][j-1]+ans[i-1][j]+ans[i-1][j-1])%2;
    }
  }
}
bool subsolve(vector<vector<ll>> ans){
  for(int i=2;i<=ans.size();i++){
    for(int x=0;x+i<ans.size();x++){
      for(int z=0;z+i<ans.size();z++){
        ll p=0;
        for(int a=x;a<=x+i;a++){
          for(int b=z;b<=z+i;b++){
            p+=ans[a][b];
          }
        }
        if(p%2==i%2){
          return false;
        }
      }
    }
  }
  return true;
}
int main()  {
  gbjsmzmfuuvdf();
  ll n,m;
  cin>>n>>m;
  if(n==1){
      ll x=-1;
      for(int i=0;i<m;i++){
          ll a,b,c;
          cin>>a>>b>>c;
          if(x==-1) x=c;
          else if(x!=c){
              cout<<0<<endl;
              return 0;
          }
      }
    if(x!=-1){
      cout<<1<<endl;
    }
    else{
      cout<<2<<endl;
    }
    return 0;
  }
  if(n>=7){
    bool t=true;
    while(m--){
      ll a,b,c;
      cin>>a>>b>>c;
      a--;
      b--;
      if(c==1){
        t=false;
      }
    }
    if(t){
      cout<<1<<endl;
    }
    else{
      cout<<0<<endl;
      return 0;
    }
  }
  if(n<=6){
    vector<ll> x(m),y(m),z(m);
    for(int i=0;i<m;i++){
      cin>>x[i]>>y[i]>>z[i];
      x[i]--;
      y[i]--;
    }
    ll count=0;
    for(int i=0;i<(1<<(2*n-1));i++){
      vector<vector<ll>> ans(n,vector<ll>(n));
      ll k=i;
      for(int j=0;j<n;j++){
        ans[j][0]=k%2;
        k/=2;
      }
      for(int j=1;j<n;j++){
        ans[0][j]=k%2;
        k/=2;
      }
      solve(ans);
      bool check=true;
      for(int j=0;j<m;j++){
        if(ans[x[j]][y[j]]!=z[j]){
          check=false;
        }
      }
      if(check&&subsolve(ans)){
        count++;
      }
    }
    cout<<count<<endl;
  }
}