#include <bits/stdc++.h>
using namespace std;
#define rep(i, n)  for(long long i=0;i<(long long)(n);i++)
#define REP(i,k,n) for(long long i=k;i<(long long)(n);i++)
#define pb emplace_back
#define lb(v,k) (lower_bound(all(v),(k))-v.begin())
#define ub(v,k) (upper_bound(all(v),(k))-v.begin())
#define fi first
#define se second
#define pi M_PI
#define PQ(T) priority_queue<T>
#define SPQ(T) priority_queue<T,vector<T>,greater<T>>
#define dame(a) {out(a);return 0;}
#define decimal cout<<fixed<<setprecision(15);
#define all(a) a.begin(),a.end()
#define rsort(a) {sort(all(a));reverse(all(a));}
#define dupli(a) {sort(all(a));a.erase(unique(all(a)),a.end());}
typedef long long ll;
typedef pair<ll,ll> P;
typedef tuple<ll,ll,ll> PP;
typedef tuple<ll,ll,ll,ll> PPP;
using vi=vector<ll>;
using vvi=vector<vi>;
using vvvi=vector<vvi>;
using vvvvi=vector<vvvi>;
using vp=vector<P>;
using vvp=vector<vp>;
using vb=vector<bool>;
using vvb=vector<vb>;
const ll inf=1001001001001001001;
const ll INF=1001001001;
const ll mod=1000000007;
const double eps=1e-10;
template<class T> bool chmin(T&a,T b){if(a>b){a=b;return true;}return false;}
template<class T> bool chmax(T&a,T b){if(a<b){a=b;return true;}return false;}
template<class T> void out(T a){cout<<a<<'\n';}
template<class T> void outp(T a){cout<<'('<<a.fi<<','<<a.se<<')'<<'\n';}
template<class T> void outvp(T v){rep(i,v.size())cout<<'('<<v[i].fi<<','<<v[i].se<<')';cout<<'\n';}
template<class T> void outvvp(T v){rep(i,v.size())outvp(v[i]);}
template<class T> void outv(T v){rep(i,v.size()){if(i)cout<<' ';cout<<v[i];}cout<<'\n';}
template<class T> void outvv(T v){rep(i,v.size())outv(v[i]);}
template<class T> bool isin(T x,T l,T r){return (l)<=(x)&&(x)<=(r);}
template<class T> void yesno(T b){if(b)out("yes");else out("no");}
template<class T> void YesNo(T b){if(b)out("Yes");else out("No");}
template<class T> void YESNO(T b){if(b)out("YES");else out("NO");}
template<class T> void outset(T s){auto itr=s.begin();while(itr!=s.end()){if(itr!=s.begin())cout<<' ';cout<<*itr;itr++;}cout<<'\n';}
void outs(ll a,ll b){if(a>=inf-100)out(b);else out(a);}
ll gcd(ll a,ll b){if(b==0)return a;return gcd(b,a%b);}
ll modpow(ll a,ll b){ll res=1;a%=mod;while(b){if(b&1)res=res*a%mod;a=a*a%mod;b>>=1;}return res;}

int main(){
    ll n,m;cin>>n>>m;
    assert(1<=n&&n<=100000);
    assert(0<=m&&m<=100);
    vector<PP> v;
    vi cnt(2);
    rep(i,m){
        ll a,b,c;cin>>a>>b>>c;
        assert(1<=a&&a<=n);
        assert(1<=b&&b<=n);
        assert(0<=c&&c<=1);
        v.pb(a-1,b-1,c);
        cnt[c]++;
    }
    rep(i,m)rep(j,i){
        assert(get<0>(v[i])!=get<0>(v[j])||get<1>(v[i])!=get<1>(v[j]));
    }
    if(n>=10)dame(cnt[0]==0);
    ll ans=0;
    rep(bit,1<<(n*2-1)){
        vvi k(n,vi(n));
        rep(i,n)k[i][0]=bit>>i&1;
        REP(i,n,n*2-1)k[0][i-n+1]=bit>>i&1;
        REP(i,1,n)REP(j,1,n)k[i][j]=(k[i][0]+k[0][j]+k[0][0])&1;
        bool ok=true;
        rep(i,m)if(k[get<0>(v[i])][get<1>(v[i])]!=get<2>(v[i]))ok=false;
        for(int t=3;t<=n;t+=2){
            ll s=0;
            rep(i,t)rep(j,t)s+=k[i][j];
            if(s%2==0)ok=false;
            rep(i,n)rep(j,n-t)if(k[i][j]!=k[i][j+t])ok=false;
            rep(i,n-t)rep(j,n)if(k[i][j]!=k[i+t][j])ok=false;
        }/*
        if(ok){
            outvv(k);cout<<endl;
        }*/
        if(ok)ans++;
    }
    out(ans);
}