#include<bits/stdc++.h>
#define fi first
#define se second
#define eb emplace_back
#define mp make_pair
using namespace std;
typedef long double ld;
typedef long long ll;
typedef unsigned long long ull;
typedef __int128 i128;
template<typename T,typename U>
T ceil(T x, U y) {return (x>0?(x+y-1)/y:x/y);}
template<typename T,typename U>
T floor(T x, U y) {return (x>0?x/y:(x-y+1)/y);}
template<class T,class S>
bool chmax(T &a,const S b) {return (a<b?a=b,1:0);}
template<class T,class S>
bool chmin(T &a,const S b) {return (a>b?a=b,1:0);}
int popcnt(int x) {return __builtin_popcount(x);}
int popcnt(ll x)  {return __builtin_popcountll(x);}
int topbit(int x) {return (x==0?-1:31-__builtin_clz(x));}
int topbit(ll x)  {return (x==0?-1:63-__builtin_clzll(x));}
int lowbit(int x) {return (x==0?-1:__builtin_ctz(x));}
int lowbit(ll x)  {return (x==0?-1:__builtin_ctzll(x));}

#define int long long
#define rep(i,a,b) for(int i=(a);i<=(b);i++)
#define per(i,a,b) for(int i=(a);i>=(b);i--)
typedef pair<int,int> pii; 
typedef vector<int> vi;
typedef vector<pii> vp;
typedef tuple<int,int,int> tiii;
int read() {
  int x=0,w=1; char c=getchar(); 
  while(!isdigit(c)) {if(c=='-') w=-1; c=getchar();}
  while(isdigit(c)) {x=x*10+(c-'0'); c=getchar();}
  return x*w;
}

const int N=2e5+5,inf=0x3f3f3f3f3f3f3f3f;
int n,m,f[(1<<18)+5][25][2],d[25][25],ans;
vp e[N];

signed main() {
  n=read(), m=read();
  rep(i,1,n) rep(j,1,n) d[i][j]=inf;
  rep(i,1,m) {
    int u=read(), v=read(), w=read();
    e[u].eb(v,w), e[v].eb(u,w);
    chmin(d[u][v],w), chmin(d[v][u],w);
  }
  rep(i,1,n) d[i][i]=0;
  rep(k,1,n) rep(i,1,n) rep(j,1,n) chmin(d[i][j],d[i][k]+d[k][j]);
  f[1][1][0]=1; int S=(1<<n)-1;
  rep(s,1,S) {
    rep(u,1,n) if(s&(1<<u-1)) {
      rep(k,0,1) if(f[s][u][k]) {
        for(auto [v,w]:e[u]) if(!(s&(1<<v-1))) {
          f[s|(1<<v-1)][v][k|(d[1][u]+w>d[1][v])]=1;
        }
        if(u==n&&k==1) ans=1;
      }
    }
  }
  printf("%lld\n",ans);
  return 0;
}