#include<bits/stdc++.h>
using namespace std;
using ll=long long;
template<typename T>
ostream& operator << (ostream &out,const vector<T>&x){
	if(x.empty())return out<<"[]";
	out<<'['<<x[0];
	for(int len=x.size(),i=1;i<len;i++)out<<','<<x[i];
	return out<<']';
}
template<typename T>
vector<T> ary(const T *a,int l,int r){
	return vector<T>{a+l,a+1+r};
}
template<typename T>
void debug(T x){
	cerr<<x<<'\n';
}
template<typename T,typename ...S>
void debug(T x,S ...y){
	cerr<<x<<' ',debug(y...);
}
const int N=30,M=1<<20;
int n,m,a[N][N],d[N][N];
int s1,t1,s2,t2,vis[N],id[N];
ll g[M],h[M];
void dfs(ll *f,int u,int t,int S=0){
	// debug(u,t);
	for(int v=1;v<=n;v++){
		if(!a[u][v]||a[u][v]+d[v][t]>d[u][t])continue;
		if(v==t){
			f[S]++;
		}else if(!vis[v]){
			dfs(f,v,t,S|(1<<id[v]));
		}
	}
}
int main(){
	cin>>n>>m;
	memset(d,0x3f,sizeof d);
	for(int i=1;i<=n;i++)d[i][i]=0;
	for(int u,v,w;m--;){
		cin>>u>>v>>w;
		a[u][v]=a[v][u]=w;
		d[u][v]=d[v][u]=w;
	}
	for(int k=1;k<=n;k++){
		for(int i=1;i<=n;i++){
			for(int j=1;j<=n;j++){
				d[i][j]=min(d[i][j],d[i][k]+d[k][j]);
			}
		}
	}
	cin>>s1>>t1>>s2>>t2;
	vis[s1]=vis[t1]=vis[s2]=vis[t2]=1;
	for(int i=1,k=0;i<=n;i++){
		if(!vis[i])id[i]=k++;
		else id[i]=-1;
	}
	dfs(g,s1,t1),dfs(h,s2,t2);
	int U=(1<<n-4)-1;
	for(int len=1;len<U;len<<=1){
		for(int i=0;i<=U;i+=len<<1){
			for(int j=0;j<len;j++){
				g[i|j]+=g[i|j|len],h[i|j]+=h[i|j|len];
			}
		}
	}
	for(int S=0;S<=U;S++)g[S]*=h[S];
	for(int len=1;len<U;len<<=1){
		for(int i=0;i<=U;i+=len<<1){
			for(int j=0;j<len;j++){
				g[i|j]-=g[i|j|len];
			}
		}
	}
	cout<<g[0]<<endl;
	return 0;
}