#pragma GCC optimize("O3")
#pragma GCC optimize ("unroll-loops")
#pragma GCC target("avx,avx2,fma")
#include <bits/stdc++.h>

#define EPS 1e-9
#define PI acos(-1.0)
#define ll long long
#define all(s) s.begin(),s.end()
#define rall(s) s.rbegin(),s.rend()
#define pb push_back
#define ft first
#define sc second
#define pi pair<int,int>
#define vi vector<int>
#define sz(s) s.size()
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
using namespace std;
typedef tree<ll, null_type, less<ll>, rb_tree_tag,tree_order_statistics_node_update> ordered_set;
const ll N = 25, M = (1 << 20), MOD = (1LL<<32), INF = 1e18;
int dx[] = {-1, 1, 0, 0}, Dx[] = {-1, -1, 0, 1, 1, 1, 0, -1};;
int dy[] = {0, 0, 1, -1}, Dy[] = {0, 1, 1, 1, 0, -1, -1, -1};
ll n, m, t,dp[22][M],dp2[22][M], s1,s2,t1,t2,dis[N][N],mp[N];
vector<pi> g[25];
int solve2(int node,int msk)
{
    if(mp[t2] == node){
        return 1;
    }
    int &ret = dp2[node][msk];
    if(~ret)
        return ret;
    ret = 0;
    for(auto it:g[node])
    {
        if(it.ft != mp[s1] && it.ft != mp[t1] && it.ft != mp[s2] && dis[mp[s2]][node] + it.sc + dis[it.ft][mp[t2]] == dis[mp[s2]][mp[t2]] && !(msk&(1<<it.ft)))
            ret += solve2(it.ft,msk|(1<<it.ft));
    }
    return ret;
}
int solve(int node,int msk)
{
    if(mp[t1] == node){
        return solve2(mp[s2],msk);
    }
    int &ret = dp[node][msk];
    if(~ret)
        return ret;
    ret = 0;
    for(auto it:g[node])
    {
        if(it.ft != mp[s2] && it.ft != mp[t2] && it.ft != mp[s1] && dis[mp[s1]][node] + it.sc + dis[it.ft][mp[t1]] == dis[mp[s1]][mp[t1]])
            ret += solve(it.ft,msk|(1<<it.ft));
    }
    return ret;
}
int main()
{
    ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);//freopen("lines.in", "r", stdin);
    cin >> n >> m;
    for(int i = 0; i < n ;++i)
    {
        dis[i][i] = 0;
        for(int j = i+1; j < n ;++j)
        {
            dis[i][j] = dis[j][i] = 1e9;
        }
    }
    vector<pair<pi,int>> tmp;
    for(int i = 0; i < m ;++i)
    {
        int u,v,c;
        cin >> u >> v >> c;
        u--,v--;
        tmp.pb({{u,v},c});
    }
    int id = 0;
    cin >> s1 >> t1 >> s2 >> t2;
    s1--,s2--,t1--,t2--;
    for(int i = 0; i < n ;++i){
        if(i == t1 || i == t2 or i == s1 or i == s2) continue;
        mp[i] = id++;
    }
    mp[t1] = id++;
    mp[t2] = id++;
    mp[s1] = id++;
    mp[s2] = id++;
    for(int i = 0; i < m ;++i)
    {
        int u = mp[tmp[i].ft.ft] , v = mp[tmp[i].ft.sc] , c = tmp[i].sc;
        dis[u][v] = dis[v][u] = c;
        g[u].pb({v,c});
        g[v].pb({u,c});
    }

    memset(dp,-1,sizeof dp);
    memset(dp2,-1,sizeof dp2);
    for(int i = 0; i < n ;++i)
    {
        for(int j = 0;j < n ;++j)
        {
            for(int k = 0; k < n ;++k)
            {
                dis[i][j] = min(dis[i][j] , dis[i][k] + dis[k][j]);
            }
        }
    }
    cout << solve(mp[s1],0);
    return 0;
}
/*
*/

answer.code: In function ‘int solve2(int, int)’:
answer.code:32:29: error: cannot bind non-const lvalue reference of type ‘int&’ to a value of type ‘long long int’
   32 |     int &ret = dp2[node][msk];
      |                ~~~~~~~~~~~~~^
answer.code: In function ‘int solve(int, int)’:
answer.code:48:28: error: cannot bind non-const lvalue reference of type ‘int&’ to a value of type ‘long long int’
   48 |     int &ret = dp[node][msk];
      |                ~~~~~~~~~~~~^