#include <bits/stdc++.h>
using namespace std;

#define  ll long long
#define ld long double
#define f first
#define s second
const int N = 30;

int n , m , s , t , s2 , t2;
ll ds[N][N];
vector< pair<int,int> > adj[N];
vector<int> adj2[N];

void dijk(int st)
{
    for(int i=1; i<=n; i++)
        ds[st][i] = 1e18;

    ds[st][st] = 0;
    priority_queue< pair<ll,ll> , vector< pair<ll,ll> > , greater< pair<ll,ll> > > q;
    q.push({0 , st});
    while(!q.empty())
    {
        int node = q.top().s;
        ll cst = q.top().f;
        q.pop();

        if (cst > ds[st][node]) continue;

        for(auto ch : adj[node])
        {
            ll cst2 = cst + ch.s;

            if (cst2 < ds[st][ch.f])
            {
                ds[st][ch.f] = cst2;
                q.push({ds[st][ch.f] , ch.f});
            }
        }
    }
}

ll cnt = 0;

vector<int> all_masks;
void dfs(int node , int msk , int sink)
{
    cnt++;
    if (node == sink)
    {
        all_masks.push_back(msk);
        return;
    }

    for(auto ch : adj2[node])
    {
        dfs(ch , msk | (1<<ch) , sink);
    }
}

int main()
{
    ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);

    cin >> n >> m;
    for(int i=1; i<=m; i++)
    {
        int x ,y , c;
        cin >> x >> y >> c;
        adj[x].push_back({y , c});
        adj[y].push_back({x , c});
    }

    for(int i=1; i<=n; i++)
        dijk(i);


    cin >> s >> t >> s2 >> t2;
    for(int i=1; i<=n ;i++)
    {
        for(auto it : adj[i])
        {
            int v = i , u = it.f , cst = it.s;
            if (ds[s][v] + cst + ds[u][t] == ds[s][t])
            {
                adj2[v].push_back(u);
            }
        }
    }

    vector<int> masks , masks2; //masks of path 1 and path 2

    dfs(s , 1<<s , t);
    masks = all_masks;

    all_masks.clear();
    for(int i=1; i<=n; i++)
        adj2[i].clear();

    for(int i=1; i<=n ;i++)
    {
        for(auto it : adj[i])
        {
            int v = i , u = it.f , cst = it.s;
            if (ds[s2][v] + cst + ds[u][t2] == ds[s2][t2])
            {
                adj2[v].push_back(u);
            }
        }
    }
    dfs(s2 , 1<<s2 , t2);

    assert(cnt <= (ll)3e9);

    masks2 = all_masks;

    ll ans = 0;

    for(auto it : masks)
    {
        for(auto it2 : masks2)
        {
            if (it&it2) continue;
            ans++;
        }
    }


    cout << ans << "\n";

    return 0;
}