#include <bits/stdc++.h>

#define ll long long
#define ld  double
using namespace std;

const int N = 500 + 5, M = (1 << 20), mod = 998244353;


int dp[M + 5][25][2];
ll f[M + 5];


int n, mp[30], s1, s2, t1, t2, cnt[M + 5], dis[30][30], Edge[30][30];

vector<int> Masks[30], Bits[M + 5], BitsOff[M + 5];



int solve(int mask, int last, bool t) {
    int lastNode = mp[last], target = t1;
    if(t == 1) target = t2;
    if(cnt[mask] == 0) {
        if(dis[lastNode][target] == Edge[lastNode][target]) return 1;
        return 0;
    }
    if(dp[mask][last][t] != -1) return dp[mask][last][t];

    int ans = 0;

    for(int bit = 0; bit < (n - 4); bit++) {
        if(mask >> bit & 1) {
            int curNode = mp[bit];
            if(dis[lastNode][target] == Edge[lastNode][curNode] + dis[curNode][target]) {
                ans += solve(mask ^ (1 << bit), bit, t);
            }
        }
    }
    return dp[mask][last][t] = ans;

}





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

    int m;
    cin >> n >> m;

    for(int i = 0; i < n; i++) {
        for(int j = 0; j < n; j++) {
            Edge[i][j] = dis[i][j] = mod;
        }
    }


    for(int i = 0; i < m; i++) {
        int u, v, c;
        cin >> u >> v >> c;
        u--; v--;
        dis[u][v] = dis[v][u] = Edge[u][v] = Edge[v][u] = min(dis[u][v], c);
    }

    cin >> s1 >> t1 >> s2 >> t2;
    s1--; t1--;
    s2--; t2--;

    for(int k = 0; k < n; k++) {
        for(int i = 0; i < n; i++) {
            for(int j = 0; j < n; j++) {
                dis[i][j] = min(dis[i][j], dis[i][k] + dis[k][j]);
            }
        }
    }

    for(int i = 1; i < (1 << (n - 4)); i++) {
        cnt[i] = 0;
        for(int bit = 0; bit < (n - 4); bit++) {
            if(i >> bit & 1) {
                cnt[i]++;
                Bits[i].push_back(bit);
            }
            else BitsOff[i].push_back(bit);
        }
        // cnt[i] = __builtin_popcount(i);
        Masks[cnt[i]].push_back(i);
    }

    // cout << dis[0][1] << ' ' << dis[2][3] << '\n';
    int curId = 0;
    for(int i = 0; i < n; i++) {
        if(i == s1 || i == s2 || i == t1 || i == t2) continue;
        mp[curId] = i;
        curId++;
    }
    mp[n - 4] = s1;
    mp[n - 3] = s2;
    mp[n - 2] = t1;
    mp[n - 1] = t2;

    int lastNode, curNode;
    for(int i = 0; i < (n - 2); i++) {
        lastNode = mp[i];
        dp[0][i][0] = (Edge[lastNode][t1] == dis[lastNode][t1]);
        dp[0][i][1] = (Edge[lastNode][t2] == dis[lastNode][t2]);
    }

    // cout << dp[0][0][0] << ' ' << dp[0][1][1] << '\n';

    for(int kam = 1; kam < (n - 4); kam++) {
        for(int mask: Masks[kam]) {
            for(int bit: Bits[mask]) {
                curNode = mp[bit];
                for(int last: BitsOff[mask]) {
                    lastNode = mp[last];
                    if(dis[lastNode][t1] == Edge[lastNode][curNode] + dis[curNode][t1]) {
                        dp[mask][last][0] += dp[mask ^ (1 << bit)][bit][0];
                    }
                    if(dis[lastNode][t2] == Edge[lastNode][curNode] + dis[curNode][t2]) {
                        dp[mask][last][1] += dp[mask ^ (1 << bit)][bit][1];
                    }
                }
                if(dis[s1][t1] == Edge[s1][curNode] + dis[curNode][t1]) {
                    dp[mask][n - 4][0] += dp[mask ^ (1 << bit)][bit][0];
                }
                if(dis[s2][t2] == Edge[s2][curNode] + dis[curNode][t2]) {
                    dp[mask][n - 3][0] += dp[mask ^ (1 << bit)][bit][1];
                }
            }
        }

    }


    // memset(dp, -1, sizeof dp);

//    for(int mask = 0; mask < (1 << (n - 4)); mask++) {
//        bool found = 0;
//        for(int bit = 0; bit < (n - 4); bit++) {
//            if(mask >> bit & 1) {
//                int curNode = mp[bit];
//                if(dis[s1][t1] != dis[s1][curNode] + dis[curNode][t1]) {
//                    found = 1;
//                    break;
//                }
//            }
//        }
//        if(found) continue;
//        f[mask] = solve(mask, n - 4, 0);
//    }

    for(int mask = 0; mask < (1 << (n - 4)); mask++) {
        f[mask] = dp[mask][n - 4][0];
    }

    for(int bit = 0; bit < (n - 4); bit++) {
        for(int mask = 0; mask < (1 << (n - 4)); mask++) {
            if(mask >> bit & 1) {
                f[mask] += f[mask ^ (1 << bit)];
            }
        }
    }

    ll ans = 0;
    for(int mask = 0; mask < (1 << (n - 4)); mask++) {
        int compMask = (1 << (n - 4)) - 1 - mask;
        ans += dp[mask][n - 3][1] * f[compMask];
    }
    cout << ans;






    return 0;
}


/*
 for(int kam = 1; kam < (n - 4); kam++) {
        for(auto mask: Masks[kam]) {
            for(auto bit: Bits[mask]) {

            }
        }
    }
 */