#pragma GCC optimize ("O3")
#pragma GCC optimize ("unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")

#include <bits/stdc++.h>

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

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


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


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


ll 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];

    ll 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] = __builtin_popcount(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;

    memset(dp, -1, sizeof dp);

    for(int mask = (1 << (n - 4)) - 1; mask >= 0; mask--) {
        f[mask] = solve(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;
        // cout << "Answer: " << solve(mask, mp[s2], 1) << ' ' << f[compMask] << '\n';
        ans += solve(mask, n - 3, 1) * f[compMask];
    }
    cout << ans;






    return 0;
}

In file included from /usr/include/x86_64-linux-gnu/c++/11/bits/gthr.h:148,
                 from /usr/include/c++/11/ext/atomicity.h:35,
                 from /usr/include/c++/11/bits/ios_base.h:39,
                 from /usr/include/c++/11/ios:42,
                 from /usr/include/c++/11/istream:38,
                 from /usr/include/c++/11/sstream:38,
                 from /usr/include/c++/11/complex:45,
                 from /usr/include/c++/11/ccomplex:39,
                 from /usr/include/x86_64-linux-gnu/c++/11/bits/stdc++.h:54,
                 from answer.code:5:
/usr/include/x86_64-linux-gnu/c++/11/bits/gthr-default.h:102:1: error: attribute value ‘tune=native’ was already specified in ‘target’ attribute
  102 | __gthrw(pthread_once)
      | ^~~~~~~
/usr/include/x86_64-linux-gnu/c++/11/bits/gthr-default.h:102:1: error: attribute value ‘tune=native’ was already specified in ‘target’ attribute
/usr/include/x86_64-linux-gnu/c++/11/bits/gthr-default.h:103:1: error: attribute value ‘tune=native’ was already specified in ‘target’ attribute
  103 | __gthrw(pthread_getspecific)
      | ^~~~~~~
/usr/include/x86_64-linux-gnu/c++/11/bits/gthr-default.h:103:1: error: attribute value ‘tune=native’ was already specified in ‘target’ attribute
/usr/include/x86_64-linux-gnu/c++/11/bits/gthr-default.h:104:1: error: attribute value ‘tune=native’ was already specified in ‘target’ attribute
  104 | __gthrw(pthread_setspecific)
      | ^~~~~~~
/usr/include/x86_64-linux-gnu/c++/11/bits/gthr-default.h:104:1: error: attribute value ‘tune=native’ was already specified in ‘target’ attribute
/usr/include/x86_64-linux-gnu/c++/11/bits/gthr-default.h:106:1: error: attribute value ‘tune=native’ was already specified in ‘target’ attribute
  106 | __gthrw(pthread_create)
      | ^~~~~~~
/usr/include/x86_64-linux-gnu/c++/11/bits/gthr-default.h:106:1: error: attribute value ‘tune=native’ was already specified in ‘target’ attribute
/usr/include/x86_64-linux-gnu/c++/11/bits/gthr-default.h:107:1: error: attribute value ‘tune=native’ was already specified in ‘target’ attribute
  107 | __gthrw(pthread_join)
      | ^~~~~~~
/usr/include/x86_64-linux-gnu/c++/11/bits/gthr-default.h:107:1: error: attribute value ‘tune=native’ was already specified in ‘target’ attribute
/usr/include/x86_64-linux-gnu/c++/11/bits/gthr-default.h:108:1: error: attribute value ‘tune=native’ was already specified in ‘target’ attribute
  108 | __gthrw(pthread_equal)
      | ^~~~~~~
/usr/include/x86_64-linux-gnu/c++/11/bits/gthr-default.h:108:1: error: attribute value ‘tune=native’ was already specified in ‘target’ attribute
/usr/include/x86_64-linux-gnu/c++/11/bits/gthr-default.h:109:1: error: attribute value ‘tune=native’ was already specified in ‘target’ attribute
  109 | __gthrw(pthread_self)
      | ^~~~~~~
/usr/include/x86_64-linux-gnu/c++/11/bits/gthr-default.h:109:1: error: attribute value ‘tune=native’ was already specified in ‘target’ attribute
/usr/include/x86_64-linux-gnu/c++/11/bits/gthr-default.h:110:1: error: attribute value ‘tune=native’ was already specified in ‘target’ attribute
  110 | __gthrw(pthread_detach)
      | ^~~~~~~
/usr/include/x86_64-linux-gnu/c++/11/bits/gthr-default.h:110:1: error: attribute value ‘tune=native’ was already specified in ‘target’ attribute
/usr/include/x86_64-linux-gnu/c++/11/bits/gthr-default.h:112:1: error: attribute value ‘tune=native’ was already specified in ‘target’ attribute
  112 | __gthrw(pthread_cancel)
      | ^~~~~~~
/usr/include/x86_64-linux-gnu/c++/11/bits/gthr-default.h:112:1: error: attribute value ‘tune=native’ was already specified in ‘target’ attribute
/usr/include/x86_64-linux-gnu/c++/11/bits/gthr-default.h:114:1: error: attribute value ‘tune=native’ was already specified in ‘target’ attribute
  114 | __gthrw(sched_yield)
      | ^~~~~~~
/usr/include/x86_64-linux-gnu/c++/11/bits/gthr-default.h:114:1: error: attribute value ‘tune=native’ was already specified in ‘target’ attribute
/usr/include/x86_64-linux-gnu/c++/11/bits/gthr-default.h:116:1: error: attribute value ‘tune=native’ was already specified in ‘target’ attribute
  116 | __gthrw(pthread_mutex_lock)
      | ^~~~~~~
/usr/include/x86_64-linux-gnu/c++/11/bits/gthr-default.h:116:1: error: attribute value ‘tune=native’ was already specified in ‘target’ attribute
/usr/include/x86_64-linux-gnu/c++/11/bits/gthr-default.h:117:1: error: attribute value ‘tune=native’ was already specified in ‘target’ attribute
  117 | __gthrw(pthread_mutex_trylock)
      | ^~~~~~~
/usr/include/x86_64-linux-gnu/c++/11/bits/gthr-default.h:117:1: error: attribute value ‘tune=native’ was already specified in ‘target’ attribute
/usr/include/x86_64-linux-gnu/c++/11/bits/gthr-default.h:119:1: error: attribute value ‘tune=native’ was already specified in ‘target’ attribute
  119 | __gthrw(pthread_mutex_timedlock)
      | ^~~~~~~
/usr/include/x86_64-linux-gnu/c++/11/bits/gthr-default.h:119:1: error: attribute value ‘tune=native’ was already specified in ‘target’ attribute
/usr/...