#include<bits/stdc++.h>
#define mp make_pair
using namespace std;
int const N = 1e3, M = 1048577, N1 = 20, M1 = 30;
int s[2], t[2], dis[M1]; //所有的点需要平移
struct stu1 {
	int x, y, w;
} ed[N];
struct stu2 {
	int y, nex, w;
} e[N * 2];
long long a[M1], g[2][M], lin[M1], cnt, tot, pw[M], n, m, f[M][N1]; //sosdp一下
int Get(int x, int s1, int t1) {
	if (x == s1) return n;
	if (x == t1) return n + 1;
	int y = lower_bound(a, a + cnt, x) - a; //从0开始
	if (x != a[y]) return n + 2;
	return y;
}
void work(int x, int y, int w) {
	e[++tot] = (stu2) {
		y, lin[x], w
	};
	lin[x] = tot;
}
bool fl[M1];
#define fi first
#define se second
int lb(int x) {
	return x & (-x);
}
void sol(int s1, int t1, int op) {
	if (s1 == t1) {
		g[op][0] = 1;
		return;
	}
	tot = 0;
	for (int i = 0; i <= n + 1; i++) lin[i] = 0, dis[i] = 1e9, fl[i] = 0; //一共是cnt个点
	int x, y, w;
	for (int i = 1; i <= m; i++) {
		x = ed[i].x;
		y = ed[i].y;
		w = ed[i].w;
		x = Get(x, s1, t1);
		y = Get(y, s1, t1);
		if (x == n + 2 || y == n + 2) continue;
		work(x, y, w);
		work(y, x, w);
	}
	dis[n] = 0;
	priority_queue<pair<int, int>> q;
	q.push(mp(0, n));
	while (q.size()) {
		x = q.top().se;
		q.pop();
		if (fl[x]) continue;
		fl[x] = 1;
		for (int i = lin[x]; i; i = e[i].nex) {
			y = e[i].y;
			if (dis[y] > dis[x] + e[i].w) {
				dis[y] = dis[x] + e[i].w;
				q.push(mp(-dis[y], y));
			}
		}
	}
	for (int i = lin[n]; i; i = e[i].nex) {
		y = e[i].y;
		if (e[i].w == dis[y]) {
			if (y == n + 1) {
				g[op][0]++;
				//cout<<"qwq"<<endl;
			} else f[1 << y][y]++;
		}
	}

	int w1;
	for (int i = 1; i < (1 << cnt); i++) {
		w1 = i;
		while (w1) {
			int j = pw[lb(w1)];
			w1 -= lb(w1);
			if (f[i][j]) {
				for (int k = lin[j]; k; k = e[k].nex) {
					y = e[k].y;
					w = e[k].w;
					if (dis[j] + w == dis[y]) {
						if (y == n + 1) g[op][i] += f[i][j];
						else f[(1 << y) | i][y] += f[i][j];
					}
				}
			}
		}
	}
	memset(f, 0, sizeof(f));
}
void pd() {
	if (s[0] == s[1] || t[0] == t[1] || s[0] == t[1] || s[1] == t[0]) {
		printf("%d", 0);
		exit(0);
	}
}
int main() {
	scanf("%d%d", &n, &m);
	int x, y, w;
	for (int i = 1; i <= m; i++) {
		scanf("%d%d%d", &x, &y, &w);
		ed[i] = (stu1) {
			x, y, w
		};
	} //s=n点 t n+1点 [0,n-1]
	scanf("%d%d%d%d", &s[0], &t[0], &s[1], &t[1]);
	pd();
	for (int i = 1; i <= n; i++)
		if (i != s[0] && i != s[1] && i != t[0] && i != t[1]) a[cnt++] = i;
	for (int i = 0; i < cnt; i++) pw[1 << i] = i;
	sol(s[0], t[0], 0);
	sol(s[1], t[1], 1);

	int sum = (1 << cnt);

	for (int i = 0; i < cnt; i++) //sosdp
		for (int s = 0; s < sum; s++)
			if (s & (1 << i)) g[0][s] += g[0][s ^ (1 << i)];

	long long ans = 0;
	sum--;
//	cout<<g[0][0]<<endl;
	for (int s = 0; s <= sum; s++) {
		ans += 1ll * g[1][s] * g[0][sum ^ s];
	}
	printf("%lld", ans);
}