#include <bits/stdc++.h>
using namespace std;
typedef long long int ll;
typedef pair<int, int> pii;
#define SZ(x) (int) x.size()
#define F first
#define S second
const int N = 2e5 + 10, MOD = 1e9 + 7;
ll dist[4][N], dp[2][N], M[N], X[N], n, m, R = 1e18, B, E, U, V;
vector<pii> adj[N]; vector<int> out[N], in[N];
void dijk(int S, int t) {
fill(dist[t], dist[t] + N, 1e18);
dist[t][S] = 0;
priority_queue<pair<ll, int>> pq;
pq.push({dist[t][S], S});
while (SZ(pq)) {
int v = pq.top().S; pq.pop();
for (pii u : adj[v]) {
if (dist[t][u.F] > dist[t][v] + u.S) {
dist[t][u.F] = dist[t][v] + u.S;
pq.push({-dist[t][u.F], u.F});
}
}
}
}
void add_edge(int u, int v) {
out[u].push_back(v);
in[v].push_back(u);
}
void DFS(int v) {
M[v] = 1;
for (int u : out[v]) {
if (!M[u]) DFS(u);
dp[0][v] = min(dp[0][v], dp[0][u]);
}
}
void SFD(int v) {
M[v] = 1;
for (int u : in[v]) {
if (!M[u]) SFD(u);
dp[1][v] = min(dp[1][v], dp[1][u]);
}
}
int main() {
scanf("%lld%lld%lld%lld%lld%lld", &n, &m, &B, &E, &U, &V);
for (int i = 1; i <= m; i++) {
int u, v, w; scanf("%d%d%d", &u, &v, &w);
adj[u].push_back({v, w});
adj[v].push_back({u, w});
}
dijk(B, 0);
dijk(E, 1);
dijk(U, 2);
dijk(V, 3);
for (int i = 1; i <= n; i++) {
if (dist[0][i] + dist[1][i] == dist[0][E]) X[i] = 1;
for (pii u : adj[i]) {
if (dist[0][i] + u.S + dist[1][u.F] == dist[0][E]) {
add_edge(i, u.F);
}
}
}
for (int i = 1; i <= n; i++) {
dp[0][i] = dp[1][i] = dist[3][i];
}
for (int i = 1; i <= n; i++) {
if (X[i] && !M[i]) DFS(i);
}
fill(M, M + N, 0);
for (int i = 1; i <= n; i++) {
if (X[i] && !M[i]) SFD(i);
}/*
for (int i = 1; i <= n; i++) {
printf("%lld %lld\n", dp[0][i], dp[1][i]);
}*/
for (int i = 1; i <= n; i++) {
if (X[i]) {
R = min(R, min(dp[0][i], dp[1][i]) + dist[2][i]);
}
}
printf("%lld\n", min(R, dist[2][V]));
return 0;
}
