#include <bits/stdc++.h>
#define ll long long
#define pll pair<ll, ll>
#define fi first
#define se second
using namespace std;
const short int S = 0, T = 1, U = 2, V = 3;
const ll maxN = 1e5 + 5, INF = 1e18;
ll N, M, node[4], dist[4][maxN], memo[maxN][2];
vector<ll> pred[maxN];
vector<pll> adj[maxN];
bool vis[maxN], mark[maxN];
void dijkstra(ll idx, ll start) {
priority_queue<pll, vector<pll>, greater<pll> > PQ;
for (ll i = 1; i <= N; i++) {
dist[idx][i] = INF;
}
PQ.push({0, start});
dist[idx][start] = 0;
memset(vis, 0, sizeof(vis));
while (!PQ.empty()) {
ll cdist = PQ.top().fi;
ll cur = PQ.top().se;
PQ.pop();
if (vis[cur]) continue;
vis[cur] = 1;
for (auto i : adj[cur]) {
ll weight = i.se;
if (dist[idx][i.fi] > dist[idx][cur] + weight) {
dist[idx][i.fi] = dist[idx][cur] + weight;
if (idx == S) {pred[i.fi].push_back(cur);}
PQ.push({dist[idx][i.fi], i.fi});
}
}
}
}
ll dp(ll idx, bool type) {
//cout << idx << " " << type << '\n';
if (idx == node[V]) return 0;
if (memo[idx][type] != -1) return memo[idx][type];
ll ret = dist[V][idx];
//cout << "here\n";
for (auto a : adj[idx]) {
ll nxt = a.fi, weight = a.se;
//cout << nxt << '\n';
if (type) {
// S to T
if (dist[S][idx] + weight + dist[T][nxt] == dist[S][node[T]]) {
ret = min(ret, dp(nxt, 1));
}
} else {
// T to S
if (dist[T][idx] + weight + dist[S][nxt] == dist[T][node[S]]) {
ret = min(ret, dp(nxt, 0));
}
}
}
return memo[idx][type] = ret;
}
int main() {
ios_base::sync_with_stdio(false); cin.tie(NULL);
cin >> N >> M >> node[S] >> node[T] >> node[U] >> node[V];
for (ll A, B, C, i = 1; i <= M; i++) {
cin >> A >> B >> C;
adj[A].push_back({B, C});
adj[B].push_back({A, C});
}
dijkstra(S, node[S]);
dijkstra(T, node[T]);
dijkstra(U, node[U]);
dijkstra(V, node[V]);
/*
for (ll i = 1; i <= N; i++) {
for (ll j = 0; j < 4; j++) {
cout << dist[j][i] << " ";
}
cout << '\n';
}
*/
/*
// mark all nodes in the shortest routes from S to T
queue<ll> Q;
Q.push(node[T]);
while (!Q.empty()) {
ll cur = Q.front();
Q.pop();
if (mark[cur]) continue;
mark[cur] = 1;
for (auto i : pred[cur]){
Q.push(i);
}
}
for (ll i = 1; i <= N; i++) {
if (mark[i]) cout << i << " ";
}
cout << '\n';
*/
memset(memo, -1, sizeof(memo));
ll ans = dist[V][node[U]];
for (ll i = 1; i <= N; i++) {
if (dist[S][i] + dist[T][i] == dist[S][node[T]]) {
// i is on one of the shortest paths from S to T
ans = min(ans, dist[U][i] + min(dp(i, 0), dp(i, 1)));
}
}
cout << ans << '\n';
}
