/**
____ ____ ____ ____ ____
||a |||t |||o |||d |||o ||
||__|||__|||__|||__|||__||
|/__\|/__\|/__\|/__\|/__\|
**/
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N_MAX = 100000;
int N, M;
int S, T;
int U, V;
struct Edge {
int to;
int cost;
};
vector <Edge> adj[N_MAX + 2];
bool seen[N_MAX + 2];
void Dijkstra (int start, ll dist[]) {
fill(dist + 1, dist + N + 1, LLONG_MAX);
fill(seen + 1, seen + N + 1, false);
priority_queue <pair <ll, int>> q;
dist[start] = 0;
q.push(make_pair(-dist[start], start));
while (q.empty() == false) {
ll d; int u; tie(d, u) = q.top();
q.pop();
if (seen[u] == true) {
continue;
}
seen[u] = true;
for (Edge e : adj[u]) {
if (dist[u] + e.cost < dist[e.to]) {
dist[e.to] = dist[u] + e.cost;
q.push(make_pair(-dist[e.to], e.to));
}
}
}
}
ll distS[N_MAX + 2];
ll distT[N_MAX + 2];
ll distU[N_MAX + 2];
ll distV[N_MAX + 2];
vector <int> out[N_MAX + 2];
int cntin[N_MAX + 2];
ll minU[N_MAX + 2];
ll minV[N_MAX + 2];
int main () {
ios_base::sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
cin >> N >> M;
cin >> S >> T;
cin >> U >> V;
for (int i = 1; i <= M; i++) {
int u, v, cost;
cin >> u >> v >> cost;
adj[u].push_back(Edge{v, cost});
adj[v].push_back(Edge{u, cost});
}
Dijkstra(S, distS);
Dijkstra(T, distT);
Dijkstra(U, distU);
Dijkstra(V, distV);
for (int u = 1; u <= N; u++) {
for (Edge e : adj[u]) {
if (distS[u] + e.cost + distT[e.to] == distS[T]) {
out[u].push_back(e.to);
cntin[e.to]++;
}
}
}
queue <int> q;
for (int u = 1; u <= N; u++) {
if (cntin[u] == 0) {
q.push(u);
}
}
vector <int> topsort;
while (q.empty() == false) {
int u = q.front();
q.pop();
topsort.push_back(u);
for (int v : out[u]) {
if (--cntin[v] == 0) {
q.push(v);
}
}
}
ll answer = LLONG_MAX;
reverse(topsort.begin(), topsort.end());
for (int u : topsort) {
minU[u] = distU[u];
minV[u] = distV[u];
for (int v : out[u]) {
minU[u] = min(minU[u], minU[v]);
minV[u] = min(minV[u], minV[v]);
}
answer = min(answer, distU[u] + minV[u]);
answer = min(answer, distV[u] + minU[u]);
}
cout << answer << "\n";
return 0;
}
