#include <bits/stdc++.h>
using namespace std;
int numNode, numEdge, S, T, U, V;
struct Edge {
int u, v, w;
int other(int x) {
return (u ^ v ^ x);
}
};
#define MAX_NODE 100100
#define MAX_EDGE 200200
vector<int> topo;
vector<int> adj[MAX_NODE], dad[MAX_NODE];
long long distS[MAX_NODE], distT[MAX_NODE], distU[MAX_NODE], distV[MAX_NODE], res[MAX_NODE];
bool vis[MAX_NODE];
Edge edges[MAX_EDGE];
void Dijkstra(int s, long long *dist) {
memset(dist, 0x3f, (numNode + 1) * sizeof(long long));
priority_queue<pair<long long, int>, vector<pair<long long, int>>, greater<pair<long long, int>>> q;
dist[s] = 0;
q.push(make_pair(dist[s], s));
while (!q.empty()) {
int u = q.top().second;
long long du = q.top().first;
q.pop();
if (du != dist[u]) continue;
for (int id : adj[u]) {
int v = edges[id].other(u);
int w = edges[id].w;
if (dist[v] > dist[u] + w) {
dist[v] = dist[u] + w;
q.push(make_pair(dist[v], v));
}
}
}
}
void buildTopo(int u) {
vis[u] = true;
for (int v : dad[u]) {
if (!vis[v]) buildTopo(v);
}
topo.push_back(u);
}
long long getAns(int en, long long *distFrom, long long *distTo) {
memset(res, 0x3f, sizeof(res));
long long ans = distFrom[en];
for (int u : topo) {
res[u] = min(res[u], distFrom[u]);
for (int v : dad[u]) res[v] = min(res[v], res[u]);
ans = min(ans, res[u] + distTo[u]);
}
return ans;
}
int main() {
ios_base::sync_with_stdio(false);cin.tie(nullptr);
cin >> numNode >> numEdge;
cin >> S >> T;
cin >> U >> V;
for (int i = 1; i <= numEdge; ++i) {
int u, v, w;
cin >> u >> v >> w;
edges[i] = {u, v, w};
adj[u].push_back(i);
adj[v].push_back(i);
}
Dijkstra(S, distS);
Dijkstra(T, distT);
Dijkstra(U, distU);
Dijkstra(V, distV);
for (int i = 1; i <= numEdge; ++i) {
int u = edges[i].u, v = edges[i].v, w = edges[i].w;
if (distS[u] + w == distS[v] && distS[T] == distS[v] + distT[v]) {
dad[u].push_back(v);
}
if (distS[v] + w == distS[u] && distS[T] == distS[u] + distT[u]) {
dad[v].push_back(u);
}
}
buildTopo(S);
reverse(topo.begin(), topo.end());
cout << min(getAns(V, distU, distV), getAns(U, distV, distU));
return 0;
}
