#include <iostream>
#include <queue>
#include <algorithm>
#include <vector>
#include <utility>
#define pii pair<int,int>
#define F first
#define S second
#define int long long int
#define ericxiao ios_base::sync_with_stdio(0);cin.tie(0);
using namespace std;
const int maxN = 2e5 + 326, INF = 1e17;
int N, M, S, T, U, V, u, v, w, fromS[maxN], fromU[maxN], toT[maxN], toV[maxN], minToV[maxN], ans = INF, deg[maxN], dp1[maxN], dp2[maxN];
bool inRoute[maxN];
vector<int> chi[maxN];
queue<int> que;
struct Dijkstra{
priority_queue<pii, vector<pii>, greater<pii>> pq;
int dist[maxN], N;
bool vis[maxN];
vector<pii> adj[maxN];
Dijkstra(){}
Dijkstra(int N): N(N){}
inline void addEdge(int u, int v, int w){
adj[u].emplace_back(v, w);
adj[v].emplace_back(u, w);
}
inline void run(int s){
fill(vis, vis + N + 1, false);
fill(dist, dist + N + 1, INF);
pq = priority_queue<pii, vector<pii>, greater<pii>>();
dist[s] = 0;
pq.push({0, s});
while(pq.size()){
auto [d, u] = pq.top();
pq.pop();
if(vis[u]) continue;
vis[u] = true;
for(auto [v, w] : adj[u]){
if(vis[v]) continue;
if(w + d < dist[v]){
dist[v] = w + d;
pq.push({w + d, v});
}
}
}
}
} sp;
signed main(){
ericxiao
cin >> N >> M >> S >> T >> U >> V;
sp = Dijkstra(N);
for(int i = 0; i < M; i++){
cin >> u >> v >> w;
sp.addEdge(u, v, w);
}
sp.run(S);
for(int i = 1; i <= N; i++) fromS[i] = sp.dist[i];
/*
for(int i = 1; i <= N; i++){
cout << S << " - " << i << " = " << fromS[i] << endl;
}
*/
sp.run(T);
for(int i = 1; i <= N; i++) toT[i] = sp.dist[i];
sp.run(U);
for(int i = 1; i <= N; i++) fromU[i] = sp.dist[i];
sp.run(V);
for(int i = 1; i <= N; i++) toV[i] = sp.dist[i];
sp.run(U);
ans = toV[U];
for(int i = 1; i <= N; i++){
for(auto [u, w] : sp.adj[i]){
if(fromS[i] + w + toT[u] == toT[S]){
//cout << i << " - " << u << " lies on a path from " << S << " to " << T << endl;
inRoute[i] = inRoute[u] = true;
chi[u].push_back(i);
deg[i]++;
}
}
}
for(int i = 1; i <= N; i++) if(inRoute[i] && !deg[i]) que.push(i);
fill(dp1, dp1 + N + 1, INF);
fill(dp2, dp2 + N + 1, INF);
while(que.size()){
int f = que.front();
que.pop();
dp1[f] = min(dp1[f], toV[f]);
dp2[f] = min(dp2[f], fromU[f]);
//cout << "toV min of childs = " << dp1[f] << ", fromU min of childs = " << dp2[f] << endl;
ans = min(ans, fromU[f] + dp1[f]);
ans = min(ans, toV[f] + dp2[f]);
for(int x : chi[f]){
dp1[x] = min(dp1[x], dp1[f]);
dp2[x] = min(dp2[x], dp2[f]);
deg[x]--;
if(!deg[x]){
que.push(x);
}
}
}
cout << ans << endl;
}
