#include<bits/stdc++.h>
using namespace std;
using pii = pair<int,int>;
using pli = pair<long long, int>;
using ll = long long;
const int MN = 1e5 + 5;
vector<pii> adj[MN];
ll distU[MN], distV[MN], distS[MN], distT[MN], dpU[MN], dpV[MN];
int deg[MN];
void dijkstra (int source, long long *dist) {
priority_queue<pli,vector<pli>,greater<pli>> pq;
dist[source] = 0; pq.push({0,source});
while (!pq.empty()) {
ll d = pq.top().first; int cur = pq.top().second; pq.pop();
if (d > dist[cur]) continue;
for (pii &p : adj[cur]) if (d + p.second < dist[p.first]) {
dist[p.first] = d + p.second;
pq.push({dist[p.first],p.first});
}
}
}
int main () { //yikes
int n,m,s,t,u,v;
scanf("%d %d %d %d %d %d",&n,&m,&s,&t,&u,&v);
while (m--) {
int a,b,c;
scanf ("%d %d %d",&a,&b,&c);
adj[a].emplace_back(b,c);
adj[b].emplace_back(a,c);
}
memset(distU,0x3f,sizeof distU); memset(distV,0x3f,sizeof distV); memset(distS,0x3f,sizeof distS); memset(distT,0x3f,sizeof distT);
dijkstra(u,distU); dijkstra(v,distV); dijkstra(s,distS); dijkstra(t,distT);
for (int i = 1; i <= n; i++) {
dpU[i] = distU[i]; dpV[i] = distV[i];
if (distS[i] + distT[i] == distS[t]) {
for (pii p : adj[i]) if (distS[i] + p.second == distS[p.first] && distS[p.first] + distT[p.first] == distS[t]) ++deg[p.first];
}
}
queue<int> q; q.push(s);
while (!q.empty()) {
int cur = q.front(); q.pop();
for (pii p : adj[cur]) if (distS[cur] + p.second == distS[p.first] && distS[p.first] + distT[p.first] == distS[t]) {
dpU[p.first] = min(dpU[p.first],dpU[cur]); dpV[p.first] = min(dpV[p.first],dpV[cur]);
if (!(--deg[p.first])) q.push(p.first);
}
}
ll ret = LLONG_MAX;
for (int i = 1; i <= n; i++) {
ret = min({ret,dpU[i]+distV[i],dpV[i]+distU[i]});
}
printf ("%lld\n",ret);
return 0;
}
