#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using vb = vector<bool>;
using vvb = vector<vb>;
using vi = vector<int>;
using vvi = vector<vi>;
using vl = vector<ll>;
using vvl = vector<vl>;
using vvvl = vector<vvl>;
const ll mod = 1e9 + 7,inf = 1e18;
#define pb push_back
#define fast ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
void setIO()
{
fast;
}
int n = 1e5 + 5,m = 2e5 + 5,S,T,U,V;
vvvl adj(n);
vl distU(n,inf),distV(n,inf),distS(n,inf),distT(n,inf);
vvl dp(n,vl(2,inf));
int main()
{
setIO();
cin>>n>>m>>S>>T>>U>>V;
while (m--){
int u,v,w;
cin>>u>>v>>w;
adj[u].pb({v,w}),adj[v].pb({u,w});
}
priority_queue<pair<ll,int>>pq;
distU[U] = 0;
distV[V] = 0;
distS[S] = 0;
distT[T] = 0;
pq.push({0,V});
while (!pq.empty()){
int cur = pq.top().second;
if (distV[cur] != -pq.top().first){pq.pop();continue;}
pq.pop();
for (auto val:adj[cur]){
int x = val[0];
ll wt = val[1];
if (distV[x] > distV[cur] + wt){
distV[x] = distV[cur] + wt;
pq.push({-distV[x],x});
}
}
}
pq.push({0,U});
while (!pq.empty()){
int cur = pq.top().second;
if (distU[cur] != -pq.top().first){pq.pop();continue;}
pq.pop();
for (auto val:adj[cur]){
int x = val[0];
ll wt = val[1];
if (distU[x] > distU[cur] + wt){
distU[x] = distU[cur] + wt;
pq.push({-distU[x],x});
}
}
}
pq.push({0,S});
while (!pq.empty()){
int cur = pq.top().second;
if (distS[cur] != -pq.top().first){pq.pop();continue;}
pq.pop();
for (auto val:adj[cur]){
int x = val[0];
ll wt = val[1];
if (distS[x] > distS[cur] + wt){
distS[x] = distS[cur] + wt;
pq.push({-distS[x],x});
}
}
}
pq.push({0,T});
while (!pq.empty()){
int cur = pq.top().second;
if (distT[cur] != -pq.top().first){pq.pop();continue;}
pq.pop();
for (auto val:adj[cur]){
int x = val[0];
ll wt = val[1];
if (distT[x] > distT[cur] + wt){
distT[x] = distT[cur] + wt;
pq.push({-distT[x],x});
}
}
}
vvl all;
for (int i = 1;i<=n;i++)
if (distS[i] + distT[i] == distS[T])all.pb({distS[i],i});
sort(all.begin(),all.end());
ll ans = distU[V];
for (auto val:all){
int x = val[1];
dp[x][0] = min(dp[x][0],distU[x]);
dp[x][1] = min(dp[x][1],distV[x]);
for (auto val:adj[x]){
int y = val[0];
dp[y][0] = min(dp[y][0],dp[x][0]);
dp[y][1] = min(dp[y][1],dp[x][1]);
}
ans = min(ans,dp[x][0] + distV[x]);
ans = min(ans,dp[x][1] + distU[x]);
}
cout<<ans<<'\n';
return 0;
}
