/*
* With a little appreciation, in a mostly hollow tone, she says, "Delightful." As if the world has any meaning.
* TASK : Commuter Pass
* AUTHOR : Marszpace
*/
#include<bits/stdc++.h>
using namespace std;
#define int long long
#define pii pair<int,int>
#define t5i tuple<int,int,int,int,int>
int32_t main(){
ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
int n,m,s,t,u,v;
cin >> n >> m >> s >> t >> u >> v;
vector<vector<pii>> edges(n+1,vector<pii>());
for(int i=0;i<m;i++){
int a,b,c;
cin >> a >> b >> c;
edges[a].push_back({c,b});
edges[b].push_back({c,a});
}
vector<int> distfromu(n+1,LLONG_MAX), distfromv(n+1,LLONG_MAX), distfin(n+1,LLONG_MAX);
{
priority_queue<pii, vector<pii>, greater<pii>> pq;
pq.push({0,u});
while(!pq.empty()){
auto [d,a]=pq.top();pq.pop();
if(distfromu[a]!=LLONG_MAX){continue;}
distfromu[a]=d;
for(auto [c,b]:edges[a]){
pq.push({d+c,b});
}
}
pq.push({0,v});
while(!pq.empty()){
auto [d,a]=pq.top();pq.pop();
if(distfromv[a]!=LLONG_MAX){continue;}
distfromv[a]=d;
for(auto [c,b]:edges[a]){
pq.push({d+c,b});
}
}
}
priority_queue<t5i, vector<t5i>, greater<t5i>> pq;
pq.push({0, distfromv[s]+distfromu[s], distfromv[s], distfromu[s], s});
while(!pq.empty()){
auto [d,ans,ans1,ans2,a]=pq.top();pq.pop();
if(distfin[a]!=LLONG_MAX){continue;}
distfin[a]=ans;
for(auto [c,b]:edges[a]){
pq.push({d+c,
min(ans1,distfromv[b])+min(ans2,distfromu[b]),
min(ans1,distfromv[b]),
min(ans2,distfromu[b]),
b});
}
}
cout << min(distfromu[v],distfin[t]);
return 0;
}
