#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define pll pair<ll,ll>
#define fs first
#define sc second
const int mxn = 1e5+10;
const ll inf = 1e18;
vector<pll> paths[mxn];
ll dist1[mxn],dist2[mxn],dist3[mxn],deg[mxn];
vector<int> dag[mxn];
bitset<mxn> done;
ll dp[2][mxn];
int n,m;
int s,e,u,v;
ll ans = 1e18;
void dijkstra(int st,ll dist[]){
priority_queue<pll,vector<pll>,greater<pll>> pq;
fill(dist,dist+n+1,inf);
dist[st] = 0;
pq.push(make_pair(0,st));
while(!pq.empty()){
auto now = pq.top().sc;
auto val = pq.top().fs;
pq.pop();
//cout<<now<<endl;
if(val != dist[now])continue;
for(auto nxt:paths[now]){
if(dist[nxt.fs]>dist[now]+nxt.sc){
dist[nxt.fs] = dist[now]+nxt.sc;
pq.push(make_pair(dist[nxt.fs],nxt.fs));
}
}
}
return;
}
void solve(){
cin>>n>>m;
cin>>s>>e>>u>>v;
fill(dp[0],dp[0]+mxn,inf);
fill(dp[1],dp[1]+mxn,inf);
for(int i = 0;i<m;i++){
int a,b,c;
cin>>a>>b>>c;
paths[a].push_back(make_pair(b,c));
paths[b].push_back(make_pair(a,c));
}
dijkstra(s,dist1);
dijkstra(u,dist2);
dijkstra(v,dist3);
queue<int> q;
q.push(e);
done[e] = true;
//for(int i = 1;i<=n;i++)cout<<dist1[i]<<' ';cout<<endl;
while(!q.empty()){
auto now = q.front();
q.pop();
for(auto nxt:paths[now]){
//cout<<nxt.fs<<":"<<now<<endl;
if(dist1[nxt.fs] + nxt.sc == dist1[now]){
if(!done[nxt.fs])q.push(nxt.fs);
done[nxt.fs] = true;
dag[now].push_back(nxt.fs);
deg[nxt.fs]++;
}
}
}
q.push(e);
/*
for(int i = 1;i<=n;i++){
for(auto nxt:dag[i])cout<<i<<','<<nxt<<endl;
}
*/
while(!q.empty()){
auto now = q.front();
q.pop();
dp[0][now] = min(dp[0][now],dist2[now]);
dp[1][now] = min(dp[1][now],dist3[now]);
ans = min({ans,dp[0][now]+dist3[now],dp[1][now]+dist2[now]});
for(auto nxt:dag[now]){
deg[nxt]--;
if(!deg[nxt])q.push(nxt);
dp[0][nxt] = min(dp[0][nxt],dp[0][now]);
dp[1][nxt] = min(dp[1][nxt],dp[1][now]);
}
}
cout<<min(ans,dist2[v]);
}
int main(){
ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
int t = 1;
while(t--)solve();
}
