#include <bits/stdc++.h>
using namespace std;
#define int long long
#define pll pair<int, int>
#define mp make_pair
#define pb push_back
#define f first
#define s second
#define endl '\n'
#define maxn 100005
#define maxc 1e15
#define iii tuple<int,int,int>
int n,m,s,t,u,v,d;
vector<vector<pair<int,int>>> al(maxn);
vector<int> ds(maxn,maxc),dt(maxn,maxc),du(maxn,maxc),dv(maxn,maxc);
vector<vector<int>> mem(maxn, vector<int>(3, maxc));
void dijkstra(int start, vector<int> & dist){
dist[start]=0;
priority_queue<pair<int,int>, vector<pair<int,int>>,greater<pair<int,int>>> pq;
pq.push({0, start});
while(!pq.empty()){
auto [cd, x] = pq.top();pq.pop();
//~ printf("cur dist %lld x is %lld\n", cd, x);
if(dist[x]<cd)continue;
for(auto [to, cost]:al[x]){
//~ printf("to %lld, cost %lld\n",to,cost);
if(cd+cost<dist[to]){
dist[to]=cd+cost;
pq.push({cd+cost, to});
}
}
}
}
signed main(){
cin>>n>>m>>s>>t>>u>>v;
for(int i=0;i<m;i++){
int a,b,c;cin>>a>>b>>c;
al[a].pb({b,c});
al[b].pb({a,c});
}
dijkstra(s, ds);
dijkstra(t, dt);
assert(dt[s]==ds[t]);
d=dt[s];
priority_queue<iii, vector<iii>,greater<iii>> pq;
pq.push({0, u, 0});
mem[u][0]=0;
//0 not started, 1 in midst of, 2 exited.
while(!pq.empty()){
auto [cd, x, st]=pq.top();pq.pop();
if(mem[x][st]<cd)continue;
for(auto [to, cost]:al[x]){
if ((ds[x]+cost+dt[to]==d)
and st!=2){
if(cd<mem[to][1]){
mem[to][1]=cd;
pq.push({cd, to, 1});
}
}
int nst=(st==1?2:st);
if(cd+cost<mem[to][nst]){
mem[to][nst]=cd+cost;
pq.push({cd+cost, to, nst});
}
}
}
int ans=maxc;
ans=min({ans, mem[v][0], mem[v][1],mem[v][2]});
for(int i=1;i<=n;i++)mem[i][0]=mem[i][1]=mem[i][2]=maxc;
pq.push({0, u, 0});
mem[u][0]=0;
//0 not started, 1 in midst of, 2 exited.
while(!pq.empty()){
auto [cd, x, st]=pq.top();pq.pop();
if(mem[x][st]<cd)continue;
for(auto [to, cost]:al[x]){
if ((ds[to]+cost+dt[x]==d)
and st!=2){
if(cd<mem[to][1]){
mem[to][1]=cd;
pq.push({cd, to, 1});
}
}
int nst=(st==1?2:st);
if(cd+cost<mem[to][nst]){
mem[to][nst]=cd+cost;
pq.push({cd+cost, to, nst});
}
}
}
ans=min({ans, mem[v][0], mem[v][1],mem[v][2]});
cout<<ans;
//~ cout<<"distance from s:\n";
//~ for(int i=1;i<=n;i++){
//~ cout<<ds[i]<<" ";
//~ }
//~ cout<<endl;
//~ cout<<"distance from t:\n";
//~ for(int i=1;i<=n;i++){
//~ cout<<dt[i]<<" ";
//~ }
//~ cout<<endl;
//~ cout<<"\ndistance from s:\n";
//~ for(int i=1;i<=n;i++){
//~ cout<<i<<": "<<mem[i][0]<<" "<<mem[i][1]<<" "<<mem[i][2]<<endl;
//~ }
//~ cout<<endl;
}
