#include<bits/stdc++.h>
#define F first
#define S second
#define MAX 500005
#define oo 1e18
#define mod 1000000007
#define fast_in ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);cout.setf(ios::fixed);cout.precision(0);
using namespace std;
typedef long long ll;
#define pll pair<ll , ll>
#define vll vector<ll>
#define vvll vector<vll>
#define vpll vector<pll>
ll t,n,m,s,s2,e,e2,a1,a2,a3;
ll pass[MAX][10],d[MAX][10],mn[MAX][10];
vpll g[MAX];
void distra(ll x,ll z,ll y){
priority_queue<pll> q;
q.push({0,x});
while(!q.empty()){
pll u=q.top();q.pop();
if(pass[u.S][z]!=0)continue;
pass[u.S][z]=1;
d[u.S][z]=-u.F;
//if(u.S==y)return;
for(auto w: g[u.S]){
q.push({u.F-w.S,w.F});
}
}
}
void distra2(ll x,ll z,ll y,ll o){
priority_queue<pair<pll,ll>> q;
q.push({{0,-d[x][o]},x});
while(!q.empty()){
pair<pll,ll> u=q.top();q.pop();
if(pass[u.S][z]!=0)continue;
pass[u.S][z]=1;
d[u.S][z]=-u.F.F;
mn[u.S][o]=min(mn[u.S][o],-u.F.S);
//if(o==1)cout<<u.S<<" "<<d[u.S][z]<<" "<<mn[u.S][o]<<" "<<u.F.S<<" "<<d[u.S][o]<<"\n";
if(u.S==y)return;
for(auto w: g[u.S]){
// if(w.S==1 && o==1)cout<<-min(d[w.F][o],-u.F.S)<<"\n";
q.push({{u.F.F-w.S,-min(d[w.F][o],-u.F.S)},w.F});
}
}
}
int main(){
fast_in
cin>>n>>m>>s>>e>>s2>>e2;
for(int i=0;i<m;i++){
cin>>a1>>a2>>a3;
g[a1].push_back({a2,a3});
g[a2].push_back({a1,a3});
}
for(int i=0;i<=n;i++){
d[i][0]=d[i][1]=d[i][2]=d[i][3]=d[i][4]=d[i][5]=oo;
pass[i][0]=pass[i][1]=pass[i][2]=pass[i][3]=pass[i][4]=pass[i][5]=0;
mn[i][0]=mn[i][1]=oo;
}
distra(s2,0,e2);distra(e2,1,s2);
distra2(s,2,e,0);distra2(e,3,s,1);
distra2(s,4,e,1);distra2(e,5,s,0);
ll r=d[e2][0];//cout<<r<<" ";
for(int i=1;i<=n;i++){
// cout<<d[i][1]<<" ";
if(d[i][4]+d[i][5]==d[e][4]){
// cout<<i<<" "<<mn[i][0]<<" "<<mn[i][1]<<"\n";
r=min(r,d[i][0]+mn[i][1]);
}
}
cout<<r<<"\n";
return 0;
}
