#include <iostream>
#include <bits/stdc++.h>
using namespace std;
struct arbore {
bool directie;///0 = s->t , 1 = t->s
long long nod,cost,stare,c_urcat;
bool operator>(const arbore & o)const {
return cost > o.cost;
}
/// 1. nu ne-am pus pe un drum cu 0 -> urcam pe unul <-> d[s][nod_curent] + cost + d[u][vecin]
/// acum, odata ce am "urcat pe o directie" s->t sau t->s, trebuie sa o mentin
///
/// +++ tinem costul cu care ne-am urcat prima data !!!
/// 2. sunt pe o secv de costuri 0 -> pot merge pe o muchie care e din acelasi drum minim
/// normal luand dupa directie, <-> atunci c_urcat + c_vecin + cost == dmin
/// daca e s->t atunci c_urcat creste
/// daca e t->s atunci c_urcat ... tot creste
///in fiecare punct cu stare 2 verificam rezultatul
};
struct arbore2 {
long long nod,cost;
bool operator>(const arbore2 & o)const {
return cost > o.cost;
}
};
vector<long long>ds,dt,dv,du;
vector<vector<arbore2>>tabel;
long long dp[100001][2],dmin=1e18,rez=1e18;///nodul, directie, folosim doar cand stare == 1, altfel doar du
///dijkstra normal
void dijksrtra1(vector<long long> & d,long long start) {
priority_queue<arbore2,vector<arbore2>,greater<arbore2>>pq;
pq.push({start,0});
d[start] = 0;
while(!pq.empty()) {
auto curent = pq.top();
pq.pop();
if(d[curent.nod] < curent.cost)
continue;
for(auto i : tabel[curent.nod]) {
if(d[i.nod] > curent.cost + i.cost) {
d[i.nod] = curent.cost + i.cost;
pq.push({i.nod,d[i.nod]});
}
}
}
}
///acum e acum
///dijkstra principala
void dijksrtra2(long long u,long long v,long long s,long long t) {
///acum initializez in main dp sa fie doar chestii mari
priority_queue<arbore,vector<arbore>,greater<arbore>>pq;
pq.push({0,u,0,0,0});
du[u] = 0;
while(!pq.empty()) {
auto curent = pq.top();
pq.pop();
if(curent.stare == 0) { ///nu am urcat inca in tren
if(du[curent.nod] < curent.cost)
continue;
for(auto i : tabel[curent.nod]) {
///acum putem continua normal sau sa urcam
///normal
if(du[i.nod] > curent.cost + i.cost){
du[i.nod] = curent.cost + i.cost;
pq.push({0,i.nod,du[i.nod],0,0});
}
///acum putem urca
///s->t
//cout<<ds[curent.nod] + i.cost + dt[i.nod]<<'\n';
if(ds[curent.nod] + i.cost + dt[i.nod] == dmin && dp[i.nod][0] > curent.cost + dv[i.nod]){
dp[i.nod][0] = curent.cost + dv[i.nod];
rez = min(rez, dp[i.nod][0]);
pq.push({0,i.nod,curent.cost,1,ds[curent.nod] + i.cost});
}
///t->s
//cout<<dt[curent.nod] + i.cost + ds[i.nod]<<'\n';
if(dt[curent.nod] + i.cost + ds[i.nod] == dmin && dp[i.nod][1] > curent.cost + dv[i.nod]){
dp[i.nod][1] = curent.cost + dv[i.nod];
rez = min(rez, dp[i.nod][1]);
pq.push({1,i.nod,curent.cost,1,dt[curent.nod] + i.cost});
}
}
}
if(curent.stare == 1){
if(curent.directie == 1){///t->s
if(dp[curent.nod][1] < curent.cost + dv[curent.nod])
continue;
for(auto i : tabel[curent.nod]){
if(curent.c_urcat + i.cost + ds[i.nod] == dmin && dp[i.nod][1] > curent.cost + dv[i.nod]){
dp[i.nod][1] = curent.cost + dv[i.nod];
rez = min(rez,dp[i.nod][1]);
pq.push({1,i.nod,curent.cost,1,curent.c_urcat + i.cost});
}
}
}
if(curent.directie == 0){///s->t
if(dp[curent.nod][0] < curent.cost + dv[curent.nod])
continue;
for(auto i : tabel[curent.nod]){
if(curent.c_urcat + i.cost + dt[i.nod] == dmin && dp[i.nod][0] > curent.cost + dv[i.nod]){
dp[i.nod][0] = curent.cost + dv[i.nod];
rez = min(rez,dp[i.nod][0]);
pq.push({0,i.nod,curent.cost,1,curent.c_urcat + i.cost});
}
}
}
}
}
}
int main() {
long long n,m;
cin>>n>>m;
long long s,t,u,v;
cin>>s>>t>>u>>v;
dt.resize(n+1,1e18);
ds.resize(n+1,1e18);
du.resize(n+1,1e18);
dv.resize(n+1,1e18);
tabel.resize(n+1);
for(long long i=1;i<=n;i++)
dp[i][0] = dp[i][1] = 1e18;
for(long long i=1;i<=m;i++){
long long a,b,c;
cin>>a>>b>>c;
tabel[a].push_back({b,c});
tabel[b].push_back({a,c});
}
dijksrtra1(dt,t);
dijksrtra1(ds,s);
dijksrtra1(dv,v);
dmin = ds[t];
rez = dv[u];
dijksrtra2(u,v,s,t);
cout<<rez;
return 0;
}
