#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define fi first
#define se second
#define sst string
#define pb push_back
#define maxco 100000+5
#define lld long double
#define cha ios_base::sync_with_stdio(false);
#define ffl cout.flush();
#define phi acos(-1)
#define mr make_pair
#define REP(i,a,b) for (int i = a; i <= b; i++)
#define pqin priority_queue<ll,vector<ll>,greater<>>
#define pqpair priority_queue<pair<ll,ll> ,vector<pair<ll,ll>>,greater<pair<ll,ll>>>
#define pqpair2 priority_queue<pair<pair<ll,ll>,pair<ll,ll>>,vector<pair<pi,pair<ll,ll>>>,greater<pair<pi,pair<ll,ll>>>>
#define INF 1000000009
#define MAXN 200006
#define pii pair<ll,ll>
#define mod 998244353
ll n,m;
ll s,t,u,v;
vector <pii> vec[MAXN];
ll dist[5][MAXN];
vector <ll> bc[MAXN];
void djikstra(ll idx,ll in){
priority_queue<pair<ll,ll> ,vector <pair<ll,ll>>,greater<pair<ll,ll>>> pq;
pq.push({0,in});
dist[idx][in]=0;
while(!pq.empty()){
ll cost=pq.top().fi;
ll fr=pq.top().se;
pq.pop();
if(cost>dist[idx][fr] && idx!=3)continue;
for(auto x : vec[fr]){
if(dist[idx][x.se]>dist[idx][fr]+x.fi){
dist[idx][x.se]=dist[idx][fr]+x.fi;
pq.push({dist[idx][x.se],x.se});
if(idx==3){
bc[x.se].clear();
bc[x.se].pb(fr);
}
}
else if(dist[idx][x.se]==dist[idx][fr]+x.fi){
if(idx==3){
bc[x.se].pb(fr);
}
}
}
}
}
ll dp[MAXN];
int main(){
cin>>n>>m;
cin>>s>>t>>u>>v;
REP(i,1,4)REP(j,1,n)dist[i][j]=1e18;
REP(i,1,n)dp[i]=1e18;
REP(i,1,m){
ll u,v,w;
cin>>u>>v>>w;
vec[u].pb({w,v});
vec[v].pb({w,u});
}
djikstra(1,u);
djikstra(2,v);
djikstra(3,s);
ll ans=1e18;
priority_queue<pair<pii,pair<ll,ll>> ,vector <pair<pii,pii>>,greater<pair<pii,pii>>> pq;
pq.push({{dist[1][t]+dist[2][t],t},{dist[1][t],dist[2][t]}});
dp[t]=dist[1][t]+dist[2][t];
ans=dp[t];
while(pq.size()){
ll node=pq.top().fi.se;
ll bf1=pq.top().se.fi;
ll bf2=pq.top().se.se;
ans=min(ans,dp[node]);
pq.pop();
for(auto x : bc[node]){
ll nwx=min(bf1,dist[1][x]);
ll nwy=min(bf2,dist[2][x]);
if(dp[x]>nwx+nwy){
dp[x]=nwx+nwy;
pq.push({{dp[x],x},{nwx,nwy}});
}
}
}
ans=min(dist[1][v],ans);
cout<<ans<<endl;
/*
1 itu dari u ke v(2,3)
2 itu dari v ke u(3,2)
*/
}
