#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define pb push_back
#define ff first
#define ss second
#define all(s) s.begin(),s.end()
#define rall(s) s.rbegin(),s.rend()
#define pll pair<ll,ll>
const ll N=1e5+5;
ll n,m,S,T,U,V;
ll dp[N][4];
ll dist[N][3];
vector<pll>g[N];
void dijkstra(ll st,ll d){//start node, dist[ ][d]
priority_queue<pll,vector<pll>,greater<pll>>pq;
pq.push({0,st});
dist[st][d]=0;
while(!pq.empty()){
auto [ds,x]=pq.top();
pq.pop();
if(dist[x][d]!=ds) continue;
for(auto [y,w]:g[x]){
if(ds+w<dist[y][d]){
dist[y][d]=ds+w;
pq.push({dist[y][d],y});
}
}
}
}
ll get(ll x,ll v){
ll res=0;
if(v&1) res+=dist[x][1];
if(v&2) res+=dist[x][2];
return res;
}
int main(){
ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
cin>>n>>m;
cin>>S>>T>>U>>V;
for(ll i=1;i<=m;i++){
ll a,b,c;
cin>>a>>b>>c;
g[a].pb({b,c});
g[b].pb({a,c});
}
for(ll i=1;i<=n;i++){
for(ll j=0;j<3;j++){
dist[i][j]=(ll)1e18;
}
}
dijkstra(S,0);
dijkstra(U,1);
dijkstra(V,2);
for(ll i=1;i<=n;i++){
for(ll j=0;j<4;j++){
dp[i][j]=(ll)1e18;
}
}
pll ds[n+5];
for(ll i=1;i<=n;i++){
ds[i]={dist[i][0],i};
}
sort(ds+1,ds+n+1,[&](pll a,pll b){
return a.ff<b.ff;
});
dp[S][0]=0;
dp[S][1]=dist[S][1];//S->x->i baih min of dis(x,U) - dp[i][1]
dp[S][2]=dist[S][2];//S->y->i baih min of dis(y,V) - dp[i][2]
dp[S][3]=dist[S][1]+dist[S][2];//S->x->y->i baih min of dis(x,U)+dis(y,V) - dp[i][3]
for(ll z=1;z<=n;z++){
ll i=ds[z].ss;
for(auto [j,w]:g[i]){
if(dist[i][0]+w!=dist[j][0]) continue; // not shortest
for(ll l=0;l<4;l++){
for(ll k=0;k<4;k++){
dp[j][l|k]=min(dp[j][l|k],dp[i][l]+get(j,k));
}
}
}
}
ll ans=min(dp[T][3],dist[V][1]);
cout<<ans;
}
