#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define pb push_back
#define fi first
#define se second
constexpr ll MAXN=1e5+5,MAXV=3e5,MOD=1e9+7,INF=1e18;
ll n,m,i,j,p,k,ans,dem,st,en,dist[3][MAXN],S,T,U,V,len[MAXN],miV[MAXN],miU[MAXN];
vector<pair<ll,ll>> adj[MAXN];
void dij(ll st,ll type){
priority_queue<pair<ll,ll>> q;
dist[type][st]=0;
q.push({0,st});
while(q.size()){
auto k=q.top();q.pop();
if(-k.fi>dist[type][k.se]) continue;
for(auto x:adj[k.se]){
if(dist[type][x.fi]>-k.fi+x.se){
dist[type][x.fi]=-k.fi+x.se;
q.push({-dist[type][x.fi],x.fi});
}
}
}
}
void solve(ll st,ll en){
vector<ll> len(n + 1, INF);
vector<ll> miU(n + 1, INF);
vector<ll> miV(n + 1, INF);
len[st]=0;
miU[st]=dist[1][st];
miV[st]=dist[2][st];
priority_queue<pair<ll,int>, vector<pair<ll,int>>, greater<pair<ll,int>>> q;
q.push({0, st});
while (!q.empty()) {
auto cur = q.top(); q.pop();
if (cur.first > len[cur.se]) continue;
for (auto &e : adj[cur.se]) {
if (cur.first+e.se < len[e.fi]) {
len[e.fi] = cur.first+e.se;
miU[e.fi] = min(miU[cur.se], dist[1][e.fi]);
miV[e.fi] = min(miV[cur.se], dist[2][e.fi]);
q.push({len[e.fi], e.fi});
}
else if (cur.first+e.se == len[e.fi]) {
if (min(miU[cur.se], dist[1][e.fi]) + min(miV[cur.se], dist[2][e.fi]) < miU[e.fi] + miV[e.fi]) {
miU[e.fi] = min(miU[cur.se], dist[1][e.fi]);
miV[e.fi] = min(miV[cur.se], dist[2][e.fi]);
q.push({len[e.fi], e.fi});
}
}
}
}
if(len[en]!=INF){
ans=min(ans,miU[en]+miV[en]);
}
}
int main(){
ios::sync_with_stdio(0);
cin.tie(0);cout.tie(0);
cin>>n>>m>>S>>T>>U>>V;
for(i=1;i<=m;i++){
ll u,v,c;
cin>>u>>v>>c;
adj[u].pb({v,c});
adj[v].pb({u,c});
}
for(i=1;i<=n;i++) dist[1][i]=dist[2][i]=INF;
dij(U,1);
dij(V,2);
ans=dist[1][V];
solve(S,T);
solve(T,S);
cout<<ans;
}
