#include <bits/stdc++.h>
using namespace std;
#define int int64_t
const int N=1e5+4;
vector<array<int,2>>adj[N];
vector<int>go[N],g[N],rg[N];
int dS[N],dU[N],dV[N],dT[N],dp1[N],dp2[N],ans,n,m,U,V,S,T;
void dijkstra(int p,int d[]){
priority_queue<pair<int,int>,vector<pair<int,int>>,greater<>>pq;
fill(d,d+n+1,1e18);
d[p]=0;
pq.push({0,p});
while(!pq.empty()){
auto[dd,u]=pq.top();
pq.pop();
for(auto&[v,w]:adj[u]){
if(dd+w<d[v]){
d[v]=dd+w;
pq.push({d[v],v});
}
}
}
}
map<array<int,2>,bool>edges;
int vis[N];
void makego(int u){
vis[u]=1;
for(auto&[v,w]:adj[u]){
if(edges[{min(u,v),max(u,v)}])
continue;
if(min(dS[u]+dT[v],dS[v]+dT[u])+w==dS[T]){
go[u].push_back(v);
go[v].push_back(u);
edges[{min(u,v),max(u,v)}]=1;
}
if(!vis[v])
makego(v);
}
}
void makedir(int u){
vis[u]=1;
for(int v:go[u]){
int node1=u,node2=v;
if(dS[node1]>dS[node2])
swap(node1,node2);
assert(dT[node2]<dT[node1]);
g[node1].push_back(node2);
rg[node2].push_back(node1);
if(!vis[v])
makedir(v);
}
}
int f1(int u){
if(dp1[u]!=-1)
return dp1[u];
int ret=dV[u];
for(auto v:g[u])
ret=min(ret,f1(v));
return dp1[u]=ret;
}
int f2(int u){
if(dp2[u]!=-1)
return dp2[u];
int ret=dV[u];
for(auto v:rg[u])
ret=min(ret,f2(v));
return dp2[u]=ret;
}
signed main(){
ios::sync_with_stdio(0);
cin.tie(0);
cin>>n>>m>>S>>T>>U>>V;
for(int i=0,u,v,w;i<m;++i){
cin>>u>>v>>w;
adj[u].push_back({v,w});
adj[v].push_back({u,w});
}
dijkstra(U,dU);
dijkstra(V,dV);
dijkstra(T,dT);
dijkstra(S,dS);
makego(S);
fill(vis,vis+N,0);
makedir(S);
fill(dp1,dp1+N,-1);
fill(dp2,dp2+N,-1);
ans=dU[V];
for(int i=1;i<=n;++i)
if(dS[i]+dT[i]==dT[S])
ans=min(ans,dU[i]+min(f1(i),f2(i)));
cout<<ans;
}
