#include <bits/stdc++.h>
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,popcnt,lzcnt")
#define remin(a,b...) a=min({a,b})
#define remax(a,b...) a=max({a,b})
#define ll long long
#define ld long double
#define pii array<int,2>
#define pll array<ll,2>
#define vi vector<int>
#define vl vector<ll>
#define vb vector<bool>
#define vii vector<array<int,2>>
#define vll vector<array<ll,2>>
#define v2d(T) vector<vector<T>>
#define v3d(T) vector<vector<vector<T>>>
#define pub push_back
#define tup make_tuple
using namespace std;
const ll C=1e9;
const ll M=2e5;
ll n,m,s,t,u,v;
vector<vll> adj;
vl dij(int x){
vl d(n+1,C*M);
vb vis(n+1);
d[x]=0;
priority_queue<pll>pq;
pq.push({0,x});
while(!pq.empty()){
int i=pq.top()[1];
pq.pop();
if(vis[i]){
continue;
}
vis[i]=1;
for(auto[j,c]:adj[i]){
if(d[i]+c<d[j]){
d[j]=d[i]+c;
pq.push({-d[j],j});
}
}
}
return d;
}
int main(){
ios_base::sync_with_stdio(0);cin.tie(0);
cin>>n>>m>>s>>t>>u>>v;
adj.resize(n+1);
for(int i=0;i<m;i++){
ll a,b,c;
cin>>a>>b>>c;
adj[a].pub({b,c});
adj[b].pub({a,c});
}
vl du=dij(u);
vl dv=dij(v);
vl ds=dij(s);
vl dt=dij(t);
vb b(n+1);
for(int i=1;i<=n;i++){
b[i]=(ds[i]+dt[i]==ds[t]);
}
vll dp(n+1,{C*M,C*M});
dp[s]={du[s],dv[s]};
priority_queue<pll>pq;
pq.push({0,s});
vb vis(n+1);
ll res=M*C;
while(!pq.empty()){
int i=pq.top()[1];
pq.pop();
if(vis[i]){
continue;
}
vis[i]=1;
for(auto[j,c]:adj[i]){
if(ds[j]>ds[i]&&b[j]){
pq.push({-ds[j],j});
remin(dp[j][0],dp[i][0],du[j]);
remin(dp[j][1],dp[i][1],dv[j]);
remin(res,dp[j][0]+dv[j],dp[j][1]+du[j]);
}
}
}
cout<<min(res,du[v]);
}
