#include <bits/stdc++.h>
#include <climits>
using namespace std;
#define f first
#define s second
#define all(a) a.begin(),a.end()
#define sz(a) (int)a.size()
#define int long long
const int N=1e5+5;
const int INF=1e16;
int n,m;
vector<pair<int,int>>E[N];
int distx[N],disty[N];
void Dij(int s,int D[]){
priority_queue<pair<int,int>,vector<pair<int,int>>,greater<pair<int,int>>>pq;
for(int i=1;i<=n;++i){
D[i]=INF;
}
D[s]=0;
pq.push({0,s});
while(!pq.empty()){
auto [d,u] =pq.top();
pq.pop();
if(D[u]!=d) continue;
for(auto [v,w]:E[u]){
if(D[v]>D[u]+w){
D[v]=D[u]+w;
pq.push({D[v],v});
}
}
}
}
int DP_DAG(int st,int des){
priority_queue<pair<int,int>,vector<pair<int,int>>,greater<pair<int,int>>>pq;
vector<int>dist(n+5,INF);
dist[st]=0;
pq.push({0,st});
while(!pq.empty()){
auto [d,u] =pq.top();
pq.pop();
if(dist[u]!=d) continue;
for(auto [v,w]:E[u]){
if(dist[v]>dist[u]+w){
dist[v]=dist[u]+w;
pq.push({dist[v],v});
}
}
}
vector<int>can(n+1);
iota(all(can),0);
sort(can.begin()+1,can.begin()+n+1, [&] (int x,int y){
return dist[x]<dist[y];
});
vector<vector<int>> dp(2,vector<int>(n+5,INF));
dp[0][st] = distx[st];
dp[1][st] = distx[st] + disty[st];
for(int i=1;i<=n;++i){
int u=can[i];
for(auto [v,w]:E[u]){
if(dist[v]==dist[u]+w){
dp[0][v]=min({dp[0][v],dp[0][u],distx[v]});
dp[1][v]=min({dp[1][v],dp[1][u],dp[0][u]+disty[v]});
}
}
}
return dp[1][des];
}
void solve(){
cin>>n>>m;
int s,t,x,y;
cin>>s>>t;
cin>>x>>y;
for(int i=1;i<=m;++i) {
int u,v,w;cin>>u>>v>>w;
E[u].push_back({v,w});
E[v].push_back({u,w});
}
Dij(x,distx);
Dij(y,disty);
cout<<min({DP_DAG(s,t),DP_DAG(t,s),distx[y]});
}
signed main(){
ios_base::sync_with_stdio(0);cin.tie(0);
int T=1;
while(T--) solve();
}
