#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define fi first
#define se second
#define Task "test"
typedef pair<ll,int>ii;
const int MOD = 1e9+7;
const ll INF = 1e17+7;
const int Maxn = 1e5+7;
const int di[] = {0, 0, -1, 1};
const int dj[] = {-1, 1, 0, 0};
int n,m,u,v,s,t;
ll dp[Maxn][2],distU[Maxn],distV[Maxn],dist[Maxn];
vector<ii>g[Maxn];
void dijkstra(int s,ll dp[]){
for(int i=1;i<=n;i++) dp[i]=INF;
dp[s]=0;
priority_queue<ii,vector<ii>,greater<ii>>q;
q.push({0,s});
while(!q.empty()){
int u=q.top().se;
ll val=q.top().fi;
q.pop();
if (dp[u]<val) continue;
for(ii x:g[u]){
int v=x.fi,w=x.se;
if (dp[v]>dp[u]+1LL*w){
dp[v]=dp[u]+1LL*w;
q.push({dp[v],v});
}
}
}
}
ll calc(int s,int t){
for(int i=1;i<=n;i++){
dp[i][0]=dp[i][1]=dist[i]=INF;
}
priority_queue<ii,vector<ii>,greater<ii>>q;
q.push({0,s});
dist[s]=0;
dp[s][0]=distU[s];
dp[s][1]=distV[s];
while(!q.empty()){
int u=q.top().se;
ll val=q.top().fi;
q.pop();
if (dist[u]<val) continue;
for(ii x:g[u]){
int v=x.fi,w=x.se;
if (dist[v]>dist[u]+1LL*w){
dist[v]=dist[u]+1LL*w;
dp[v][0]=min(dp[u][0],distU[v]);
dp[v][1]=min(dp[u][1],distV[v]);
q.push({dist[v],v});
}
else if (dist[v]==dist[u]+1LL*w){
if (dp[v][0]+dp[v][1]>min(dp[u][0],distU[v])+min(dp[u][1],distV[v])){
dp[v][0]=min(dp[u][0],distU[v]);
dp[v][1]=min(dp[u][1],distV[v]);
q.push({dist[v],v});
}
}
}
}
return dp[t][0]+dp[t][1];
}
void run_case(){
cin>>n>>m>>s>>t>>u>>v;
while(m--){
int u,v,w;
cin>>u>>v>>w;
g[u].push_back({v,w});
g[v].push_back({u,w});
}
dijkstra(u,distU);
dijkstra(v,distV);
ll ans=distU[v];
ans=min(ans,min(calc(s,t),calc(t,s)));
cout<<ans;
}
int main(){
ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
if (fopen(Task ".inp", "r"))
{
freopen(Task ".inp", "r", stdin);
freopen(Task ".out", "w", stdout);
}
int t = 1;
//cin >> t;
while(t--){
run_case();
}
}
