#include <bits/stdc++.h>
#define f first
#define s second
#define ll long long
using namespace std;
const int MAXN = 1e5+10;
const ll INF = 1e18;
vector<pair<int,ll>> adj[MAXN],adj2[MAXN],readj[MAXN];
int main()
{
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
int N,M; cin >> N >> M;
int S,T; cin >> S >> T;
int U,V; cin >> U >> V;
for(int i = 0;i<M;++i){
int a,b,c; cin >> a >> b >> c;
adj[a].push_back({b,c}); adj[b].push_back({a,c});
}
vector<ll> DU(N+1,INF); DU[U] = 0;
priority_queue<pair<ll,int>,vector<pair<ll,int>>,greater<pair<ll,int>>> pq; pq.push({0,U});
while(!pq.empty()){
int u = pq.top().s; ll d = pq.top().f; pq.pop();
if(d != DU[u]) continue;
for(auto p : adj[u]){
if(p.s+d < DU[p.f]){
DU[p.f] = p.s+d;
pq.push({DU[p.f],p.f});
}
}
}
vector<ll> DV(N+1,INF); DV[V] = 0; pq.push({0,V});
while(!pq.empty()){
int u = pq.top().s; ll d = pq.top().f; pq.pop();
if(d != DV[u]) continue;
for(auto p : adj[u]){
if(p.s+d < DV[p.f]){
DV[p.f] = p.s+d;
pq.push({DV[p.f],p.f});
}
}
}
vector<ll> DS(N+1,INF); DS[S] = 0; pq.push({0,S});
while(!pq.empty()){
int u = pq.top().s; ll d = pq.top().f; pq.pop();
if(d != DS[u]) continue;
for(auto p : adj[u]){
if(p.s+d < DS[p.f]){
DS[p.f] = p.s+d;
pq.push({DS[p.f],p.f});
}
}
}
vector<ll> DT(N+1,INF); DT[T] = 0; pq.push({0,T});
while(!pq.empty()){
int u = pq.top().s; ll d = pq.top().f; pq.pop();
if(d != DT[u]) continue;
for(auto p : adj[u]){
if(p.s+d < DT[p.f]){
DT[p.f] = p.s+d;
pq.push({DT[p.f],p.f});
}
}
}
vector<int> indeg(N+1,0);
for(int i = 1;i<=N;++i){
if(DT[i]+DS[i] != DS[T]) continue;
for(auto p : adj[i]){
if(DT[p.f]+DS[p.f] != DS[T]) continue;
if(DS[i]+p.s == DS[p.f]){
adj2[i].push_back({p.f,p.s});
readj[p.f].push_back({i,p.s});
}
}
}
queue<int> q; q.push(S);
vector<ll> dp(N+1,INF);
for(int i = 1;i<=N;++i){
dp[i] = DU[i];
}
ll ans = DU[V];
vector<ll> cnt(N+1,0);
while(!q.empty()){
int u = q.front(); q.pop();
ans = min(ans,dp[u]+DV[u]);
for(auto p : adj2[u]){
dp[p.f] = min(dp[p.f],dp[u]);
++cnt[p.f];
if(cnt[p.f] == readj[p.f].size()){
q.push(p.f);
}
}
}
q.push(T);
dp = vector<ll>(N+1,INF); cnt = vector<ll>(N+1,0);
for(int i = 1;i<=N;++i){
dp[i] = DU[i];
}
while(!q.empty()){
int u = q.front(); q.pop();
ans = min(ans,dp[u]+DV[u]);
for(auto p : readj[u]){
dp[p.f] = min(dp[p.f],dp[u]);
++cnt[p.f];
if(cnt[p.f] == adj2[p.f].size()){
q.push(p.f);
}
}
}
cout << ans << "\n";
return 0;
}
