#include <bits/stdc++.h>
#define int long long
#define pii pair<int, int>
using namespace std;
const int N = 1e5 + 2;
vector<pair<int, int>>adj1[N], adj2[N];
vector<tuple<int, int, int>>edge;
int p[N], dist[N];
int32_t 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 x, y; cin >> x >> y;
for(int i = 1; i <= N; i++){
dist[i] = 1e18;
p[i] = i;
}
while(m--){
int u, v, w; cin >> u >> v >> w;
edge.emplace_back(u, v, w);
adj1[u].emplace_back(v, w);
adj1[v].emplace_back(u, w);
}
priority_queue<pii, vector<pii>, greater<pii>>pq;
pq.emplace(0LL, s);
while(!pq.empty()){
auto [curW, u] = pq.top(); pq.pop();
for(auto &[v, w]: adj1[u]){
if(dist[v] <= curW + w) continue;
dist[v] = curW + w;
p[v] = u;
pq.emplace(dist[v], v);
}
}
set<pair<int, int>>st;
int cur = t;
while(cur != s){
st.insert({cur, p[cur]});
st.insert({p[cur], cur});
cur = p[cur];
}
for(auto &[u, v, w]: edge){
if(st.count({u, v})) w = 0;
adj2[u].emplace_back(v, w);
adj2[v].emplace_back(u, w);
}
for(int i = 1; i <= n; i++) dist[i] = 1e18;
pq.emplace(0LL, x);
dist[x] = 0;
while(!pq.empty()){
auto [curW, u] = pq.top(); pq.pop();
for(auto &[v, w]: adj2[u]){
if(dist[v] <= curW + w) continue;
dist[v] = curW + w;
p[v] = u;
pq.emplace(dist[v], v);
}
}
cout << dist[y] << '\n';
return 0;
}
