#include <bits/stdc++.h>
using namespace std;
#define int long long
vector<vector<int>> p;
vector<bool> j;
int ans = 1e18;
vector<int> dis;
vector<int> dis1;
vector<pair<int, int>> dp;
vector<int> topo;
void dfs(int k){
j[k] = true;
for(int i = 0; i < p[k].size(); i++){
topo[p[k][i]]++;
if(j[p[k][i]]) continue;
dfs(p[k][i]);
}
}
main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
int n, m; cin >> n >> m;
int s, t; cin >> s >> t;
int u, v; cin >> u >> v;
topo.resize(n+1);
j.resize(n+1);
vector<vector<pair<int, int>>> g(n+1);
for(int i = 0; i < m; i++){
int a, b; cin >> a >> b;
int c; cin >> c;
g[a].push_back({b, c});
g[b].push_back({a, c});
}
p.resize(n+1);
vector<bool> d(n+1);
vector<int> mn(n+1, 1e18);
multiset<pair<int, int>> q;
q.insert({0, s});
while(!q.empty()){
auto [time, k] = *q.begin();
q.erase(q.begin());
if(d[k] || k == t) continue;
d[k] = true;
for(auto [v, ti] : g[k]){
if(mn[v] == ti + time){
p[v].push_back(k);
}
if(d[v]) continue;
if(mn[v] > ti + time){
mn[v] = ti+time;
p[v] = {k};
q.insert({mn[v], v});
}
}
}
q.clear();
q.insert({0, u});
dp.resize(n+1, {1e18, 1e18});
dis.resize(n+1, 1e18);
dis[u] = 0;
d.clear();
d.resize(n+1, false);
while(q.size() > 0){
auto [time, k] = *q.begin();
q.erase(q.begin());
if(d[k]) continue;
d[k] = true;
for(auto [v, ti] : g[k]){
if(d[v]) continue;
if(dis[v] > ti + time){
dis[v] = ti+time;
q.insert({dis[v], v});
}
}
}
q.clear();
q.insert({0, v});
dis1.resize(n+1, 1e18);
dis1[v] = 0;
d.clear();
d.resize(n+1, false);
while(q.size() > 0){
auto [time, k] = *q.begin();
q.erase(q.begin());
if(d[k]) continue;
d[k] = true;
for(auto [v, ti] : g[k]){
if(d[v]) continue;
if(dis1[v] > ti + time){
dis1[v] = ti+time;
q.insert({dis1[v], v});
}
}
}
queue<int> r;
r.push(t);
dfs(t);
j.clear();
j.resize(n+1, false);
while(!r.empty()){
int k = r.front();
r.pop();
if(j[k]) continue;
j[k] = true;
dp[k].first = min(dp[k].first, dis[k]);
dp[k].second = min(dp[k].second, dis1[k]);
for(int i = 0; i < p[k].size(); i++){
if(j[p[k][i]]){
continue;
}
topo[p[k][i]]--;
dp[p[k][i]].first = min(min(dp[k].first, dis[k]), dp[p[k][i]].first);
dp[p[k][i]].second = min(dp[p[k][i]].second, min(dp[k].second, dis1[k]));
if(topo[p[k][i]] == 0){
r.push(p[k][i]);
}
}
ans = min(ans, min(dp[k].first + dis1[k], dp[k].second + dis[k]));
}
cout << min(ans, dis[v]) << "\n";
return 0;
}
