#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const int N = 1e5+10;
int n, m, st, en, U, V;
ll dist1[N], dist2[N], dist3[3][N];
vector<pair<int, int>> adj[N];
inline void dijsktra(){
priority_queue<pair<ll, int>, vector<pair<ll, int>>,greater<pair<ll, int>>> pq;
memset(dist1, 0x3f, sizeof dist1);
memset(dist2, 0x3f, sizeof dist2);
pq.push({dist1[st] = 0, st});
while(!pq.empty()){
auto [d, u] = pq.top(); pq.pop();
if(dist1[u] < d) continue;
for(auto [v, w] : adj[u]){
if(dist1[v] > d+w){
pq.push({dist1[v] = d+w, v});
}
}
}
pq.push({dist2[en] = 0, en});
while(!pq.empty()){
auto [d, u] = pq.top(); pq.pop();
if(dist2[u] < d) continue;
for(auto [v, w] : adj[u]){
if(dist2[v] > d+w){
pq.push({dist2[v] = d+w, v});
}
}
}
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
cin >> n >> m >> st >> en >> U >> V;
while(m--){
int u, v, w;
cin >> u >> v >> w;
adj[u].push_back({v, w});
adj[v].push_back({u, w});
}
dijsktra();
const ll mn = dist1[en];
memset(dist3, 0x3f, sizeof dist3);
//cost, node, in_node, state, dist, prev
priority_queue<tuple<ll, int, int, int, ll, int>, vector<tuple<ll, int, int, int, ll, int>>, greater<tuple<ll, int, int, int, ll, int>>> pq;
pq.push({dist3[0][U] = 0, U, -1, 0, 0, -1});
if(dist1[U] + dist2[U] == mn) pq.push({dist3[1][U] = 0, U, U, 1, 0, -1});
while(!pq.empty()){
auto [c, u, in_node, state, d, prev] = pq.top(); pq.pop();
if(dist3[state][u] < c) continue;
if(state == 0){
for(auto [v, w] : adj[u]){
// if(v == prev) continue;
if(dist1[v]+dist2[v] == mn){
if(dist3[1][v] > c+w)
pq.push({dist3[1][v] = c+w, v, v, 1, 0, u});
}
if(dist3[0][v] > c+w)
pq.push({dist3[0][v] = c+w, v, -1, 0, 0, u});
}
}else if(state == 1){
for(auto [v, w] : adj[u]){
// if(v == prev) continue;
if(d+w == mn - dist1[v] - dist2[in_node] || d+w == mn - dist1[in_node] - dist2[v]){
if(dist3[1][v] > c)
pq.push({dist3[1][v] = c, v, in_node, 1, d+w, u});
}
if(dist3[2][v] > c+w)
pq.push({dist3[2][v] = c+w, v, -1, 2, 0, u});
}
}else{
for(auto [v, w] : adj[u]){
// if(v == prev) continue;
if(dist3[2][v] > c+w)
pq.push({dist3[2][v] = c+w, v, -1, 0, 0, u});
}
}
}
cout << min({dist3[0][V], dist3[1][V], dist3[2][V]}) << '\n';
}
