#include <bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define pb push_back
#define eb emplace_back
#define all(x) begin(x), end(x)
#define sz(x) ((int)(x).size())
#define el '\n'
using ll = long long;
using pii = pair<int,int>;
using vi = vector<int>;
using vll = vector<ll>;
const ll INF = (ll)4e18;
void fastIO() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
}
int main(){
fastIO();
int N, M;
cin >> N >> M;
int S, T, U, V;
cin >> S >> T >> U >> V;
struct E{int u,v; ll w;};
vector<E> edges(M);
vector<vector<pair<int,ll>>> adj(N+1);
for(int i=0;i<M;i++){
cin >> edges[i].u >> edges[i].v >> edges[i].w;
adj[edges[i].u].eb(edges[i].v, edges[i].w);
adj[edges[i].v].eb(edges[i].u, edges[i].w);
}
auto dijkstra = [&](int src){
vll dist(N+1, INF);
priority_queue<pair<ll,int>, vector<pair<ll,int>>, greater<>> pq;
dist[src] = 0;
pq.emplace(0, src);
while(!pq.empty()){
auto [d,u] = pq.top(); pq.pop();
if(d > dist[u]) continue;
for(auto &pr : adj[u]){
int v = pr.fi; ll w = pr.se;
if(dist[v] > d + w){
dist[v] = d + w;
pq.emplace(dist[v], v);
}
}
}
return dist;
};
// 1) Dijkstra từ S, T
vll distS = dijkstra(S);
vll distT = dijkstra(T);
ll bestST = distS[T];
// 2) Build graph with free edges weight=0
vector<vector<pair<int,ll>>> adj2(N+1);
for(auto &e : edges){
bool free_edge =
(distS[e.u] + e.w + distT[e.v] == bestST) ||
(distS[e.v] + e.w + distT[e.u] == bestST);
ll w2 = free_edge ? 0 : e.w;
adj2[e.u].eb(e.v, w2);
adj2[e.v].eb(e.u, w2);
}
// 3) Dijkstra từ U trên adj2
vll distU(N+1, INF);
priority_queue<pair<ll,int>, vector<pair<ll,int>>, greater<>> pq;
distU[U] = 0;
pq.emplace(0, U);
while(!pq.empty()){
auto [d,u] = pq.top(); pq.pop();
if(d > distU[u]) continue;
for(auto &pr : adj2[u]){
int v = pr.fi; ll w = pr.se;
if(distU[v] > d + w){
distU[v] = d + w;
pq.emplace(distU[v], v);
}
}
}
cout << distU[V] << el;
return 0;
}
/*
⢀⡴⠑⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣀⡀ Monkey D. LUFFY
⠸⡇⠀⠿⡀⠀⣀⡴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀ "I’m gonna be..."
⠀⠀⠀⠀⠑⢄⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣯⣍⠻⣷⡄ ...King of the Pirates!
⠀⠀⠀⠀⢀⡀⠁⠈⠙⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠋ ⠀
⠀⠀⠀⢀⡾⣁⣀⠀⠴⠂⠙⣗⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣴⣷⠘⠿⠛⠃⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣴⣿⠙⣆⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠊⠁⠀⠀⠀⠀⠀
⢀⣼⣿⠀⣇⣀⠀⠀⣠⣤⣶⣾⣿⣶⣶⣶⣶⠆⠀⠀⠀⠀
*/
