#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'
#define int long long
using ll = long long;
using pii = pair<int,int>;
using vi = vector<int>;
using vll = vector<ll>;
const int INF = 1e18 + 7;
const int MOD = 1e9 + 7;
void fastIO() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
}
struct Edge { int v; ll w; };
signed main(){
fastIO();
ios::sync_with_stdio(false);
cin.tie(nullptr);
int N, M;
cin >> N >> M;
int S, T, U, V;
cin >> S >> T >> U >> V;
vector<tuple<int,int,ll>> edges;
edges.reserve(M);
vector<vector<Edge>> adj(N+1);
for(int i = 0; i < M; i++){
int A, B; ll C;
cin >> A >> B >> C;
edges.emplace_back(A,B,C);
adj[A].push_back({B,C});
adj[B].push_back({A,C});
}
auto dijkstra = [&](int src){
vector<ll> 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 [du,u] = pq.top(); pq.pop();
if(du > dist[u]) continue;
for(auto &e: adj[u]){
int v = e.v; ll w = e.w;
if(dist[v] > du + w){
dist[v] = du + w;
pq.emplace(dist[v], v);
}
}
}
return dist;
};
// 1) Dijkstra từ S và T
auto distS = dijkstra(S);
auto distT = dijkstra(T);
ll D = distS[T];
// 2) đánh dấu “free” cạnh
// build new graph with cost'=0 for free, else original
vector<vector<Edge>> adj2(N+1);
for(auto &ed: edges){
int u,v; ll w;
tie(u,v,w) = ed;
bool free_edge =
(distS[u] + w + distT[v] == D) ||
(distS[v] + w + distT[u] == D);
ll w2 = free_edge ? 0 : w;
adj2[u].push_back({v,w2});
adj2[v].push_back({u,w2});
}
// 3) Dijkstra từ U trên đồ thị mới
vector<ll> 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 [du,u] = pq.top(); pq.pop();
if(du > distU[u]) continue;
for(auto &e: adj2[u]){
int v = e.v; ll w = e.w;
if(distU[v] > du + w){
distU[v] = du + w;
pq.emplace(distU[v], v);
}
}
}
ll ans = distU[V];
cout << ans << el;
return 0;
}
