#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 LINF = (ll)4e18;
void fastIO(){
ios::sync_with_stdio(false);
cin.tie(nullptr);
}
vector<vector<pii>> adj;
int n, m;
vll dU, dV, distS, distT, dpF, dpB, distF, distB;
vll dijkstra(int src){
vll d(n, LINF);
priority_queue<pair<ll,int>, vector<pair<ll,int>>, greater<>> pq;
d[src] = 0; pq.emplace(0, src);
while(!pq.empty()){
auto [du,u] = pq.top(); pq.pop();
if(du > d[u]) continue;
for(auto [v,w]: adj[u]){
ll nd = du + w;
if(nd < d[v]){
d[v] = nd;
pq.emplace(nd, v);
}
}
}
return d;
}
void dp_run(int start, vll &dist, vll &dp){
// dist[...] and dp[...] initialized to LINF
dist[start] = 0;
dp[start] = dV[start];
priority_queue<pair<ll,int>, vector<pair<ll,int>>, greater<>> pq;
pq.emplace(0, start);
while(!pq.empty()){
auto [du,u] = pq.top(); pq.pop();
if(du > dist[u]) continue;
ll pre = dp[u];
for(auto [v,w]: adj[u]){
ll nd = du + w;
if(nd < dist[v]){
dist[v] = nd;
dp[v] = min(pre, dV[v]);
pq.emplace(nd, v);
} else if(nd == dist[v]){
dp[v] = min(dp[v], min(pre, dV[v]));
}
}
}
}
int main(){
fastIO();
cin >> n >> m;
int S, T, U, V;
cin >> S >> T >> U >> V;
--S; --T; --U; --V;
adj.assign(n, {});
for(int i = 0; i < m; i++){
int a,b; ll c;
cin >> a >> b >> c;
--a; --b;
adj[a].eb(b,c);
adj[b].eb(a,c);
}
dU = dijkstra(U);
dV = dijkstra(V);
distS = dijkstra(S);
distT = dijkstra(T);
ll bestST = distS[T];
// 3) Forward DP from S
distF.assign(n, LINF);
dpF .assign(n, LINF);
dp_run(S, distF, dpF);
// 4) Backward DP from T
// reuse adj but run from T
distB.assign(n, LINF);
dpB .assign(n, LINF);
dp_run(T, distB, dpB);
ll ans = dU[V]; // no pass
for(int i = 0; i < n; i++){
if(distF[i] + distB[i] == bestST){
ll via = min(dpF[i], dpB[i]) + dU[i];
ans = min(ans, via);
}
}
cout << ans << el;
return 0;
}
/*
⢀⡴⠑⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣀⡀ Monkey D. LUFFY
⠸⡇⠀⠿⡀⠀⣀⡴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀ "I’m gonna be..."
⠀⠀⠀⠀⠑⢄⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣯⣍⠻⣷⡄ ...King of the Pirates!
⠀⠀⠀⠀⢀⡀⠁⠈⠙⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠋ ⠀
⠀⠀⠀⢀⡾⣁⣀⠀⠴⠂⠙⣗⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣴⣷⠘⠿⠛⠃⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣴⣿⠙⣆⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠊⠁⠀⠀⠀⠀⠀
⢀⣼⣿⠀⣇⣀⠀⠀⣠⣤⣶⣾⣿⣶⣶⣶⣶⠆⠀⠀⠀⠀
*/
