#include<bits/stdc++.h>
#define st first
#define nd second
#define mp make_pair
#define pb push_back
#ifndef LOCAL
#define cerr if(0)cerr
#endif
using namespace std;
using ll = long long;
using ld = long double;
using pii = pair<int, int>;
using vi = vector<int>;
const ll INF = 1e16+1;
void dijkstra(int s, vector<vector<pii>>& g, vector<ll>& d) {
int n = g.size()-1;
vector<bool> vis(n+1);
priority_queue<pair<ll, int>> Q;
d[s] = 0;
Q.push({d[s], s});
while(Q.size()) {
int cur = Q.top().nd;
Q.pop();
if(vis[cur]) continue;
vis[cur] = 1;
for(auto nxt: g[cur]) {
if(!vis[nxt.st] && d[nxt.st] > d[cur] + nxt.nd) {
d[nxt.st] = d[cur] + nxt.nd;
Q.push({-d[nxt.st], nxt.st});
}
}
}
}
int main() {
ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
int n, m; cin>>n>>m;
int s, t; cin>>s>>t;
int u, v; cin>>u>>v;
vector<vector<pii>> g(n+1);
for(int i=0; i<m; ++i) {
int a, b, c;
cin>>a>>b>>c;
g[a].push_back({b, c});
g[b].push_back({a, c});
}
vector<ll> d_s(n+1, INF), d_t(n+1, INF);
dijkstra(s, g, d_s);
dijkstra(t, g, d_t);
auto G = g;
for(int i=n+1; i<=3*n; ++i) {
G.push_back({});
}
for(int i=1; i<=n; ++i) {
for(auto edge: g[i]) {
int j = edge.st, w = edge.nd;
G[i+2*n].push_back({j+2*n, w});
if(d_s[i] + w + d_t[j] == d_s[t]) {
G[i+n].push_back({j+n, 0});
}
else {
G[i+n].push_back({j+2*n, w});
}
}
}
for(int i=1; i<=n; ++i) {
G[i].push_back({i+n, 0});
G[i+n].push_back({i+2*n, 0});
}
vector<ll> d(3*n+1, INF);
auto D = d;
dijkstra(u, G, d);
dijkstra(v, G, D);
cout<<min(d[v+2*n], D[u+2*n]);
}
