#include <bits/stdc++.h>
using namespace std;
# define int long long
# define fir first
# define sec second
# define pb push_back
# define endl "\n"
const int cnst = 2e5+5;
bool mutipletestcase = 0;
//bool debug = false;
void solve() {
// cerr << "IN" << endl;
int n, m; cin >> n >> m;
int s, t; cin >> s >> t;
int u, v; cin >> u >> v;
vector<pair<int, int>> vec[cnst];
tuple<int, int, int> edge[m+5];
map<pair<int, int>, int> mp;
int par[n+5];
for(int i = 1; i<=m; i++) {
int a, b, c; cin >> a >> b >> c;
// cerr << a << " " << b << " " << c << endl;
vec[a].pb({b, c});
vec[b].pb({a, c});
mp[{a, b}] = i;
mp[{b, a}] = i;
edge[i] = {a, b, c};
}
priority_queue<tuple<int, int, int>, vector<tuple<int, int, int>>, greater<tuple<int, int, int>>> pq;
pq.push({0, s, 0});
bool vis[n+5];
bool check[m+5];
memset(vis, 0, sizeof(vis));
memset(check, 0, sizeof(check));
while(!pq.empty()) {
auto[ene, idx, pr] = pq.top(); pq.pop();
cerr << ene << " " << idx << " " << pr << endl;
if(idx == t) {
int now = t;
par[now] = pr;
while(par[now] != 0) {
check[mp[{now, par[now]}]] = 1;
now = par[now];
}
}
if(vis[idx]) continue;
vis[idx] = 1;
par[idx] = pr;
for(auto[v, wei]: vec[idx]) if(!vis[v]) {
pq.push({ene+wei, v, idx});
}
}
vector<pair<int, int>> vec2[n+5];
for(int i = 1; i<=m; i++)
if(!check[i]) {
auto[a, b, c] = edge[i];
vec2[a].pb({b, c});
vec2[b].pb({a, c});
}
else {
auto[a, b, c] = edge[i];
vec2[a].pb({b, 0});
vec2[b].pb({a, 0});
}
memset(vis, 0, sizeof(vis));
pq.push({0, u, 0});
while(!pq.empty()) {
auto[ene, idx, pr] = pq.top(); pq.pop();
if(idx == v) {
cout << ene << endl; return;
}
if(vis[idx]) continue;
vis[idx] = 1;
par[s] = pr;
for(auto[v, wei]: vec2[idx]) if(!vis[v]) {
pq.push({ene+wei, v, idx});
}
}
}
signed main() {
ios_base::sync_with_stdio(false); cin.tie(0);
int t = 1;
if(mutipletestcase) cin >> t;
while(t--) solve();
}
