This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
//#pragma GCC optimize("O3")
#include <bits/stdc++.h>
using namespace std;
#define MAXN 100005
#define MAXM 100005
#define mix(a, b) a = min(a,b)
using ll = long long;
const ll mod = 1e9 + 7;
vector<pair<int, ll>> g[MAXN];
vector<pair<int, ll>> gc[MAXN];
vector<ll> ds, dt;
ll st;
void dijkstra(vector<ll> &dist, int s) {
dist[s] = 0;
set<pair<ll, int>> q;
q.insert({0, s});
while (!q.empty()) {
int v = q.begin()->second;
q.erase(q.begin());
for (auto[u, c] : g[v]) {
if (dist[v] + c < dist[u]) {
q.erase({dist[u], u});
dist[u] = dist[v] + c;
q.insert({dist[u], u});
}
}
}
}
void spec(vector<ll> &dist, int s) {
dist[s] = 0;
set<pair<ll, int>> q;
q.insert({0, s});
vector<int> flex(dist.size(), false);
while (!q.empty()) {
int v = q.begin()->second;
q.erase(q.begin());
for (auto[u, c] : g[v]) {
if (ds[v] < ds[u] && flex[v] != 2)
if (ds[v] + c + dt[u] == st)
c = 0;
if (dist[v] + c < dist[u]) {
q.erase({dist[u], u});
dist[u] = dist[v] + c;
if (c == 0) flex[u] = true;
else if (flex[v] != 0) flex[u] = 2;
q.insert({dist[u], u});
}
}
}
}
void solve() {
int n, m;
cin >> n >> m;
int s, t;
cin >> s >> t;
int u, v;
cin >> u >> v;
for (int i = 0; i < m; i++) {
int a, b, c;
cin >> a >> b >> c;
g[a].emplace_back(b, c);
g[b].emplace_back(a, c);
gc[a].emplace_back(b, c);
gc[b].emplace_back(a, c);
}
ds.resize(n + 1, 1e18), dt.resize(n + 1, 1e18);
dijkstra(ds, s);
dijkstra(dt, t);
st = ds[t];
vector<ll> bebra(n + 1, 1e18);
spec(bebra, u);
ll ans = bebra[v];
bebra.assign(n + 1, 1e18);
spec(bebra, v);
ans = min(ans, bebra[u]);
cout << ans;
}
signed main() {
#ifdef LOCAL
freopen("input.txt", "r", stdin);
#endif
ios::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
int t = 1;
// cin >> t;
while (t--)
solve();
return 0;
}
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