This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
using namespace std;
// Types
typedef long long ll;
typedef string str;
typedef vector<ll> vll;
typedef vector<int> vi;
typedef vector<string> vs;
typedef vector<char> vc;
template <class T> using V = vector<T>;
template <class T, class E> using PR = pair<T, E>;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef set<ll> sll;
typedef map<ll, ll> mll;
typedef priority_queue<pll, V<pll>, greater<pll>> pqll;
#define umap unordered_map
#define uset unordered_set
// Firsts
#define FAST cin.tie(0); cout.tie(0); ios::sync_with_stdio(0)
#define READ_FILE(i, o) freopen(i, "r", stdin); freopen(o, "w", stdout)
#define PRECISION(n) cout << fixed << setprecision(n)
// Pair
#define MP make_pair
#define F first
#define S second
// For
#define rep(i,n) for (ll i = 0; i < (n); i++)
#define repOnto(i,n) for (ll i = 1; i < (n); i++)
#define per(i,n) for (ll i = (n)-1; i >= 0; i--)
#define loop(i,s,n,in) for (ll i = (s); i < (n); i+=(in))
#define pool(i,s,n,de) for (ll i = (n)-1; i >= (s); i-=(de))
#define each(e,v) for(auto &e : v)
// Input
#define gets(val) cin >> val
template <class T> void get(T &t) {
cin >> t;
}
template <class T, class... U> void get(T &t, U &... u) {
get(t); get(u...);
}
template <class T> void get(V<T> &v) {
each(e, v) get(e);
}
// Output
#define puts(val) cout << val << "\n"
template <class T> void put(T &t) {
cout << t;
}
template <class T, class... U> void put(T &t, U &... u) {
put(t); put(u...);
}
#define NXT "\n"
#define SB " "
#define nxt() cout << "\n"
#define sp() cout << " "
#define yes() cout << "YES\n";
#define no() cout << "NO\n";
// Extras
#define all(v) (v).begin(), (v).end()
#define sz(x) ((ll) ((x).size()))
#define PB push_back
#define P push
#define I insert
const double eps = 1e-9;
const ll INF = 1e16;
const ll MOD = 1e9 + 7;
void solve() {
ll n,m; get(n,m);
ll s,t; get(s,t);
s--; t--;
ll u,v; get(u,v);
u--; v--;
V<V<pll>> adj(n);
ll a,b,c;
rep(i,m){
get(a,b,c);
a--;b--;
adj[a].PB(MP(b,c));
adj[b].PB(MP(a,c));
}
pqll pq;
pq.P(MP(s,0));
vll dist(n, INF);
ll node, distance;
while(!pq.empty()){
tie(distance, node) = pq.top();
pq.pop();
if(dist[node] <= distance) continue;
dist[node] = distance;
each(e, adj[node]){
pq.P(MP(distance+e.second, e.first));
}
}
V<V<bool>> saved(n, V<bool>(n, false));
queue<ll> que;
V<bool> vis(n, 0);
que.P(t);
while (sz(que)) {
ll v = que.front();
que.pop();
ll d = dist[v];
if (vis[v]) continue;
vis[v] = 1;
each(p, adj[v]){
ll u, d_u;
tie(u, d_u) = p;
if (d == dist[u] + d_u) {
saved[p.first][v] = true;
saved[v][p.first] = true;
que.P(u);
}
}
}
pq.P(MP(u,0));
vll dist2(n, INF);
while(!pq.empty()){
tie(distance, node) = pq.top();
pq.pop();
if(dist2[node] <= distance) continue;
dist2[node] = distance;
each(e, adj[node]){
if(saved[e.first][node]){
pq.P(MP(distance, e.first));
}else{
pq.P(MP(distance+e.second, e.first));
}
}
}
puts(dist2[v]);
}
int main() {
// FAST;
// READ_FILE("test.in", "test.out");
ll t = 1;
// cin >> t;
loop(k,1,t+1,1) {
// put("Case #", k, ": ");
solve();
}
// cout << flush;
return 0;
}
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