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> // PLEASE
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair <ll, ll> pp;
#define MAXN 300005
#define MAXM 1005
#define MAXP 25
#define A first
#define B second
#define MP make_pair
#define PB push_back
const ll INF = 2e9+13;
const ll MOD = 1e9+7;
int N, M;
int S[4]; // S T U V
vector <pp> g[MAXN];
ll d[4][MAXN];
ll dp[2][MAXN];
bool vis[MAXN];
void run(int i) {
priority_queue <pp> PQ;
memset(vis, 0, sizeof(vis));
PQ.push({0, S[i]});
while(!PQ.empty()) {
ll di = -PQ.top().A;
int u = PQ.top().B;
PQ.pop();
if(vis[u]) continue;
vis[u] = 1; d[i][u] = di;
for(auto e : g[u]) if(!vis[e.A]) PQ.push({-1LL*(di + e.B), e.A});
}
}
void run2(int i) {
priority_queue <pp> PQ;
memset(vis, 0, sizeof(vis));
PQ.push({0, S[i]});
while(!PQ.empty()) {
ll di = -PQ.top().A;
int u = PQ.top().B;
PQ.pop();
if(vis[u]) continue;
dp[i][u] = min(dp[i][u], d[2][u]);
vis[u] = 1; d[i][u] = di;
for(auto e : g[u]) if(!vis[e.A]) if(di + e.B == d[i][e.A]) { // shortest path
PQ.push({-1LL*(di + e.B), e.A});
dp[i][e.A] = min(dp[i][e.A], dp[i][u]);
}
}
}
int main(void)
{
ios_base::sync_with_stdio(false);
cin.tie(0);
cin >> N >> M;
for(int i=0; i<4; i++) cin >> S[i];
for(int i=0; i<M; i++) {
int a, b; ll c;
cin >> a >> b >> c;
g[a].PB({b, c});
g[b].PB({a, c});
}
for(int i=0; i<4; i++) run(i);
for(int i=0; i<2; i++) for(int j=1; j<=N; j++) dp[i][j] = 1e18;
for(int i=0; i<2; i++) run2(i);
ll ans = d[2][S[3]];
ll sp = d[0][S[1]];
for(int i=1; i<=N; i++)
if(d[0][i] + d[1][i] == sp) {
ans = min(ans, d[3][i] + min(dp[0][i], dp[1][i]));
}
cout << ans << endl;
}
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