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>
#define name "cownav"
#define fi(i,a,b) for(int i = a; i <= b; i++)
#define fid(i,a,b) for(int i = a; i >= b; i--)
#define ll long long
#define f first
#define se second
#define pii pair<ll, int>
#define getbit(i, j) ((i >> j) & 1)
#define pb push_back
#define all(v) v.begin(), v.end()
#define maxn 200005
const int M = 1e9 + 7;
using namespace std;
int n, m, S, T, U, V, xd[2*maxn];
struct dl{int f, se, id;};
vector <dl> g[maxn];
ll L[maxn];
void dij(){
fi(i, 1, n) L[i] = 1e18;
L[S] = 0;
priority_queue <pii> q;
q.push({0, S});
while(q.size()){
ll h = -q.top().f;
int u = q.top().se;
q.pop();
if(h != L[u]) continue;
for(auto e: g[u]){
int v = e.f, w = e.se;
if(L[v] > L[u] + w){
L[v] = L[u] + w;
q.push({-L[v], v});
}
}
}
}
void dfs(int u){
for(auto e: g[u]){
int v = e.f, w = e.se, id = e.id;
if(xd[id]) continue;
xd[id] = 1;
if(L[v] + w == L[u]) xd[id] = 2;
dfs(v);
}
}
void dij1(){
fi(i, 1, n) L[i] = 1e18;
L[U] = 0;
priority_queue <pii> q;
q.push({0, U});
while(q.size()){
ll h = -q.top().f;
int u = q.top().se;
q.pop();
if(h != L[u]) continue;
for(auto e: g[u]){
int v = e.f, w = e.se, id = e.id;
if(xd[id] == 2) w = 0;
if(L[v] > L[u] + w){
L[v] = L[u] + w;
q.push({-L[v], v});
}
}
}
}
signed main(){
ios_base::sync_with_stdio(0);
cin.tie(NULL);
// freopen(name".in", "r", stdin);
// freopen(name".out", "w", stdout);
cin >> n >> m;
cin >> S >> T >> U >> V;
fi(i, 1, m){
int u, v, z; cin >> u >> v >> z;
g[u].pb({v, z, i});
g[v].pb({u, z, i});
}
dij();
dfs(T);
// fi(i, 1, m) cout << xd[i] << " "; cout << endl;
dij1();
cout << L[V];
}
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