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#include<bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
using namespace std;
typedef long long int ll;
typedef vector<ll> vi;
typedef vector<vector<ll>> vvi;
typedef pair<ll,ll> pi;
typedef map<ll,ll> mi;
typedef long double ld;
typedef vector<ld> vd;
typedef vector<vector<ld>> vvd;
typedef pair<ld,ld> pd;
#define ff first
#define ss second
#define srt(a) sort(a.begin(),a.end());
#define fip(k, n) for (ll i = k; i < n; i++)
#define fjp(k, n) for (ll j = k; j < n; j++)
#define fin(k, n) for (ll i = k; i >= n; i--)
#define fjn(k, n) for (ll j = k; j >= n; j--)
#define fp(k, n, m) for (ll k = n; k < m; k++)
#define fn(k, n, m) for (ll k = n; k >= m; k--)
#define ordered_set tree<pi, null_type,less< pi >, rb_tree_tag,tree_order_statistics_node_update>
#define totalOne(n) __builtin_popcount(n)
#define backZero(n) __builtin_ctzll(n)
#define frontZero(n) __builtin_clzll(n)
#define fx(k) for ( auto x : k )
#define test ll t;cin >> t;while (t--)
#define nli "\n"
// ==========================(debug)============================================================================================== //
#ifndef ONLINE_JUDGE
#define debug(x) cerr << #x <<" "; _printn(x); cerr << nli;
#else
#define debug(x)
#endif
void _printn(ll x){ cerr<<x<<" "; }
void _printn(int x){ cerr<<x<<" "; }
void _printn(ld x){ cerr<<x<<" "; }
void _printn(double x){ cerr<<x<<" "; }
void _printn(string x){ cerr<<x<<" "; }
void _printn(char x){ cerr<<x<<" "; }
void _printn(bool x){ cerr<<x<<" "; }
template<class T,class V>void _printn(pair<T,V> vv);
template<class T> void _printn(vector<T> vv);
template<class T> void _printn(set<T> vv);
template<class T,class V> void _printn(map<T,V> vv);
template<class T> void _printn(multiset<T> vv);
template<class T,class V>void _printn(pair<T,V> vv){ cerr<<"( ";_printn(vv.ff);cerr<<",";_printn(vv.ss);cerr<<")";}
template<class T> void _printn(vector<T> vv){ cerr<<"[ "; for(auto xx:vv){ _printn(xx);cerr<<" "; } cerr<<"]"; };
template<class T> void _printn(set<T> vv){ cerr<<"{ "; for(auto xx:vv){ _printn(xx);cerr<<" "; } cerr<<"}"; };
template<class T> void _printn(multiset<T> vv){ cerr<<"{ "; for(auto xx:vv){ _printn(xx);cerr<<" "; } cerr<<"}"; };
template<class T,class V> void _printn(map<T,V> vv){ cerr<<"{ "; for(auto xx:vv){ _printn(xx);cerr<<" "; } cerr<<"}"; };
// ==========================(debug)============================================================================================== //
ll n,m,tp,tp2,res,cnt,sum,tptp,ans;
const ll mx = 1e5+5;
const ll mod = 1e9+7;
// ==========================(MOD)=============================================================================================== //
ll mod_add(ll aa,ll bb){ return ((aa%mod)+(bb%mod))%mod; }
ll mod_minus(ll aa,ll bb){ return (((aa%mod)-(bb%mod))+10*mod)%mod; }
ll mod_mul(ll aa,ll bb){ return ((aa%mod)*(bb%mod))%mod; }
ll mod_power(ll aa,ll bb){ aa%=mod; ll empowered = 1; bb%=mod-1; while(bb > 0){ if(bb & 1) empowered = mod_mul(empowered,aa); bb = bb >> 1; aa = mod_mul(aa,aa); } return empowered; }
ll mod_divi(ll aa,ll bb){ aa=mod_mul(aa,mod_power(bb,mod-2)); return aa; }
// ==========================(MOD)=============================================================================================== //
bool f = false;
ll u,v;
ll sr,de;
vector<pi> adj[mx];
ll dis[mx][3];
ll dp[mx][4];
priority_queue<pi,vector<pi>,greater<pi>> pq,pq2;
void deb(){
pq2 = pq;
cerr<<"st->";
while(pq2.size()){
auto it = pq2.top();
pq2.pop();
debug(it);
}
cerr<<"en.";
return;
}
void get(ll u,ll i){
fjp(0,n+2)dis[j][i] = 1e18;
dis[u][i] = 0;
pq.push({0,u});
ll id,wet;
while(pq.size()){
auto it = pq.top();
id = it.ss;
wet = it.ff;
pq.pop();
if(dis[id][i] < wet)
continue;
fx(adj[id]){
if(dis[x.ff][i] > dis[id][i] + x.ss){
dis[x.ff][i] = dis[id][i] + x.ss;
pq.push({dis[x.ff][i],x.ff});
}
}
// cerr<<nli;
}
return;
}
ll rs = 0;
ll empowered(ll x,ll y){
rs = 0;
if(y&1)rs += dis[x][1];
if(y&2)rs += dis[x][2];
return rs;
}
int main(){
ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
// #ifndef ONLINE_JUDGE
// freopen("input1.txt", "r", stdin);
// freopen("output1.txt", "w", stdout);
// freopen("error1.txt", "w", stderr);
// #endif // ONLINE_JUDGE
cin>>n>>m;
cin>>tp>>tp2;
cin>>u>>v;
fip(0,m){
cin>>sr>>de>>tptp;
adj[sr].push_back({de,tptp});
adj[de].push_back({sr,tptp});
}
get(tp,0);
get(u,1);
get(v,2);
// fip(1,n+1)
// cout<<dis[i][0]<<" ";
// cout<<nli;
fip(1,n+1)
fjp(0,4)
dp[i][j] = 1e18;
dp[tp][0] = 0;
dp[tp][1] = dis[tp][1];
dp[tp][2] = dis[tp][2];
dp[tp][3] = dis[tp][2] + dis[tp][1];
vector<pi> vc;
fip(1,n+1)
vc.push_back({dis[i][0],i});
srt(vc);
ans = dis[v][1];
for(auto y : vc){
res = y.ss;
fx(adj[res]){
if(dis[res][0]+x.ss==dis[x.ff][0]){
// debug(x.ff);
fp(d,0,4)
fp(e,0,4)
dp[x.ff][d|e] = min(dp[x.ff][d|e],dp[res][d]+empowered(x.ff,e));
}
}
}
ans = min(ans,dp[tp2][3]);
cout<<ans<<nli;
cerr << "Time elapsed: " << setprecision(6) << 1000.0 * clock() / CLOCKS_PER_SEC << "ms\n";
return 0;
}
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