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;
struct point{
	int64_t d,u,pp,bb;
};
struct cm {
    bool operator()(const point& a, const point& b) const {
        return a.d < b.d;
    }
};
int main(){
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	int64_t n,m;cin>>n>>m;
	int64_t S,T;cin>>S>>T;
	--S;--T;
	int64_t U,V;cin>>U>>V;
	--U;--V;
	vector<vector<pair<int64_t,int64_t>>>adj(n);
	for (int64_t i = 0;i<m;++i){
		int64_t x,y,z;cin>>x>>y>>z;
		--x;--y;
		adj[x].push_back({y,z});
		adj[y].push_back({x,z});
	}
	const int64_t mxn = 1e18;
	priority_queue<pair<int64_t,pair<int64_t,int64_t>>>q;
	vector<vector<int64_t>>dist(n,vector<int64_t>(2,mxn));
	q.push({0,{U,0}});
	q.push({0,{V,1}});
	dist[U][0] = 0;
	dist[V][1] = 0;
	while(!q.empty()){
		auto u = q.top().second;
		q.pop();
		for (auto x:adj[u.first]){
			if (dist[x.first][u.second] > dist[u.first][u.second] + x.second){
				dist[x.first][u.second] = dist[u.first][u.second] + x.second;
				q.push({-dist[x.first][u.second],{x.first,u.second}});
			}
		}
	}
	int64_t ans = dist[U][1];
	vector<int64_t>dis(n,mxn);
	map<int64_t,pair<int64_t,int64_t>>mp;
	auto bfs = [&](){
		multiset<point,cm>qq;
		qq.insert({0LL,S,dist[S][0],dist[S][1]});
		dis[S] = 0LL;
		while(!qq.empty()){
			auto u = *qq.begin();
			qq.erase(qq.begin());
			if (u.d > dis[u.u])continue;
			if (u.u == T){
				ans = min(ans,u.pp + u.bb);
			}
			for (auto x:adj[u.u]){
				if (dis[x.first] > dis[u.u] + x.second){
					dis[x.first] = dis[u.u] + x.second;
					qq.insert({dis[x.first],x.first,min(u.pp,dist[x.first][0]),min(u.bb,dist[x.first][1])});
					mp[x.first] = make_pair(min(u.pp,dist[x.first][0]),min(u.bb,dist[x.first][1]));
				}
				else if (dis[x.first] == dis[u.u] + x.second){
					if (min(u.pp,dist[x.first][0]) < mp[x.first].first && min(u.bb,dist[x.first][1]) < mp[x.first].second){
						auto it = qq.find({dis[x.first],x.first,mp[x.first].first,mp[x.second].second});
						if (it!=qq.end()){
							qq.erase(it);
							qq.insert({dis[x.first],x.first, min(u.pp,dist[x.first][0]),min(u.bb,dist[x.first][1])});
							mp[x.first] = make_pair(min(u.pp,dist[x.first][0]),min(u.bb,dist[x.first][1]));
						}
					}
					else if (min(u.pp,dist[x.first][0]) < mp[x.first].first || min(u.bb,dist[x.first][1]) < mp[x.first].second){
						qq.insert({dis[x.first],x.first,min(u.pp,dist[x.first][0]),min(u.bb,dist[x.first][1])});
						mp[x.first] = make_pair(min(min(u.pp,dist[x.first][0]),mp[x.first].first),min(mp[x.first].second,min(u.bb,dist[x.first][1])));
					}
				}
 
			}
		}
	};
	bfs();
	cout<<ans<<'\n';
	return 0;
}
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