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;
using ll = long long;
int n, m, s, t, u, v, a, b, c, x;
vector<bool> vis;
vector<ll> dis, diss, dist, disu, disv;
int main() {
	ios::sync_with_stdio(false); cin.tie(nullptr);
	cin >> n >> m >> s >> t >> u >> v;
	vector<pair<int, int>> E[n + 1];
	while (m--) {
		cin >> a >> b >> c;
		E[a].push_back({b, c});
		E[b].push_back({a, c});
	}
	auto f = [&](int st) -> vector<ll>{
		dis.assign(n + 1, LLONG_MAX); dis[st] = 0;
		priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<>> q; q.push({0, st});
		while (!q.empty()) {
			x = q.top().second; q.pop();
			for (auto i : E[x]) {
				if (dis[x] + i.second < dis[i.first]) {
					dis[i.first] = dis[x] + i.second;
					q.push({dis[i.first], i.first});
				}
			}
		}
		return dis;
	};
	diss = f(s); dist = f(t);
	disu = f(u); disv = f(v);
	ll ans = disu[v];
	vis.assign(n + 1, false);
	priority_queue<vector<ll>> q;
	q.push({0, -disu[s] - disv[s], s, disu[s], disv[s]});
	while (!q.empty()) {
		vector<ll> v = q.top(); q.pop();
		if (v[2] == t) {
			ans = min(ans, -v[1]);
			continue;
		}
		if (vis[v[2]]) continue;
		vis[v[2]] = true;
		for (auto i : E[v[2]]) {
			if (diss[v[2]] + i.second == diss[i.first] && diss[i.first] + dist[i.first] == diss[t]) {
				ll a = min(v[3], disu[i.first]), b = min(v[4], disv[i.first]);
				q.push({-diss[i.first], - a - b, i.first, a, b});
			}
		}
	}
	cout << ans;
}
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