#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define ll long long
#define ld long double
using namespace std;
using namespace __gnu_pbds;
typedef tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;
const int NMAX = 1e5;
const ll INF = 1e18;
struct PQElement {
int node;
ll d;
int type;
bool operator < (const PQElement &other) const {
return other.d < d;
}
};
struct Edge {
int next_node, d, type;
Edge(int next_node, int d, int type) : next_node(next_node), d(d), type(type) {}
};
int n, m, s, t, x, y;
vector<pair<int, int>> g[NMAX + 1];
vector<Edge> g1[NMAX + 1];
ll d[3][NMAX + 1];
void Dijkstra(int start, int which_start) {
for(int i = 1; i <= n; i++) {
d[which_start][i] = INF;
}
priority_queue<PQElement> pq;
pq.push({start, 0, 0});
while(!pq.empty()) {
auto [node, curent_d, type] = pq.top();
pq.pop();
if(d[which_start][node] == INF) {
d[which_start][node] = curent_d;
for(auto [next_node, edge_d] : g[node]) {
pq.push({next_node, curent_d + edge_d, 0});
}
}
}
}
void CreateNewGraph() {
for(int i = 1; i <= n; i++) {
for(auto [j, edge_d] : g[i]) {
if(d[0][i] + edge_d + d[1][j] == d[0][t]) {
g1[i].emplace_back(j, 0, 1);
g1[j].emplace_back(i, 0, 2);
}
else {
g1[i].emplace_back(j, edge_d, 0);
}
}
}
}
void Dijkstra1() {
for(int i = 1; i <= n; i++) {
d[0][i] = d[1][i] = d[2][i] = INF;
}
priority_queue<PQElement> pq;
pq.push({x, 0, 0});
while(!pq.empty()) {
auto [node, curent_d, type] = pq.top();
pq.pop();
if(d[type][node] == INF) {
d[type][node] = curent_d;
for(auto [next_node, edge_d, edge_type] : g1[node]) {
if(edge_type == 0 || type == edge_type || x == node) {
pq.push({next_node, curent_d + edge_d, edge_type});
}
}
}
}
}
int main() {
ios::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
cin >> n >> m >> s >> t >> x >> y;
for(int i = 1; i <= m; i++) {
int a, b, c;
cin >> a >> b >> c;
g[a].emplace_back(b, c);
g[b].emplace_back(a, c);
}
Dijkstra(s, 0);
Dijkstra(t, 1);
CreateNewGraph();
// cout << '\n';
// for(int i = 1; i <= n; i++) {
// for(auto [j, edge_d, edge_type] : g1[i]) {
// cout << i << ' ' << j << ' ' << edge_d << ' ' << edge_type << '\n';
// }
// }
Dijkstra1();
cout << min({d[0][y], d[1][y], d[2][y]}) << '\n';
return 0;
}
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