#include <bits/stdc++.h>
#define int long long
using namespace std;
int n, m, s, t, u, v;
void dijkstra(vector<vector<pair<int, int>>>& adj, int ss, vector<int>& dis) {
priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;
dis[ss] = 0;
pq.push({0, ss});
while (!pq.empty()) {
auto [curw, curn] = pq.top();
pq.pop();
if (curw != dis[curn]) continue;
for (auto& [nextn, nextw] : adj[curn]) {
if (curw + nextw < dis[nextn]) {
dis[nextn] = curw + nextw;
pq.push({dis[nextn], nextn});
}
}
}
}
signed main() {
cin.tie(nullptr)->sync_with_stdio(false);
cin >> n >> m >> s >> t >> u >> v;
s--;
t--;
u--;
v--;
vector<vector<pair<int, int>>> adj(n);
for (int i = 0; i < m; i++) {
int a, b, c;
cin >> a >> b >> c;
a--;
b--;
adj[a].push_back({b, c});
adj[b].push_back({a, c});
}
vector<int> dis1(n, LLONG_MAX);
vector<int> dis2(n, LLONG_MAX);
dijkstra(adj, u, dis1);
dijkstra(adj, v, dis2);
priority_queue<tuple<int, int, int, int, int>, vector<tuple<int, int, int, int, int>>, greater<tuple<int, int, int, int, int>>> pq;
vector<pair<int, int>> dis(n, {LLONG_MAX, LLONG_MAX});
dis[s] = {0, dis1[s] + dis2[s]};
pq.push({0, dis1[s] + dis2[s], dis1[s], dis2[s], s});
while (!pq.empty()) {
auto [curw, curs, curu, curv, curn] = pq.top();
pq.pop();
if (make_pair(curw, curs) != dis[curn]) continue;
for (auto& [nextn, nextw] : adj[curn]) {
int nu = min(curu, dis1[nextn]), nv = min(curv, dis2[nextn]);
if (curw + nextw < dis[nextn].first) {
dis[nextn] = {curw + nextw, nu + nv};
pq.push({dis[nextn].first, nu + nv, nu, nv, nextn});
} else if (curw + nextw == dis[nextn].first and nu + nv < dis[nextn].second) {
dis[nextn].second = nu + nv;
pq.push({dis[nextn].first, nu + nv, nu, nv, nextn});
}
}
}
cout << min(dis[t].second, dis1[v]);
}
