#include <bits/stdc++.h>
using namespace std;
using ll = long long;
pair<ll, ll> y;
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);
vis.assign(n + 1, false);
priority_queue<pair<ll, pair<int, pair<ll, ll>>>, vector<pair<ll, pair<int, pair<ll, ll>>>>, greater<>> q;
q.push({0, {s, {disu[s], disv[s]}}});
while (!q.empty()) {
x = q.top().second.first;
y = q.top().second.second; q.pop();
if (x == t) {
return cout << min(disu[v], y.first + y.second), 0;
}
if (vis[x]) continue;
vis[x] = true;
for (auto i : E[x]) {
if (diss[x] + i.second == diss[i.first] && diss[i.first] + dist[i.first] == diss[t]) {
q.push({diss[i.first], {i.first, {min(y.first, disu[i.first]), min(y.second, disv[i.first])}}});
}
}
}
}
