/*input
6 6
1 6
1 4
1 2 1
2 3 1
3 5 1
2 4 3
4 5 2
5 6 1
*/
#include <bits/stdc++.h>
using namespace std;
int n, m, s, t, u, v;
vector<pair<int, int>> ad[100010];
void dij(int fw, vector<long long>&f) {
fill(f.begin(), f.end(), 1e15);
priority_queue<pair<long long, int>, vector<pair<long long, int>>, greater<pair<long long, int>>> q;
q.push({0, fw}); f[fw] = 0;
while (q.size()) {
long long w; int u; tie(w, u) = q.top(); q.pop();
for (auto v : ad[u]) {
if (f[v.first] > w + v.second) {
f[v.first] = w + v.second;
q.push({w + v.second, v.first});
}
}
}
}
main() {
cin >> n >> m >> s >> t >> u >> v;
for (int i = 0; i < m; ++i) {
int x, y, w; cin >> x >> y >> w;
ad[x].push_back({y, w});
ad[y].push_back({x, w});
}
vector<long long> fs(n + 1), ft(n + 1), fu(n + 1), fv(n + 1);
dij(t, ft);
dij(u, fu);
dij(v, fv);
dij(s, fs);
long long ret = fu[v];
for (int i = 0; i < 2; ++i) {
vector<long long> f(n + 1, 1e15), pf(n + 1, 1e15);
priority_queue<pair<long long, int>, vector<pair<long long, int>>, greater<pair<long long, int>>> q; q.push({0, s}); f[s] = 0; pf[s] = fu[s];
while (q.size()) {
long long w; int u; tie(w, u) = q.top(); q.pop();
ret = min(ret, pf[u] + fv[u]);
for (auto v : ad[u]) {
if (fs[v.first] + ft[v.first] == fs[t]) {
pf[v.first] = min({pf[v.first], fu[v.first], pf[u]});
if (f[v.first] > w + v.second) {
f[v.first] = w + v.second;
q.push({w + v.second, v.first});
}
}
}
}
swap(fu, fv);
}
cout << ret;
}
