#include <iostream>
#include <cstdio>
#include <vector>
#include <queue>
#include <algorithm>
using namespace std;
using I = int;
using Lli = long long int;
const I N = 100000;
const Lli MAX = 1e18;
vector<pair<I, I>> adjs[N];
priority_queue<pair<Lli, I>, vector<pair<Lli, I>>, greater<pair<Lli, I>>> que;
Lli diss1[N];
Lli diss2[N];
Lli diss3[N];
Lli mins1[N];
Lli mins2[N];
Lli tots[N];
void cmb(Lli& a, Lli b) {
a = min(a, b);
}
I main(void) {
cin.tie(0)->sync_with_stdio(0);
I n, m;
cin >> n >> m;
I s, t;
cin >> s >> t;
s--;
t--;
I u, v;
cin >> u >> v;
u--;
v--;
for (I i = 0; i < m; i++) {
I a, b, c;
cin >> a >> b >> c;
a--;
b--;
adjs[a].push_back({b, c});
adjs[b].push_back({a, c});
}
fill_n(diss1, n, MAX);
fill_n(diss2, n, MAX);
fill_n(diss3, n, MAX);
que.push({diss1[u] = 0, u});
while (!que.empty()) {
const auto [dis, a] = que.top();
que.pop();
if (dis != diss1[a])
continue;
for (const auto [b, c] : adjs[a])
if (dis + c < diss1[b])
que.push({diss1[b] = dis + c, b});
}
que.push({diss2[v] = 0, v});
while (!que.empty()) {
const auto [dis, a] = que.top();
que.pop();
if (dis != diss2[a])
continue;
for (const auto [b, c] : adjs[a])
if (dis + c < diss2[b])
que.push({diss2[b] = dis + c, b});
}
for (I i = 0; i < n; i++)
tots[i] = diss1[i] + diss2[i];
copy_n(diss1, n, mins1);
copy_n(diss2, n, mins2);
que.push({diss3[s] = 0, s});
while (!que.empty()) {
const auto [dis, a] = que.top();
que.pop();
if (dis != diss3[a])
continue;
for (const auto [b, c] : adjs[a]) {
if (dis + c < diss3[b]) {
tots[b] = min(tots[a], diss1[b] + diss2[b]);
cmb(tots[b], mins1[a] + diss2[b]);
cmb(tots[b], mins2[a] + diss1[b]);
mins1[b] = min(mins1[a], diss1[b]);
mins2[b] = min(mins2[a], diss2[b]);
que.push({diss3[b] = dis + c, b});
} else if (dis + c == diss3[b]) {
cmb(tots[b], tots[a]);
cmb(tots[b], mins1[a] + diss2[b]);
cmb(tots[b], mins2[a] + diss1[b]);
cmb(mins1[b], mins1[a]);
cmb(mins2[b], mins2[a]);
}
}
}
printf("%lli\n", min(tots[t], diss2[u]));
return 0;
}
