#define USE_MATH_DEFINES 1
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
#define MOD 998244353ll
#define INF 1000000000000000000ll
#define EPS 1e-9
#define getchar_unlocked _getchar_nolock
#define putchar_unlocked _putchar_nolock
typedef long long ll;
typedef long double ld;
typedef pair <ll,ll> pl;
typedef tuple <ll,ll,ll> tl;
ll N, M, S, T, U, V, D1[100005], D2[100005], C1[100005], C2[100005];
vector <pl> adj[100005];
std::priority_queue <pl, vector<pl>, greater<pl> > pq;
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
cin >> N >> M >> S >> T >> U >> V;
for (ll i = 1; i <= M; i++) {
ll a, b, c;
cin >> a >> b >> c;
adj[a].emplace_back(c, b);
adj[b].emplace_back(c, a);
}
for (ll i = 1; i <= N; i++) {
D1[i] = INF;
D2[i] = INF;
C1[i] = INF;
C2[i] = INF;
}
D1[S] = 0;
pq.emplace(0, S);
while (!pq.empty()) {
ll curnode = pq.top().second;
ll curdist = pq.top().first;
pq.pop();
if (curdist > D1[curnode]) continue;
for (pl edge : adj[curnode]) {
ll nexnode = edge.second;
ll nexdist = D1[curnode] + edge.first;
if (nexdist < D1[nexnode]) {
D1[nexnode] = nexdist;
pq.emplace(D1[nexnode], nexnode);
}
}
}
D2[T] = 0;
pq.emplace(0, T);
while (!pq.empty()) {
ll curnode = pq.top().second;
ll curdist = pq.top().first;
pq.pop();
if (curdist > D2[curnode]) continue;
for (pl edge : adj[curnode]) {
ll nexnode = edge.second;
ll nexdist = D2[curnode] + edge.first;
if (nexdist < D2[nexnode]) {
D2[nexnode] = nexdist;
pq.emplace(D2[nexnode], nexnode);
}
}
}
C1[U] = 0;
pq.emplace(0, U);
while (!pq.empty()) {
ll curnode = pq.top().second;
ll curdist = pq.top().first;
pq.pop();
if (curdist > C1[curnode]) continue;
for (pl edge : adj[curnode]) {
ll nexnode = edge.second;
ll nexdist;
if (D1[curnode] + edge.first + D2[nexnode] == D1[T]) nexdist = C1[curnode];
else nexdist = C1[curnode] + edge.first;
if (nexdist < C1[nexnode]) {
C1[nexnode] = nexdist;
pq.emplace(C1[nexnode], nexnode);
}
}
}
C2[U] = 0;
pq.emplace(0, U);
while (!pq.empty()) {
ll curnode = pq.top().second;
ll curdist = pq.top().first;
pq.pop();
if (curdist > C2[curnode]) continue;
for (pl edge : adj[curnode]) {
ll nexnode = edge.second;
ll nexdist;
if (D2[curnode] + edge.first + D1[nexnode] == D1[T]) nexdist = C2[curnode];
else nexdist = C2[curnode] + edge.first;
if (nexdist < C2[nexnode]) {
C2[nexnode] = nexdist;
pq.emplace(C2[nexnode], nexnode);
}
}
}
cout << min(C1[V], C2[V]);
return 0;
}
