#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;
#ifdef TEST
#define getchar_unlocked _getchar_nolock
#endif
#define int long long
#define ins insert
#define mp make_pair
#define mt make_tuple
#define pb push_back
#define pf push_front
#define pp pop
#define ppb pop_back
#define ppf pop_front
#define eb emplace_back
#define g0(a) get<0>(a)
#define g1(a) get<1>(a)
#define g2(a) get<2>(a)
#define g3(a) get<3>(a)
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
typedef long double ld;
typedef long long ll;
typedef pair<int, int> ii;
typedef tuple<int, int, int> iii;
typedef tree<pair<int, int>, null_type, less<pair<int, int> >, rb_tree_tag, tree_order_statistics_node_update> ordered_set;
int N, M, S, T, U, V, a, d, O = LLONG_MAX, distS[100005], distT[100005], distU[100005], distV[100005], ret[100005], ret2[100005];
bool vis[100005], vis2[100005];
vector<ii> adj[100005];
vector<int> nadj[100005], n2adj[100005];
iii ed[200005];
priority_queue<ii, vector<ii>, greater<ii> > pq;
int dfs(int n) {
if (vis[n]) return ret[n];
vis[n] = 1;
ret[n] = distU[n];
for (auto u : nadj[n])
ret[n] = min(ret[n], dfs(u));
return ret[n];
}
int dfs2(int n) {
if (vis2[n]) return ret2[n];
vis2[n] = 1;
ret2[n] = distV[n];
for (auto u : nadj[n])
ret2[n] = min(ret2[n], dfs2(u));
return ret2[n];
}
main() {
ios::sync_with_stdio(0);
cin.tie(0);
cin >> N >> M >> S >> T >> U >> V;
for (int A, B, C, i = 1; i <= M; i++) {
cin >> A >> B >> C;
adj[A].eb(B, C);
adj[B].eb(A, C);
ed[i] = mt(A, B, C);
}
memset(distS, 127, sizeof distS);
memset(distT, 127, sizeof distT);
memset(distU, 127, sizeof distU);
memset(distV, 127, sizeof distV);
distS[S] = 0;
pq.emplace(0, S);
while (!pq.empty()) {
d = pq.top().first, a = pq.top().second;
pq.pop();
if (d > distS[a]) continue;
for (auto u : adj[a])
if (distS[u.first] > d + u.second) {
distS[u.first] = d + u.second;
pq.emplace(distS[u.first], u.first);
}
}
distT[T] = 0;
pq.emplace(0, T);
while (!pq.empty()) {
d = pq.top().first, a = pq.top().second;
pq.pop();
if (d > distT[a]) continue;
for (auto u : adj[a])
if (distT[u.first] > d + u.second) {
distT[u.first] = d + u.second;
pq.emplace(distT[u.first], u.first);
}
}
distU[U] = 0;
pq.emplace(0, U);
while (!pq.empty()) {
d = pq.top().first, a = pq.top().second;
pq.pop();
if (d > distU[a]) continue;
for (auto u : adj[a])
if (distU[u.first] > d + u.second) {
distU[u.first] = d + u.second;
pq.emplace(distU[u.first], u.first);
}
}
distV[V] = 0;
pq.emplace(0, V);
while (!pq.empty()) {
d = pq.top().first, a = pq.top().second;
pq.pop();
if (d > distV[a]) continue;
for (auto u : adj[a])
if (distV[u.first] > d + u.second) {
distV[u.first] = d + u.second;
pq.emplace(distV[u.first], u.first);
}
}
for (int A, B, C, i = 1; i <= M; i++) {
tie(A, B, C) = ed[i];
if (distT[B] + distS[A] + C == distS[T]) {
nadj[A].pb(B);
n2adj[B].pb(A);
}
swap(A, B);
if (distT[B] + distS[A] + C == distS[T]) {
nadj[A].pb(B);
n2adj[B].pb(A);
}
}
for (int i = 1; i <= N; i++) {
int M = 1e16;
for (int j : nadj[i]) M = min(M, dfs(j));
O = min(O, M + distV[i]);
M = 1e16;
for (int j : nadj[i]) M = min(M, dfs2(j));
O = min(O, M + distU[i]);
}
for (int i = 1; i <= N; i++)
nadj[i] = n2adj[i];
memset(vis, 0, sizeof vis);
memset(vis2, 0, sizeof vis2);
for (int i = 1; i <= N; i++) {
int M = 1e16;
for (int j : nadj[i]) M = min(M, dfs(j));
O = min(O, M + distV[i]);
M = 1e16;
for (int j : nadj[i]) M = min(M, dfs2(j));
O = min(O, M + distU[i]);
}
cout << min(O, distU[V]) << '\n';
}
