#include <bits/stdc++.h>
using namespace std;
int main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
int N, M, S, T, U, V;
cin >> N >> M >> S >> T >> U >> V;
vector<vector<pair<int, int>>> adj(N + 1);
for (int i = 0; i < M; i++) {
int u, v, w;
cin >> u >> v >> w;
adj[u].emplace_back(v, w);
adj[v].emplace_back(u, w);
}
const long long inf = 1e18;
vector<long long> ds(N + 1, inf), dt(N + 1, inf), du(N + 1, inf), dv(N + 1, inf);
{
ds[S] = 0;
priority_queue<pair<long long, int>> q;
q.emplace(0LL, S);
while (!q.empty()) {
auto [d, u] = q.top();
q.pop();
d = -d;
if (d != ds[u]) continue;
for (auto [v, w] : adj[u]) {
long long nd = w + d;
if (nd < ds[v]) {
ds[v] = nd;
q.emplace(-nd, v);
}
}
}
}
{
dt[T] = 0;
priority_queue<pair<long long, int>> q;
q.emplace(0LL, T);
while (!q.empty()) {
auto [d, u] = q.top();
q.pop();
d = -d;
if (d != dt[u]) continue;
for (auto [v, w] : adj[u]) {
long long nd = w + d;
if (nd < dt[v]) {
dt[v] = nd;
q.emplace(-nd, v);
}
}
}
}
{
du[U] = 0;
priority_queue<pair<long long, int>> q;
q.emplace(0LL, U);
while (!q.empty()) {
auto [d, u] = q.top();
q.pop();
d = -d;
if (d != du[u]) continue;
for (auto [v, w] : adj[u]) {
long long nd = w + d;
if (nd < du[v]) {
du[v] = nd;
q.emplace(-nd, v);
}
}
}
}
{
dv[V] = 0;
priority_queue<pair<long long, int>> q;
q.emplace(0LL, V);
while (!q.empty()) {
auto [d, u] = q.top();
q.pop();
d = -d;
if (d != dv[u]) continue;
for (auto [v, w] : adj[u]) {
long long nd = w + d;
if (nd < dv[v]) {
dv[v] = nd;
q.emplace(-nd, v);
}
}
}
}
long long ans = du[V];
vector<long long> dp1(N + 1, inf), dp2(N + 1, inf), dp3(N + 1, inf), dp4(N + 1, inf), dp5(N + 1, inf);
vector<int> ord(N);
iota(ord.begin(), ord.end(), 1);
sort(ord.begin(), ord.end(), [&](int i, int j) {
return ds[i] < ds[j];
});
{
dp1[S] = du[S];
for (int v : ord) {
if (ds[v] + dt[v] != ds[T]) continue;
for (auto [u, w] : adj[v]) {
if (ds[u] + dt[u] != ds[T]) continue;
if (ds[v] == w + ds[u] && dt[v] + w == dt[u]) {
dp1[v] = min({dp1[u], du[v], dp1[v]});
}
}
}
}
{
dp2[S] = dv[S];
for (int v : ord) {
if (ds[v] + dt[v] != ds[T]) continue;
for (auto [u, w] : adj[v]) {
if (ds[u] + dt[u] != ds[T]) continue;
if (ds[v] == w + ds[u] && dt[v] + w == dt[u]) {
dp2[v] = min({dp2[u], dv[v], dp2[v]});
}
}
}
}
sort(ord.begin(), ord.end(), [&](int i, int j) {
return dt[i] < dt[j];
});
{
dp4[T] = du[T];
for (int v : ord) {
if (ds[v] + dt[v] != ds[T]) continue;
for (auto [u, w] : adj[v]) {
if (ds[u] + dt[u] != ds[T]) continue;
if (ds[v] == w + ds[u] && dt[v] + w == dt[u]) {
dp4[v] = min({dp4[u], du[v], dp4[v]});
}
}
}
}
{
dp5[T] = dv[T];
for (int v : ord) {
if (ds[v] + dt[v] != ds[T]) continue;
for (auto [u, w] : adj[v]) {
if (ds[u] + dt[u] != ds[T]) continue;
if (ds[v] == w + ds[u] && dt[v] + w == dt[u]) {
dp5[v] = min({dp5[u], dv[v], dp5[v]});
}
}
}
}
sort(ord.begin(), ord.end(), [&](int i, int j) {
return ds[i] < ds[j];
});
{
dp3[S] = dp1[S] + dp2[S];
for (int v : ord) {
if (ds[v] + dt[v] != ds[T]) continue;
for (auto [u, w] : adj[v]) {
if (ds[u] + dt[u] != ds[T]) continue;
if (ds[v] == w + ds[u] && dt[v] + w == dt[u]) {
dp3[v] = min({dp1[v] + dp5[v], dp2[v] + dp4[v], dp3[u], dp3[v]});
}
}
}
}
ans = min(ans, *min_element(dp3.begin(), dp3.end()));
cout << ans;
return 0;
}
