#include <iostream>
#include <cstdio>
#include <vector>
#include <array>
#include <string>
#include <algorithm>
#include <numeric>
#include <map>
#include <unordered_map>
#include <set>
#include <unordered_set>
#include <queue>
#include <cmath>
#include <climits>
#include <iomanip>
#include <limits>
#include <tuple>
#include <stack>
#include <bitset>
#include <cstring>
#include <sstream>
#include <functional>
#include <random>
using namespace std;
using ll = long long;
ll inf = 4e18;
vector<vector<pair<int, ll>>> g;
vector<ll> dijkstra(int n, int src) {
vector<ll> dist(n, inf);
dist[src] = 0;
priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<pair<ll, int>>> pq;
pq.push({ 0,src });
while (!pq.empty()) {
auto [d, u] = pq.top();
pq.pop();
if (d > dist[u]) {
continue;
}
for (auto& [v, w] : g[u]) {
ll nd = d + w;
if (nd < dist[v]) {
dist[v] = nd;
pq.emplace(nd, v);
}
}
}
return dist;
}
void solve() {
int n, m, s, t, u, v;
cin >> n >> m >> s >> t >> u >> v;
s--, t--, u--, v--;
g.assign(n, {});
for (int i = 0; i < m; ++i) {
int a, b;
ll w;
cin >> a >> b >> w;
--a, --b;
g[a].push_back({ b, w });
g[b].push_back({ a, w });
}
vector<ll> ds = dijkstra(n, s);
vector<ll> dt = dijkstra(n, t);
vector<ll> du = dijkstra(n, u);
vector<ll> dv = dijkstra(n, v);
ll d = ds[t];
vector<bool> mark(n, 0);
for (int i = 0; i < n; ++i) {
if (ds[i] + dt[i] == d) {
mark[i] = true;
}
}
vector<int> ord(n);
iota(ord.begin(), ord.end(), 0);
sort(ord.begin(), ord.end(), [&](int a, int b) { return ds[a] < ds[b]; });
vector<ll> dp1u(n, inf), dp1v(n, inf);
for (int i = 0; i < n; ++i) {
if (mark[i]) {
dp1u[i] = du[i];
dp1v[i] = dv[i];
}
}
for (auto& a : ord) {
if (!mark[a]) {
continue;
}
for (auto& e : g[a]) {
int b = e.first;
ll w = e.second;
if (!mark[b]) {
continue;
}
if (ds[a] + w + dt[b] == d) {
dp1u[b] = min(dp1u[b], dp1u[a]);
dp1v[b] = min(dp1v[b], dp1v[a]);
}
}
}
vector<ll> dp2u(n, inf), dp2v(n, inf);
for (int i = 0; i < n; ++i) {
if (mark[i]) {
dp2u[i] = du[i];
dp2v[i] = dv[i];
}
}
for (int i = n - 1; i >= 0; --i) {
int a = ord[i];
if (!mark[a]) {
continue;
}
for (auto& e : g[a]) {
int b = e.first;
ll w = e.second;
if (!mark[b]) {
continue;
}
if (ds[a] + w + dt[b] == d) {
dp2u[a] = min(dp2u[a], dp2u[b]);
dp2v[a] = min(dp2v[a], dp2v[b]);
}
}
}
ll ans = du[v];
for (int i = 0; i < n; ++i) {
if (dp1u[i] < inf && dp2v[i] < inf) {
ans = min(ans, dp1u[i] + dp2v[i]);
}
if (dp1v[i] < inf && dp2u[i] < inf) {
ans = min(ans, dp1v[i] + dp2u[i]);
}
}
cout << ans << '\n';
}
signed main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
solve();
return 0;
}
