#include <bits/stdc++.h>
#define ll long long
#define ld long double
#define pii pair<int, int>
#define pll pair<ll, ll>
using namespace std;
const ll INF = 1e15;
int n;
vector<vector<pii>> adj;
vector<vector<int>> spadj;
vector<ll> dp;
vector<ll> sp, dist_u, dist_v;
ll dfs(int node) {
if (dp[node] != -1) return dp[node];
ll best = dist_v[node];
for (int dest : spadj[node]) {
best = min(best, dfs(dest));
}
return dp[node] = best;
}
vector<ll> dijkstra(int start_node) {
vector<ll> dist(n + 1, INF);
priority_queue<pll, vector<pll>, greater<pll>> q;
dist[start_node] = 0;
q.push({0, start_node});
while (!q.empty()) {
auto p = q.top();
q.pop();
ll curr_cost = p.first, node = p.second;
for (pii &edge : adj[node]) {
int dest = edge.first, edge_cost = edge.second;
if (dist[dest] > curr_cost + edge_cost) {
dist[dest] = curr_cost + edge_cost;
q.push({dist[dest], dest});
}
}
}
return dist;
}
int32_t main() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
int m, S, T, U, V;
cin >> n >> m >> S >> T >> U >> V;
adj.resize(n + 1);
spadj.resize(n + 1);
for (int i = 0; i < m; i++) {
int u, v, cost;
cin >> u >> v >> cost;
adj[u].push_back({v, cost});
adj[v].push_back({u, cost});
}
// shortest path, dist to u, dist to v
sp = dijkstra(S), dist_u = dijkstra(U), dist_v = dijkstra(V);
vector<bool> vis(n + 1, false);
// construct the shortest path
queue<int> q;
q.push(T);
while (!q.empty()) {
int node = q.front();
q.pop();
ll mn_dist = INF;
for (pii &edge : adj[node]) {
mn_dist = min(mn_dist, sp[edge.first]);
}
for (pii &edge : adj[node]) {
int dest = edge.first, edge_cost = edge.second;
if (sp[dest] + edge_cost == sp[node]) {
spadj[node].push_back(dest);
if (!vis[dest]) {
vis[dest] = true;
q.push(dest);
}
}
}
}
// dfs from T, calculate, reverse spadj and dfs from S and recalculate
ll best = dist_v[U];
dp = vector<ll>(n + 1, -1);
for (int i = 1; i <= n; i++) {
dfs(i);
best = min(best, dp[i] + dist_u[i]);
}
vector<vector<int>> tmp(n + 1);
// reverse the edges
for (int i = 1; i <= n; i++) {
for (int j : spadj[i]) {
tmp[j].push_back(i);
}
}
spadj = tmp;
dp = vector<ll>(n + 1, -1);
for (int i = 1; i <= n; i++) {
dfs(i);
best = min(best, dp[i] + dist_u[i]);
}
cout << best << '\n';
}
