#include <bits/stdc++.h>
using namespace std;
#define task "main"
#define no "NO"
#define yes "YES"
#define F first
#define S second
#define vec vector
#define _mp make_pair
#define ii pair<int, int>
#define li pair<long long, int>
#define sz(x) (int)x.size()
#define all(x) x.begin(), x.end()
#define evoid(val) return void(std::cout << val)
#define FOR(i, a, b) for(int i = (a); i <= (b); ++i)
#define FOD(i, b, a) for(int i = (b); i >= (a); --i)
const int MAX_N = (int)1e5 + 5;
const long long INF = (long long)1e18;
int numNode, numEdge;
int startSchool, endSchool, startStore, endStore;
vector<ii> adj[MAX_N];
vector<long long> dist[3]; // minimum paths from s, u, v -> i (i = 1..n)
vector<int> dag[MAX_N], trace[MAX_N];
void dijkstra(vector<long long> &dist, int s, bool isTrace) {
dist.assign(numNode + 1, INF);
dist[s] = 0;
priority_queue<li, vector<li>, greater<li>> pq;
pq.push({0, s});
while (!pq.empty()) {
int u = pq.top().S;
pq.pop();
for (auto [v, w] : adj[u]) {
if (dist[v] > dist[u] + w) {
dist[v] = dist[u] + w;
pq.push({dist[v], v});
if (isTrace) {
trace[v].clear();
trace[v].push_back(u);
}
}
else if (dist[v] == dist[u] + w && isTrace) {
trace[v].push_back(u);
}
}
}
}
bool vis[MAX_N];
void dfs(int u) {
if (vis[u] || u == startSchool) return;
vis[u] = 1;
for (int v : trace[u]) {
dag[v].push_back(u);
dfs(v);
}
}
// dpIn: v -> x -> y -> u, dpOut: u -> x -> y -> v, with x, y is a sub-path of the optimal path from s -> t
long long dpIn[MAX_N], dpOut[MAX_N];
void calc(int u) {
if (u == endSchool) return;
dpOut[u] = dist[2][u];
for (int v : dag[u]) {
dpIn[v] = min(dist[2][v], dpIn[u]);
calc(v);
dpOut[u] = min(dpOut[u], dpOut[v]);
}
}
void solve() {
cin >> numNode >> numEdge >> startSchool >> endSchool >> startStore >> endStore;
FOR(i, 1, numEdge) {
int u, v, w;
cin >> u >> v >> w;
adj[u].push_back({v, w});
adj[v].push_back({u, w});
}
dijkstra(dist[0], startSchool, 1);
dijkstra(dist[1], startStore, 0);
dijkstra(dist[2], endStore, 0);
dfs(endSchool);
long long ans = dist[1][endStore]; // just go from u -> v
FOR(i, 0, numNode) dpIn[i] = dpOut[i] = INF;
dpIn[startSchool] = dist[2][startSchool];
dpOut[endSchool] = dist[2][endSchool];
calc(startSchool);
FOR(i, 1, numNode) ans = min(ans, dist[1][i] + min(dpIn[i], dpOut[i]));
cout << ans << "\n";
}
int32_t main() {
if (fopen(task".inp", "r")) {
freopen(task".inp", "r", stdin);
freopen(task".out", "w", stdout);
}
ios_base::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
bool multitest = 0;
int numTest = 1;
if (multitest) cin >> numTest;
while (numTest--) {
solve();
}
return 0;
}
/* Lak lu theo dieu nhac!!!! */
