#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define int ll
const int N = (int) 1e5 + 7;
const int INF = (ll) 1e18;
int cnt[N];
vector<int> adj[N];
ll dist[N], minU[N], minV[N];
bool vis[N];
int n, m, s, t, u, v;
struct Edge {
int to;
int cost;
};
vector<Edge> g[N];
void dijkstra(int start, vector<ll> &dist) {
for (int i = 1; i <= n; i++) {
dist[i] = INF;
vis[i] = 0;
}
priority_queue<pair<int, int>> pq;
dist[start] = 0;
pq.push({0, start});
while (!pq.empty()) {
int u = pq.top().second;
pq.pop();
if (vis[u] == 1) {
continue;
}
vis[u] = 1;
for (auto &edg : g[u]) {
int v = edg.to, relax = edg.cost;
if (dist[u] + relax < dist[v]) {
dist[v] = dist[u] + relax;
pq.push({-dist[v], v});
}
}
}
}
signed main() {
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
cin >> n >> m >> s >> t >> u >> v;
for (int i = 1; i <= m; i++) {
int x, y, z;
cin >> x >> y >> z;
g[x].push_back({y, z});
g[y].push_back({x, z});
}
vector<ll> distS(n + 1), distT(n + 1), distU(n + 1), distV(n + 1);
dijkstra(s, distS);
dijkstra(t, distT);
dijkstra(u, distU);
dijkstra(v, distV);
for (int u = 1; u <= n; u++) {
for (auto &edg : g[u]) {
if (distS[u] + edg.cost + distT[edg.to] == distS[t]) {
adj[u].push_back(edg.to);
cnt[edg.to]++;
}
}
}
queue<int> q;
for (int i = 1; i <= n; i++) {
if (cnt[i] == 0) {
q.push(i);
}
}
vector<int> topsort;
while (!q.empty()) {
int u = q.front();
q.pop();
topsort.push_back(u);
for (auto &v : adj[u]) {
cnt[v]--;
if (cnt[v] == 0) {
q.push(v);
}
}
}
reverse(topsort.begin(), topsort.end());
ll ret = INF;
for (auto &u : topsort) {
minU[u] = distU[u];
minV[u] = distV[u];
for (auto &v : adj[u]) {
minU[u] = min(minU[u], minU[v]);
minV[u] = min(minV[u], minV[v]);
}
ret = min({ret, distU[u] + minV[u], distV[u] + minU[u]});
}
cout << ret;
return 0;
}
