/*ㅤ∧＿∧
( ･∀･)
( つ┳⊃
ε (_)へ⌒ヽﾌ
( ( ･ω･)
◎―◎ ⊃ ⊃
BePhuongSuperSiuwi
From TK4 - CHT
ㅤㅤ／ ⌒＼____
/・ ） \
/ノへ ノ /|
ノ ＼\ |/_/_/*/
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define task "main"
#define endl '\n'
#define int ll
#define pb push_back
#define fi first
#define se second
#define ii pair<int,int>
#define iii pair<int,ii>
const ll INF = (ll)1e18;
const int MAXN = 100000 + 5;
int n, m, s, t, x, y;
vector<ii> g[MAXN];
vector<int> dag[MAXN];
int ds[MAXN], dt[MAXN], dx_[MAXN], dy[MAXN];
vector<iii> edges;
vector<char> inPath;
void djk(int st, int dist[]) {
priority_queue<ii, vector<ii>, greater<ii>> pq;
for(int i = 1; i <= n; i++) dist[i] = INF;
dist[st] = 0;
pq.push({0, st});
while(!pq.empty()) {
auto [d, u] = pq.top(); pq.pop();
if(d > dist[u]) continue;
for(auto &e : g[u]) {
int v = e.fi, w = e.se;
if(dist[v] > d + w) {
dist[v] = d + w;
pq.push({dist[v], v});
}
}
}
}
// DFS to produce topo order on inPath subgraph
vector<int> topo;
vector<char> vis;
void dfs(int u) {
vis[u] = 1;
for(int v : dag[u]) {
if(!inPath[v] || vis[v]) continue;
dfs(v);
}
topo.pb(u);
}
int32_t main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
if(fopen(task ".inp", "r")) {
freopen(task ".inp", "r", stdin);
freopen(task ".out", "w", stdout);
}
cin >> n >> m >> s >> t >> x >> y;
for(int i = 0; i < m; i++) {
int u, v, w;
cin >> u >> v >> w;
g[u].pb({v, w});
g[v].pb({u, w});
edges.pb({u, {v, w}});
}
// Compute shortest paths
djk(s, ds);
djk(t, dt);
djk(x, dx_);
djk(y, dy);
ll D = ds[t];
// Build DAG edges on shortest S->T paths
inPath.assign(n+1, false);
for(int i = 1; i <= n; i++) {
if(ds[i] + dt[i] == D) inPath[i] = true;
}
for(auto &e : edges) {
int u = e.fi, v = e.se.fi, w = e.se.se;
if(inPath[u] && inPath[v] && ds[u] + w + dt[v] == D) dag[u].pb(v);
if(inPath[v] && inPath[u] && ds[v] + w + dt[u] == D) dag[v].pb(u);
}
// DFS-based topo sort on inPath subgraph
vis.assign(n+1, 0);
topo.clear();
for(int u = 1; u <= n; u++) {
if(inPath[u] && !vis[u]) dfs(u);
}
reverse(topo.begin(), topo.end());
// DP initialization
vector<ll> dp(n+1, INF);
ll ans = dx_[y]; // option: not use ticket
for(int u : topo) dp[u] = dx_[u];
// DP propagation on topo
for(int u : topo) {
ans = min(ans, dp[u] + dy[u]);
for(int v : dag[u]) {
// already ensured v in inPath
dp[v] = min(dp[v], dp[u]);
}
}
cout << ans;
return 0;
}
