#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define pii pair<ll, ll>
const int nx = 1e5+5;
const ll INF = 1e18;
int n, m, s, t, U, V;
vector<pii> adj[nx], dag[nx], revdag[nx];
vector<ll> distu, distv, dists, distt;
priority_queue<pii, vector<pii>, greater<pii>> pq;
void dijkstra(int src, vector<ll>& d)
{
vector<ll> dist(nx, INF);
dist[src] = 0;
pq.push({0, src});
while(!pq.empty())
{
auto [cw, u] = pq.top();
pq.pop();
if(cw > dist[u]) continue;
for(auto [v, nw] : adj[u])
{
if(dist[v] > dist[u] + nw)
{
dist[v] = dist[u] + nw;
pq.push({dist[v], v});
}
}
}
d = dist;
}
vector<ll> mindist(int src, vector<pii> DAG[])
{
vector<ll> mn(nx, INF);
mn[src] = distv[src];
pq.push({0, src});
while(!pq.empty())
{
auto [cw, u] = pq.top();
pq.pop();
if(cw > dists[u]) continue;
for(auto [v, nw] : DAG[u])
{
if(mn[u] < mn[v])
{
mn[v] = mn[u];
pq.push({dists[v], v});
}
mn[v] = min(mn[v], distv[v]);
}
}
return mn;
}
int main()
{
cin.tie(NULL)->sync_with_stdio(false);
cin >> n >> m >> s >> t >> U >> V;
for(int i=0;i<m;i++)
{
ll a, b, c;
cin >> a >> b >> c;
adj[a].push_back({b, c});
adj[b].push_back({a, c});
}
dijkstra(U, distu);
dijkstra(V, distv);
dijkstra(s, dists);
dijkstra(t, distt);
ll D = dists[t];
for(int u=1;u<=n;u++)
for(auto [v, w] : adj[u])
if(dists[u] + w + distt[v] == D)
dag[u].push_back({v, w});
for(int u=1;u<=n;u++)
for(auto [v, w] : dag[u])
revdag[v].push_back({u, w});
vector<ll> minToV = mindist(s, dag);
vector<ll> minToV2 = mindist(t, revdag);
for(int i=1;i<=n;i++)
minToV[i] = min(minToV[i], minToV2[i]);
ll res = distu[V];
for(int i=1;i<=n;i++)
{
if(dists[i] + distt[i] == D)
res = min(res, distu[i] + minToV[i]);
}
cout << res ;
return 0;
}
