#include <bits/stdc++.h>
using namespace std;
#define ll long long
const ll INF = 1e18;
struct Edge { int v; ll w; };
int main(){
ios::sync_with_stdio(false);
cin.tie(nullptr);
int n, m;
cin >> n >> m;
int s, t, u, v;
cin >> s >> t >> u >> v;
s--, t--, u--, v--;
vector<vector<Edge>> adj(n);
for(int i = 0; i < m; i++){
int a, b; ll c;
cin >> a >> b >> c;
a--, b--;
adj[a].push_back({b, c});
adj[b].push_back({a, c});
}
auto dijkstra = [&](int src){
vector<ll> dist(n, INF);
vector<vector<int>> par(n);
dist[src] = 0;
priority_queue<
pair<ll,int>,
vector<pair<ll,int>>,
greater<pair<ll,int>>
> pq;
pq.emplace(0, src);
while(!pq.empty()){
auto [d, u] = pq.top();
pq.pop();
if(d != dist[u]) continue;
for(auto &e : adj[u]){
int v = e.v;
ll w = e.w;
if(dist[v] > d + w){
dist[v] = d + w;
par[v].clear();
par[v].push_back(u);
pq.emplace(dist[v], v);
}
else if(dist[v] == d + w){
par[v].push_back(u);
}
}
}
return make_pair(dist, par);
};
auto [dists, par] = dijkstra(s);
auto [distu, _1] = dijkstra(u);
auto [distv, _2] = dijkstra(v);
// Build shortest-path DAG from s to t
vector<vector<int>> new_edges(n);
stack<int> st2;
vector<char> vis(n, 0);
st2.push(t);
vis[t] = 1;
while(!st2.empty()){
int x = st2.top(); st2.pop();
for(int p : par[x]){
new_edges[p].push_back(x); // O(1)
if(!vis[p]){
vis[p] = 1;
st2.push(p);
}
}
}
ll ans = INF;
// DFS without recursion
stack<tuple<int,ll,ll>> st;
st.emplace(s, INF, INF);
while(!st.empty()){
auto [x, ud, vd] = st.top();
st.pop();
ud = min(ud, distu[x]);
vd = min(vd, distv[x]);
ans = min(ans, ud + vd);
for(int nx : new_edges[x])
st.emplace(nx, ud, vd);
}
ans = min(ans, distv[u]);
cout << ans << "\n";
}
