// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
template<typename T> using ordered_set = tree<T,null_type,less_equal<T>,rb_tree_tag,
tree_order_statistics_node_update>;
#define ll long long
#define pi pair<int,int>
#define vi vector<int>
#define pb push_back
#define all(a) a.begin(),a.end()
const ll inf = 1e18;
const int mxn = 1e5+1;
vector<pi> g[mxn];
vector<int> g2[mxn];
bool vis[mxn];
int n,m;
void dijskitra(int s, vector<ll> &vec){
priority_queue<pair<ll,int>,vector<pair<ll,int>>,greater<pair<ll,int>>> pq;
vec[s] = 0; pq.push({0,s});
while(!pq.empty()){
auto [d,u] = pq.top(); pq.pop();
if(vec[u]!=d) continue;
for(auto [v,c] : g[u]) if(vec[v] > d+c)
pq.push({vec[v]=d+c,v});
}
}
vector<int> topo;
void dfs(int u){
vis[u] = 1;
for(auto v : g2[u]) if(!vis[v])
dfs(v);
topo.push_back(u);
}
void solve(){
cin >> n >> m;
int s,t,s2,t2;
cin >> s >> t;
cin >> s2 >> t2;
for(int i = 1; i <= m; i++){
int u,v,c; cin >> u >> v >> c;
g[u].pb({v,c}); g[v].pb({u,c});
}
vector<ll> dps(n+1,inf);
dijskitra(s,dps);
vector<ll> dpt(n+1,inf);
dijskitra(t,dpt);
vector<ll> dps2(n+1,inf);
dijskitra(s2,dps2);
vector<ll> dpt2(n+1,inf);
dijskitra(t2,dpt2);
fill(vis+1,vis+n+1,true);
for(int u = 1; u <= n; u++)
for(auto [v,c] : g[u]) if(dps[u] + c + dpt[v] == dps[t]){
g2[u].push_back(v);
vis[u] = vis[v] = false;
}
for(int i = 1; i <= n; i++) if(!vis[i])
dfs(i);
ll ans = dps2[t2];
for(auto u : topo){
ll dp0 = dps2[u], dp1 = dpt2[u];
for(auto v : g2[u])
dp0 = min(dp0,dps2[v]),
dp1 = min(dp1,dpt2[v]);
ans = min(ans,dp0 + dpt2[u]);
ans = min(ans,dp1 + dps2[u]);
dps2[u] = dp0;
dpt2[u] = dp1;
}
cout << ans;
}
signed main(){
cin.tie(0)->sync_with_stdio(0);
int t = 1;
// cin >> t;
while(t--){solve();}
}
