#include<bits/stdc++.h>
using namespace std;
#define endl '\n'
using ll = long long;
using ld = long double;
#define pb push_back
#define sz size()
#define fi first
#define se second
typedef pair<int, int> pii;
typedef pair<int, ll> pil;
const int maxn = 1e5 + 1;
const ll inf = 1e15;
vector<vector<pil>> graph(maxn);
struct comp{
bool operator() (pil a, pil b){
return a.second > b.second;
}
};
// Complejidad O(m*log(n))
void dijkstra(int source, int n, vector<ll>& d){
for(int i = 1; i <= n; i++) d[i] = inf;
d[source] = 0;
priority_queue<pil, vector<pil>, comp> pq;
pq.push({source, 0});
while(!pq.empty()){
int u = pq.top().first; ll w1 = pq.top().second;
pq.pop();
if(d[u] < w1) continue;
for(pil edge : graph[u]){
int v = edge.first; ll w2 = edge.second;
if(d[v] > w1 + w2){
d[v] = w1 + w2;
pq.push({v, d[v]});
}
}
}
}
ll dijkstra2(int s, int t, int n, vector<ll>& du, vector<ll>& dv){
vector<bool> visited(n+1);
vector<ll> dpU(n+1, inf), dpV(n+1, inf), ds(n+1, inf);
priority_queue<pair<ll, pii>> pq;
pq.push({0, {s, 0}});
while(!pq.empty()){
ll w1 = pq.top().fi; int u = pq.top().se.fi, par = pq.top().se.se;
pq.pop();
if(!visited[u]){
visited[u] = 1;
ds[u] = -w1;
dpU[u] = min(du[u], dpU[par]);
dpV[u] = min(dv[u], dpV[par]);
for(pil edge : graph[u]){
int v = edge.fi; ll w2 = edge.se;
if(ds[u] + w2 <= ds[v]) pq.push({-(ds[u] + w2), {v, u}});
}
}
else if(ds[u] == -w1){
if(min(du[u], dpU[par]) + min(dv[u], dpV[par]) <= dpU[u] + dpV[u]){
dpU[u] = min(du[u], dpU[par]);
dpV[u] = min(dv[u], dpV[par]);
}
}
}
return dpU[t] + dpV[t];
}
void solver(){
int n, m, s, t, u, v; cin>>n>>m>>s>>t>>u>>v;
for(int i = 0; i < m; i++){
int a, b; ll w;
cin>>a>>b>>w;
graph[a].pb({b, w});
graph[b].pb({a, w});
}
vector<ll> ds(n+1), du(n+1), dv(n+1);
dijkstra(u, n, du);
dijkstra(v, n, dv);
ll ans = du[v];
ans = min(ans, dijkstra2(s, t, n, du, dv));
ans = min(ans, dijkstra2(t, s, n, du, dv));
cout<<ans<<endl;
}
int main(){
ios_base::sync_with_stdio(0);cin.tie(NULL);
int t = 1;
// cin>>t;
while(t--){
solver();
}
return 0;
}
