// chill roi
#include <bits/stdc++.h>
#define int long long
#define fi first
#define se second
#define pii pair <int , int>
#define arr3 array <int , 3>
#define arr4 array <int , 4>
/*
+ array limit ???
+ special case ??? n = 1?
+ time limit ???
*/
using namespace std;
const int INF = 1e18 + 7;
const int maxn = 2e5 + 7;
int n , m;
int S , T;
int U , V;
int ans = INF;
vector <pii> g[maxn];
vector <int> dijkstra(int start)
{
vector <int> d(maxn , INF);
vector <bool> vis(maxn , false);
priority_queue <pii , vector <pii> , greater <pii>> PQ;
d[start] = 0;
PQ.push({0 , start});
while(!PQ.empty())
{
int u = PQ.top().se;
PQ.pop();
if(vis[u]) continue;
vis[u] = 1;
for(pii edge: g[u])
{
int v = edge.fi;
int w = edge.se;
if(d[v] > d[u] + w)
{
d[v] = d[u] + w;
PQ.push({d[v] , v});
}
}
}
return d;
}
void dijkstra2()
{
vector <int> du = dijkstra(U);
vector <int> dv = dijkstra(V);
vector <bool> vis(maxn , false);
vector <arr4> d(maxn , {INF,INF,INF});
d[S] = {0 , du[S] , dv[S]};
priority_queue <arr4 , vector <arr4> , greater <arr4>> PQ;
PQ.push({0 , du[S] , dv[S] , S});
while(!PQ.empty())
{
int u = PQ.top()[3];
PQ.pop();
if(vis[u]) continue;
vis[u] = 1;
for(pii edge: g[u])
{
int v = edge.fi;
int w = edge.se;
if(d[v][0] > d[u][0] + w)
{
d[v][0] = d[u][0] + w;
d[v][1] = min(d[u][1] , du[v]);
d[v][2] = min(d[u][2] , dv[v]);
PQ.push({d[v][0] , d[v][1] , d[v][2] , v});
}
else if(d[v][0] == d[u][0] + w && d[v][1] + d[v][2] > d[u][1] + d[u][2])
{
d[v][1] = d[u][1];
d[v][2] = d[u][2];
PQ.push({d[v][0] , d[v][1] , d[v][2] , v});
}
}
}
cout << min(du[V] , d[T][1] + d[T][2]);
}
void solve()
{
cin >> n >> m;
cin >> S >> T;
cin >> U >> V;
for(int i = 1; i <= m; i++)
{
int u , v , w;
cin >> u >> v >> w;
g[u].push_back({v , w});
g[v].push_back({u , w});
}
dijkstra2();
}
signed main()
{
ios_base::sync_with_stdio(false);
cin.tie(0); cout.tie(0);
solve();
return 0;
}
