// Author : Thao Nguyen Xinh
// Codeforces Handle : thaonguyendethuongvai
#include<bits/stdc++.h>
using namespace std;
#define endl "\n"
#define tn long long
#define fi first
#define se second
#define pair pair< tn, tn >
#define thaonguyen( i, a, b ) for( tn i = a; i <= b; i++ )
#define nguyenthao( i, a, b ) for( tn i = a; i >= b; i-- )
#define thaonguyenxinh ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
const tn N = 1e5 + 5;
struct mimi{
tn u, w, a, b;
};
struct cmp{
bool operator()( const mimi a, const mimi b ){
return a.w < b.w;
}
};
vector< pair > g[N];
tn n, m, w, a, b, s, t, u, v, result = 1e18, dist[N][2];
mimi dick[N];
priority_queue< mimi, vector< mimi >, cmp > Q;
priority_queue< pair, vector< pair >, greater< pair > > q;
void dijkstra( tn start, tn type ){
dist[start][type] = 0;
q.push( { 0, start } );
while(!q.empty() ){
u = q.top().se;
tn cost = q.top().fi;
q.pop();
if ( cost > dist[u][type] )
continue;
for ( auto v : g[u] ){
if ( dist[v.fi][type] > cost + v.se ){
dist[v.fi][type] = cost + v.se;
q.push( { dist[v.fi][type], v.fi } );
}
}
}
}
void bfs(){
dick[s].w = 0; dick[s].a = dist[s][0]; dick[s].b = dist[s][1];
result = min( result, dick[s].a + dick[s].b );
q.push( { 0, s } );
while ( !q.empty() ){
tn u = q.top().se;
tn cost = q.top().fi;
q.pop();
if ( cost > dick[u].w )
continue;
for ( auto v : g[u] ){
if ( dick[v.fi].w > dick[u].w + v.se ){
dick[v.fi].w = dick[u].w + v.se;
dick[v.fi].a = min( dick[u].a, dist[v.fi][0] );
dick[v.fi].b = min( dick[u].b, dist[v.fi][1] );
q.push( { dick[v.fi].w, v.fi } );
}
else if ( dick[v.fi].w == dick[u].w + v.se ){
if ( dick[v.fi].a + dick[v.fi].b > dick[u].a + dick[u].b )
dick[v.fi].a = dick[u].a,
dick[v.fi].b = dick[u].b;
}
}
}
}
signed main(){
thaonguyenxinh
// hi skibidi
cin >> n >> m >> s >> t >> a >> b;
thaonguyen( i, 1, n )
dist[i][0] = dist[i][1] = dist[i][2] = dick[i].w = 1e18;
thaonguyen( i, 1, m ){
cin >> u >> v >> w;
g[u].push_back( { v, w } );
g[v].push_back( { u, w } );
}
dijkstra( a, 0 ); dijkstra( b, 1 ); bfs();
cout << min( dist[a][1], dick[t].a + dick[t].b );
}
