// 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, p;
};
struct skibidi{
tn u, a, b;
};
vector< tn > previous[N];
vector< pair > g[N];
tn n, m, w, a, b, s, t, u, v, result = 1e18, dist[N][3];
mimi dick[N];
//priority_queue< skibidi, vector< skibidi >, cmp > Q;
priority_queue< pair, vector< pair >, greater< pair > > q;
queue< skibidi > 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;
if ( type == 2 ){
previous[v.fi].clear();
previous[v.fi].push_back( u );
}
q.push( { dist[v.fi][type], v.fi } );
}
else if ( dist[v.fi][type] == cost + v.se and type == 2 )
previous[v.fi].push_back(u);
}
}
}
void trace(){
Q.push( { t, dist[t][0], dist[t][1] } );
while ( !Q.empty() ){
tn u = Q.front().u;
tn a = Q.front().a;
tn b = Q.front().b;
result = min( result, a + b );
Q.pop();
for ( auto v : previous[u] ){
Q.push( { v, min( a, dist[v][0] ), min( b, dist[v][1] ) } );
}
}
}
signed main(){
thaonguyenxinh
// hi skibidi
cin >> n >> m >> s >> t >> a >> b;
thaonguyen( i, 1, n )
dist[i][0] = 1e18,
dist[i][1] = 1e18,
dist[i][2] = 1e18,
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 ); dijkstra( s, 2 ); trace();
cout << min( dist[a][1], result );
}
