#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const int N = 1e5+5;
const ll INF = LLONG_MAX/2;
int n, m, u, v, s, t;
vector<pair<int,int>> adj[N];
vector<int> adj2[N];
ll disu[N], disv[N], disS[N];
ll dp[N][2][2];
void dijkstra( int st, ll dis[] )
{
for( int i=1;i<=n;i++ ) dis[i] = INF;
dis[st] = 0;
priority_queue<pair<ll,ll>, vector<pair<ll,ll>>, greater<pair<ll,ll>>> pq;
pq.push( {0, st} );
while( !pq.empty() )
{
auto [cost, u] = pq.top();
pq.pop();
for( auto [v, w] : adj[u] )
{
if( dis[v] > cost+w )
{
dis[v] = cost+w;
pq.push( {cost+w, v} );
}
}
}
}
int main()
{
ios_base::sync_with_stdio(0); cin.tie(0);
cin >> n >> m >> s >> t >> u >> v;
while( m-- )
{
int u, v, w;
cin >> u >> v >> w;
adj[u].push_back( {v, w} );
adj[v].push_back( {u, w} );
}
dijkstra( u, disu );
dijkstra( v, disv );
dijkstra( s, disS );
for( int u=1;u<=n;u++ )
{
for( auto [v, w] : adj[u] )
{
if( disS[v]+w == disS[u] )
{
adj2[u].push_back( v );
}
}
}
vector<int> ord(n);
iota( ord.begin(), ord.end(), 1 );
sort( ord.begin(), ord.end(), [&](int i, int j){
return disS[i] < disS[j];
} );
for( int i=1;i<=n;i++ )
{
for( int j=0;j<2;j++ ) for( int k=0;k<2;k++ ) dp[i][j][k] = INF;
}
dp[s][0][0] = 0;
for( auto u : ord )
{
for( auto v : adj2[u] )
{
for( int i=0;i<2;i++ )
{
for( int j=0;j<2;j++ ) dp[u][i][j] = min( dp[u][i][j], dp[v][i][j] );
}
}
dp[u][0][1] = min( dp[u][0][1], dp[u][0][0]+disu[u] );
dp[u][1][0] = min( dp[u][1][0], dp[u][0][0]+disv[u] );
dp[u][1][1] = min( {dp[u][1][1], dp[u][1][0]+disu[u], dp[u][0][1]+disv[u]} );
}
cout << min( dp[t][1][1], disu[v] ) << "\n";
}
