#include <bits/stdc++.h>
using namespace std;
struct edge {
int u, v, c;
int other( int w ) {
return u ^ v ^ w;
}
};
struct elemPQ {
int u;
long long d;
bool operator < ( const elemPQ &x ) const {
return x.d < d;
}
};
struct distancee {
long long d1, d2;
bool operator < ( const distancee &x ) const {
if ( d1 == x.d1 )
return d2 < x.d2;
return d1 < x.d1;
}
};
struct elemPQ2 {
int u;
distancee d;
bool operator < ( const elemPQ2 &x ) const {
return x.d < d;
}
};
const int MAX_N = 1e5;
const int MAX_M = 2e5;
const long long INF = 1e18;
int n;
bool vis[4 * MAX_N + 1];
distancee minDist[4 * MAX_N + 1];
long long distX[MAX_N + 1], distY[MAX_N + 1];
vector<int> adj[MAX_N + 1];
edge edges[MAX_M];
void calcDist( int s, long long dist[] ) {
priority_queue<elemPQ> pq;
for ( int v = 1; v <= n; v++ ) {
dist[v] = INF;
vis[v] = false;
}
dist[s] = 0;
pq.push( { s,dist[s] } );
while ( !pq.empty() ) {
int u = pq.top().u;
pq.pop();
if ( vis[u] )
continue;
vis[u] = true;
for ( int e: adj[u] ) {
int v = edges[e].other( u ), c = edges[e].c;
if ( dist[u] + c < dist[v] ) {
dist[v] = dist[u] + c;
pq.push( { v, dist[v] } );
}
}
}
}
int main() {
int m, s, t, x, y;
cin >> n >> m >> s >> t >> x >> y;
for ( int e = 0; e < m; e++ ) {
cin >> edges[e].u >> edges[e].v >> edges[e].c;
adj[edges[e].u].push_back( e );
adj[edges[e].v].push_back( e );
}
calcDist( x, distX );
calcDist( y, distY );
for ( int v = 1; v <= 4 * n; v++ ) {
vis[v] = false;
minDist[v] = { INF, INF };
}
priority_queue<elemPQ2> pq;
minDist[s] = { 0, 0 };
minDist[n + s] = { 0, distX[s] };
minDist[2 * n + s] = { 0, distY[s] };
minDist[3 * n + s] = { 0, distX[s] + distY[s] };
pq.push( { s, minDist[s] } );
pq.push( { n + s, minDist[n + s] } );
pq.push( { 2 * n + s, minDist[2 * n + s] } );
pq.push( { 3 * n + s, minDist[3 * n + s] } );
while ( !pq.empty() ) {
int u = pq.top().u;
int p = (u - 1) / n;
u = (u - 1) % n + 1;
pq.pop();
if ( vis[p * n + u] )
continue;
vis[p * n + u] = true;
//printf( "%d %d %lld %lld\n", p, u, minDist[p * n + u].d1, minDist[p * n + u].d2 );
for ( int e: adj[u] ) {
int v = edges[e].other( u ), c = edges[e].c;
for ( int q = 0; q < 4; q++ ) {
if ( (p & q) != p )
continue;
distancee newDist = minDist[p * n + u];;
newDist.d1 += c;
if ( (p ^ q) & 1 )
newDist.d2 += distX[v];
if ( (p ^ q) & 2 )
newDist.d2 += distY[v];
if ( newDist < minDist[q * n + v] ) {
minDist[q * n + v] = newDist;
pq.push( { q * n + v, minDist[q * n + v] } );
}
}
}
}
cout << min( distX[y], minDist[3 * n + t].d2 ) << "\n";
}
