#include <bits/stdc++.h>
using namespace std;
#define int long long
#define pi pair<int, int>
#define pii pair<int, pi>
#define fi first
#define se second
#ifdef _WIN32
#define getchar_unlocked _getchar_nolock
#endif
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
int dist1[300005], dist2[300005], n, m, s, t, u, v;
vector <pi> adj[100005];
int brr[100005][4];
void dijk(int dist[], int ss){
for(int i = 1; i <= n; i++)dist[i] = 1e18;
dist[ss] = 0;
priority_queue <pi, vector <pi>, greater<pi> > pq;
pq.push({0, ss});
while(!pq.empty()){
int x = pq.top().fi, y = pq.top().se;
pq.pop();
if(dist[y] < x)continue;
for(auto [i, j] : adj[y]){
if(dist[i] > x + j)dist[i] = x + j, pq.push({dist[i], i});
}
}
}
void solve(){
cin >> n >> m >> s >> t >> u >> v;
while (m--){
int a, b, c; cin >> a >> b >> c;
adj[a].push_back({b, c});
adj[b].push_back({a, c});
}
dijk(dist1, s);
dijk(dist2, t);
for(int i = 1; i <= n; i++)for(int j = 0; j < 4; j++)brr[i][j] = 1e18;
brr[u][0] = brr[u][1] = brr[u][2] = brr[u][3] = 0;
priority_queue <pii, vector<pii>, greater<pii> > pq;
pq.push({0, {u, 0}});
while(!pq.empty()){
int x = pq.top().fi, y = pq.top().se.fi, z = pq.top().se.se;
pq.pop();
if(brr[y][z] < x)continue;
for(auto [i, j] : adj[y]){
if(z == 0){
if(dist1[y] + dist2[i] + j == dist1[t]){
if(brr[i][1] > x)brr[i][1] = x, pq.push({brr[i][1], {i, 1}});
}
else if(dist1[i] + dist2[y] + j == dist1[t]){
if(brr[i][2] > x)brr[i][2] = x, pq.push({brr[i][2], {i, 2}});
}
if(brr[i][0] > x + j)brr[i][0] = x + j, pq.push({brr[i][0], {i, 0}});
}
else if(z == 1){
if(dist1[y] + j + dist2[i] == dist1[t]){
if(brr[i][1] > x)brr[i][1] = x, pq.push({brr[i][1], {i, 1}});
}
else{
if(brr[i][3] > x + j)brr[i][3] = x + j, pq.push({brr[i][3], {i, 3}});
}
}
else if(z == 2){
if(dist1[i] + dist2[y] + j == dist1[t]){
if(brr[i][2] > x)brr[i][2] = x, pq.push({brr[i][2], {i, 2}});
}
else{
if(brr[i][3] > x + j)pq.push({x + j, {i, 3}}), brr[i][3] = x + j;
}
}
else{
if(brr[i][3] > x + j)brr[i][3] = x + j, pq.push({brr[i][3], {i, 3}});
}
}
}
cout << min({brr[v][0], brr[v][1], brr[v][2], brr[v][3]});
}
main(){
ios::sync_with_stdio(0);cin.tie(0);
int tc = 1;
//cin >> tc;
for(int tc1=1;tc1<=tc;tc1++){
// cout << "Case #" << tc1 << ": ";
solve();
}
}
