/* Author : Mychecksdead */
#include<bits/stdc++.h>
using namespace std;
typedef long long int ll;
#define MOD (1000000000+7)
#define MOD1 (998244353)
#define PI 3.1415926535
#define pb push_back
#define all(x) x.begin(), x.end()
const int N = 1e6+100, M = 1e5+10, K = 20;
int n, m, s, t, x, y;
ll d[N], dp[N][3];
vector<array<ll, 3>> g[N];
vector<bool> vis;
vector<array<bool, 3>> vis2;
vector<array<int, 2>> good;
void solve(){
cin >> n >> m >> s >> t >> x >> y;
for(int i = 0; i < m; ++i){
int u, v, w; cin >> u >> v >> w;
g[u].pb({v, w, i});
g[v].pb({u, w, i});
}
vis.resize(n + 1);
good.resize(m);
//first dijkstra
priority_queue<pair<ll, int>> q;
q.push({0, s});
for(int i = 1; i <= n; ++i) d[i] = i == s ? 0 : LONG_LONG_MAX;
while(!q.empty()){
int v = q.top().second; q.pop();
if(vis[v]) continue;
vis[v] = 1;
for(auto U: g[v]){
ll u = U[0], w = U[1];
if(!vis[u] && d[u] > d[v] + w){
d[u] = d[v] + w;
q.push({-d[u], u});
}
}
}
//path recovering
queue<int> Q;
Q.push(t);
fill(all(vis), 0);
vis[t] = 1;
while(!Q.empty()){
int v = Q.front(); Q.pop();
for(auto U: g[v]){
int u = U[0], w = U[1];
if(d[u] == d[v] - w){
good[U[2]] = {v, u};
if(!vis[u]){
vis[u] = 1;
Q.push(u);
}
}
}
}
//last dijkstra
priority_queue<array<ll, 4>> q2;
ll ans = LONG_LONG_MAX;
for(int i = 1; i <= n; ++i) dp[i][0] = dp[i][1] = dp[i][2] = LONG_LONG_MAX;
dp[x][0] = 0;
q2.push({0, x, 0, 0}); // cost, node, type, direction
vis2.resize(n + 1, {0, 0, 0});
while(!q2.empty()){
int v = q2.top()[1], tp = q2.top()[2], dir = q2.top()[3]; q2.pop();
if(vis2[v][tp]) continue;
vis2[v][tp] = 1;
for(auto U: g[v]){
int u = U[0], w = U[1];
if(good[U[2]][0] == u && good[U[2]][1] == v && tp != 2 && dir != 1){
if(!vis2[u][1] && dp[u][1] > dp[v][tp]){
dp[u][1] = dp[v][tp];
q2.push({-dp[u][1], u, 1, 2});
}
}else if(good[U[2]][0] == v && good[U[2]][1] == u && tp != 2 && dir != 2){
if(!vis2[u][1] && dp[u][1] > dp[v][tp]){
dp[u][1] = dp[v][tp];
q2.push({-dp[u][1], u, 1, 1});
}
}else{
int tt = tp >= 1 ? 2 : 0;
if(!vis2[u][tt] && dp[u][tt] > dp[v][tp] + w){
dp[u][tt] = dp[v][tp] + w;
q2.push({-dp[u][tt], u, tt, dir});
}
}
}
}
ans = min({dp[y][0], dp[y][1], dp[y][2]});
cout << ans;
}
int main(){
cin.tie(0); ios::sync_with_stdio(0);
int T = 1, aa;
// cin >> T;aa=T;
while(T--){
// cout << "Case #" << aa-T << ": ";
solve();
cout << '\n';
}
return 0;
}
