#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> pi;
typedef pair<ll, ll> pll;
typedef pair<ll, pi> E;
#define pb push_back
#define siz(x) (int)x.size()
#define ms(x, a) memset(x, a, sizeof(x))
#define deb(...) logger(#__VA_ARGS__, __VA_ARGS__)
template<typename ...Args>
void logger(string vars, Args&&... values){
cout << vars << " = ";
string delim = "";
(...,(cout << delim << values, delim = ", "));
cout << endl;
}
const ll LLINF = 0x3f3f3f3f3f3f3f3f;
//===========================================
const int MAX = 1e5+5;
vector<pll> adj[MAX];
vector<int> pp[MAX], adj2[MAX], radj[MAX];
ll dis[MAX], dis2[4][MAX];
bool vis[MAX];
int main(){
cin.tie(0)->sync_with_stdio(0);
int n, m; cin >> n >> m;
int s, t, src, tar;
cin >> s >> t >> src >> tar;
for (int i = 1; i <= m; i++){
int a, b, w; cin >> a >> b >> w;
adj[a].pb({b, w});
adj[b].pb({a, w});
}
ms(dis, 0x3f3f3f3f);
ms(dis2, 0x3f3f3f3f);
priority_queue<pll, vector<pll>, greater<pll>> pq;
pq.push({dis[s] = 0, s});
while (siz(pq)){
auto[d, v] = pq.top(); pq.pop();
if (d != dis[v]) continue;
for (auto[u, w]: adj[v]){
if (dis[u] > dis[v]+w){
pq.push({dis[u] = dis[v]+w, u});
pp[u] = {v};
} else if (dis[u] == dis[v]+w) pp[u].pb(v);
}
}
//for (int i = 1; i <= n; i++) deb(i, dis[i]);
queue<int> q;
vis[t] = true; q.push(t);
while (siz(q)){
int v = q.front(); q.pop();
for (int u: pp[v]){
adj2[v].pb(u);
radj[u].pb(v);
if (!vis[u]){ vis[u] = true; q.push(u); }
}
}
priority_queue<E, vector<E>, greater<E>> q2;
q2.push({dis2[0][src] = 0, {0, src}});
while (siz(q2)){
auto[d, x] = q2.top(); q2.pop();
auto[i, v] = x;
if (v == tar){ cout << d << "\n"; return 0; }
if (d != dis2[i][v]) continue;
for (auto[u, w]: adj[v]){
int ni = (!i? 0 : 3);
if (dis2[ni][u] > dis2[i][v]+w){
q2.push({dis2[ni][u] = dis2[i][v]+w, {ni, u}});
}
}
if (!i || i == 1){
for (int u: adj2[v]){
if (dis2[1][u] > dis2[i][v]){
q2.push({dis2[1][u] = dis2[i][v], {1, u}});
}
}
}
if (!i || i == 2){
for (int u: radj[v]){
if (dis2[2][u] > dis2[i][v]){
q2.push({dis2[2][u] = dis2[i][v], {2, u}});
}
}
}
}
}
