/*
* Author: Nonoze
* Created: Tuesday 23/07/2024
*/
#include <bits/stdc++.h>
using namespace std;
#ifndef _IN_LOCAL
#define dbg(...)
#endif
#define endl '\n'
#define endlfl '\n' << flush
#define quit(x) return (void)(cout << x << endl)
template<typename T> void read(T& x, bool write=0, bool write2=1) { if (write && write2) cout << x << endl; else if (write) cout << x << ' '; else cin >> x;}
template<typename T1, typename T2> void read(pair<T1, T2>& p, bool write=0, bool write2=1) { read(p.first, write, 0), read(p.second, write, 0); if (write && write2) cout << endl;}
template<typename T> void read(vector<T>& v, bool write=0) { for (auto& x : v) read(x, write, 0); if (write) cout << endl; }
template<typename T1, typename T2> void read(T1& x, T2& y, bool write=0) { read(x, write), read(y, write); if (write) cout << endl; }
template<typename T1, typename T2, typename T3> void read(T1& x, T2& y, T3& z, bool write=0) { read(x, write), read(y, write), read(z, write); if (write) cout << endl; }
template<typename T1, typename T2, typename T3, typename T4> void read(T1& x, T2& y, T3& z, T4& zz, bool write=0) { read(x, write), read(y, write), read(z, write), read(zz, write); if (write) cout << endl; }
template<typename T> void print(T x) { read(x, 1); }
template<typename T1, typename T2> void print(T1 x, T2 y) { read(x, y, 1); }
template<typename T1, typename T2, typename T3> void print(T1 x, T2 y, T3 z) { read(x, y, z, 1); }
template<typename T1, typename T2, typename T3, typename T4> void print(T1 x, T2 y, T3 z, T4 zz) { read(x, y, z, zz, 1); }
#define sz(x) (int)(x.size())
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define cmin(a, b) a = min(a, b)
#define cmax(a, b) a = max(a, b)
#define int long long
const int inf = numeric_limits<int>::max() / 4;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
const int MOD = 1e9+7, LOG=25;
void solve();
signed main() {
ios::sync_with_stdio(0);
cin.tie(0);
int tt=1;
// cin >> tt;
while(tt--) solve();
return 0;
}
int n, m;
vector<vector<pair<int, int>>> adj, prec, nxt;
vector<bool> used;
void dfs(int u) {
used[u]=1;
for (auto [v, w]: prec[u]) if (!used[v]) dfs(v);
}
void dijkstra(int s, int t) {
vector<int> dist(n, inf);
vector<bool> visited(n);
priority_queue<pair<int, int>, vector<pair<int, int>>, greater<>> pq;
pq.push({0, s});
dist[s]=0;
while (!pq.empty()) {
auto [d, u]=pq.top(); pq.pop();
if (visited[u]) continue;
visited[u]=1;
for (auto [v, w]: adj[u]) {
if (dist[v]>dist[u]+w) {
dist[v]=dist[u]+w;
prec[v].clear();
prec[v].pb({u, w});
pq.push({dist[v], v});
} else if (dist[v]==dist[u]+w) {
prec[v].pb({u, w});
}
}
}
dfs(t);
}
void solve() {
read(n, m);
int s, t, s2, t2; read(s, t, s2, t2); s--, t--, s2--, t2--;
adj.resize(n);
for (int i=0; i<m; i++) {
int a, b, c; read(a, b, c); a--, b--;
adj[a].pb({b, c});
adj[b].pb({a, c});
}
prec.resize(n), nxt.resize(n), used.resize(n);
dijkstra(t, s); swap(prec, nxt); dijkstra(s, t);
// dbg(prec);
// dbg(nxt);
// dbg(used);
s=s2, t=t2;
vector<vector<vector<int>>> dist(n, vector<vector<int>>(3, vector<int>(3, inf)));
vector<vector<vector<bool>>> visited(n, vector<vector<bool>>(3, vector<bool>(3)));
priority_queue<vector<int>, vector<vector<int>>, greater<> > pq;
pq.push({0, s, 0, 0});
dist[s][0][0]=0;
while (!pq.empty()) {
auto vec=pq.top(); pq.pop(); int d=vec[0], u=vec[1], already=vec[2], dir=vec[3];
if (visited[u][already][dir]) continue;
visited[u][already][dir]=1;
if (u==t) {
cout << d << endl;
return;
}
if (used[u] && already!=2) {
if (dir!=1) {
for (auto [v, w]: prec[u]) {
if (d<dist[v][1][2]) dist[v][1][2]=d, pq.push({d, v, 1, 2});
}
}
if (dir!=2) {
for (auto [v, w]: nxt[u]) {
if (d<dist[v][1][1]) dist[v][1][1]=d, pq.push({d, v, 1, 1});
}
}
}
if (already==1) already=2, dir=0;
for (auto [v, w]: adj[u]) {
if (dist[v][already][dir]>d+w) {
dist[v][already][dir]=d+w;
pq.push({d+w, v, already, dir});
}
}
}
}
