#include <bits/stdc++.h>
using namespace std;
#define pb push_back
#define st first
#define nd second
typedef long long ll;
typedef long double ld;
const ll I = 1'000'000'000'000'000'000LL;
const int II = 2'000'000'000;
const ll M = 1'000'000'007LL;
const int N = 1<<19;
ll d1[N], d2[N];
pair<pair<int, int>, int> e[N];
vector<pair<int, int>> ed[N];
ll dis[N];
int vis[N];
void Dijkstra(int n, int s)
{
int v;
priority_queue<pair<ll, int>> q;
for(int i = 1; i <= n; ++i)
{dis[i] = I; vis[i] = 0;}
dis[s] = 0;
q.push(make_pair(0LL, s));
while((int)q.size() > 0)
{
v = q.top().nd; q.pop();
if(vis[v]) continue;
vis[v] = 1;
for(int i = 0; i < (int)ed[v].size(); ++i)
{
ll o = dis[v] + (ll)ed[v][i].nd;
if(o < dis[ed[v][i].st])
{
dis[ed[v][i].st] = o;
q.push(make_pair(-o, ed[v][i].st));
}
}
}
}
void Solve()
{
int n, m, a, b, c;
int s, t, u, v;
cin >> n >> m;
cin >> s >> t;
cin >> u >> v;
for(int i = 1; i <= m; ++i)
{
cin >> a >> b >> c;
ed[a].pb(pair{b, c});
ed[b].pb(pair{a, c});
e[i] = pair{pair{a, b}, c};
}
Dijkstra(n, s);
for(int i = 1; i <= n; ++i) d1[i] = dis[i];
Dijkstra(n, t);
for(int i = 1; i <= n; ++i) d2[i] = dis[i];
for(int i = 1; i <= n; ++i)
{
ed[i].pb(pair{i + n, 0});
ed[i].pb(pair{i + 2 * n, 0});
ed[i + n].pb(pair{i + 3 * n, 0});
ed[i + 2 * n].pb(pair{i + 3 * n, 0});
}
for(int i = 1; i <= m; ++i)
{
a = e[i].st.st; b = e[i].st.nd; c = e[i].nd;
if(d1[a] > d1[b]) swap(a, b);
// cout << "E: " << a << " " << b << " " << c << " | " << d1[a] << " " << d2[b] << "\n";
ed[a + 3 * n].pb(pair{b + 3 * n, c});
ed[b + 3 * n].pb(pair{a + 3 * n, c});
if(d1[a] + c + d2[b] != d1[t]) continue;
ed[a + n].pb(make_pair(b + n, 0));
ed[b + 2 * n].pb(make_pair(a + 2 * n, 0));
}
Dijkstra(n * 4, u);
cout << dis[v + 3 * n] << "\n";
}
int main()
{
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
//int t; cin >> t;
//while(t--)
Solve();
return 0;
}
