// #pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4,sse4.1,sse4.2,popcnt,abm,mmx,avx")
// #pragma comment(linker, "/stack:200000000"]
#include <iostream>
#include <vector>
#include <cmath>
#include <algorithm>
#include <unordered_set>
#include <unordered_map>
#include <set>
#include <map>
#include <queue>
#include <deque>
#include <bitset>
#include <stack>
#include <random>
#include <fstream>
#include <sstream>
#include <chrono>
#define fi first
#define se second
#define pb push_back
#define ll long long
#define ld long double
#define hm unordered_map
#define pii pair<int, int>
#define sz(a) (int)a.size()
#define all(a) a.begin(), a.end()
#define cinv(v) for (auto& x: v) cin >> x
#define fr(i, n) for (int i = 0; i < n; ++i)
#define fl(i, l, n) for (int i = l; i < n; ++i)
#define int ll
template <typename T1, typename T2> inline bool chkmin(T1 &x, const T2 &y) {if (x > y) {x = y; return 1;} return 0;}
template <typename T1, typename T2> inline bool chkmax(T1 &x, const T2 &y) {if (x < y) {x = y; return 1;} return 0;}
using namespace std;
#ifdef LOCAL
#define dbg(x) cerr << #x << " : " << x << '\n'
const int maxn = 20;
#else
#define dbg(x)
const int maxn = 1e5 + 20;
#endif
//tg: @galebickosikasa
ostream& operator << (ostream& out, const pii& v) {
out << v.fi << ", " << v.se;
return out;
}
template<typename T> ostream& operator << (ostream& out, const vector<T>& v) {
for (auto& x: v) out << x << " ";
return out;
}
istream& operator >> (istream& in, pii& a) {
in >> a.fi >> a.se;
return in;
}
const ll inf = (ll) 1e18;
const ld pi = asin (1) * 2;
const ld eps = 1e-8;
const ll mod = (ll)1e9 + 7;
const ll ns = 97;
mt19937 rnd(chrono::steady_clock::now().time_since_epoch().count());
vector<pii> g[maxn];
vector<int> G[maxn];
int dp[maxn], used[maxn];
vector<int> Dijkstra (int s, int n) {
vector<int> d (n, inf);
d[s] = 0;
set <pii> a;
a.insert ({0, s});
while (!a.empty ()) {
int v = a.begin ()->se;
a.erase (a.begin ());
for (auto& u: g[v]) {
if (d[u.fi] > d[v] + u.se) {
a.erase ({d[u.fi], u.fi});
d[u.fi] = d[v] + u.se;
a.insert ({d[u.fi], u.fi});
}
}
}
return d;
}
void calc (int v, vector<int>& d) {
used[v] = 1;
dp[v] = d[v];
for (auto& u: G[v]) {
if (!used[u]) calc (u, d);
chkmin (dp[v], dp[u]);
}
}
signed main () {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
cout.tie(nullptr);
int n, m;
cin >> n >> m;
int s, t;
cin >> s >> t;
--s, --t;
int u, v;
cin >> u >> v;
--u, --v;
for (int i = 0; i < m; ++i) {
int a, b, c;
cin >> a >> b >> c;
--a, --b;
g[a].pb ({b, c});
g[b].pb ({a, c});
}
auto d = Dijkstra (s, n);
vector<int> kek;
queue<int> a;
a.push (t);
while (!a.empty ()) {
int v = a.front ();
kek.pb (v);
a.pop ();
for (auto& u: g[v]) {
if (d[u.fi] + u.se == d[v]) {
G[v].pb (u.fi);
if (!used[u.fi]) {
a.push (u.fi);
used[u.fi] = 1;
}
}
}
}
for (auto& x: kek) {
dbg (x + 1);
for (auto& ch: G[x]) {
dbg (ch + 1);
}
}
int ans = 1e18;
{
for (auto& x: used) x = 0;
d = Dijkstra (u, n);
chkmin (ans, d[v]);
dbg (ans);
for (auto& x: kek) {
if (!used[x]) calc (x, d);
dbg (x + 1);
dbg (dp[x]);
}
d = Dijkstra (v, n);
for (auto& x: kek) {
chkmin (ans, d[x] + dp[x]);
dbg (x + 1);
dbg (ans);
}
}
{
swap (v, u);
for (auto& x: used) x = 0;
d = Dijkstra (u, n);
chkmin (ans, d[v]);
// dbg (ans);
for (auto& x: kek) {
if (!used[x]) calc (x, d);
// dbg (x + 1);
// dbg (dp[x]);
}
d = Dijkstra (v, n);
for (auto& x: kek) {
chkmin (ans, d[x] + dp[x]);
// dbg (x + 1);
// dbg (ans);
}
}
cout << ans << '\n';
}
