#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define pb push_back
#define ff first
#define ss second
#define _ << " " <<
#define yes cout<<"YES\n"
#define no cout<<"NO\n"
#define ull unsigned long long
#define lll __int128
#define all(x) x.begin(),x.end()
#define rall(x) x.rbegin(),x.rend()
#define BlueCrowner ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define FOR(i, a, b) for (ll i = (a); i < (b); i++)
#define FORD(i, a, b) for (ll i = (a); i >= (b); i--)
const ll mod = 1e9 + 7;
const ll mod1 = 998244353;
const ll naim = 1e9;
const ll max_bit = 60;
const ull tom = ULLONG_MAX;
const ll MAXN = 100005;
const ll LOG = 20;
const ll NAIM = 1e18;
const ll N = 2e6 + 5;
// ---------- GCD ----------
ll gcd(ll a, ll b) {
while (b) {
a %= b;
swap(a, b);
}
return a;
}
// ---------- LCM ----------
ll lcm(ll a, ll b) {
return a / gcd(a, b) * b;
}
// ---------- Modular Exponentiation ----------
ll modpow(ll a, ll b, ll m = mod) {
ll c = 1;
a %= m;
while (b > 0) {
if (b & 1) c = c * a % m;
a = a * a % m;
b >>= 1;
}
return c;
}
// ---------- Modular Inverse (Fermat’s Little Theorem) ----------
ll modinv(ll a, ll m = mod) {
return modpow(a, m - 2, m);
}
// ---------- Factorials and Inverse Factorials ----------
ll fact[N], invfact[N];
void pre_fact(ll n = N-1, ll m = mod) {
fact[0] = 1;
for (ll i = 1; i <= n; i++) fact[i] = fact[i-1] * i % m;
invfact[n] = modinv(fact[n], m);
for (ll i = n; i > 0; i--) invfact[i-1] = invfact[i] * i % m;
}
// ---------- nCr ----------
ll nCr(ll n, ll r, ll m = mod) {
if (r < 0 || r > n) return 0;
return fact[n] * invfact[r] % m * invfact[n-r] % m;
}
// ---------- Sieve of Eratosthenes ----------
vector<ll> primes;
bool is_prime[N];
void sieve(ll n = N-1) {
fill(is_prime, is_prime + n + 1, true);
is_prime[0] = is_prime[1] = false;
for (ll i = 2; i * i <= n; i++) {
if (is_prime[i]) {
for (ll j = i * i; j <= n; j += i)
is_prime[j] = false;
}
}
for (ll i = 2; i <= n; i++)
if (is_prime[i]) primes.pb(i);
}
void dijkstra(ll u, vector<ll> &d, vector<vector<pair<ll, ll>>> &g) {
priority_queue<pair<ll, ll>, vector<pair<ll, ll>>, greater<pair<ll, ll>>> pq;
d[u] = 0;
pq.push({0, u});
while (!pq.empty()) {
auto [dist, node] = pq.top();
pq.pop();
if (dist > d[node]) continue;
for (auto &[adj, w] : g[node]) {
if (d[node] + w < d[adj]) {
d[adj] = d[node] + w;
pq.push({d[adj], adj});
}
}
}
}
void solve() {
ll n, m, s, t, u, v; cin >> n >> m >> s >> t >> u >> v;
vector<vector<pair<ll, ll>>> g(n + 1);
FOR(i, 0, m) {
ll u, v, c; cin >> u >> v >> c;
g[u].pb({v, c});
g[v].pb({u, c});
}
vector<ll> ds(n + 1, NAIM), dt(n + 1, NAIM), du(n + 1, NAIM), dv(n + 1, NAIM);
dijkstra(s, ds, g);
dijkstra(t, dt, g);
dijkstra(v, dv, g);
dijkstra(u, du, g);
ll ans = du[v];
vector<ll> dp(n + 1, NAIM);
vector<ll> ord;
FOR(i, 1, n + 1) {
if (ds[i] + dt[i] == ds[t]) ord.pb(i);
}
sort(all(ord), [&](ll a, ll b) {
return ds[a] < ds[b];
});
for (auto &x : ord) dp[x] = du[x];
for (auto &x : ord) {
ans = min(ans, dp[x] + dv[x]);
for (auto [y, w] : g[x]) {
if (ds[x] + w == ds[y] && ds[x] + w + dt[y] == ds[t]) {
dp[y] = min(dp[y], dp[x]);
}
}
}
sort(all(ord), [&](ll a, ll b) {
return dt[a] < dt[b];
});
for (auto &x : ord) dp[x] = du[x];
for (auto &x : ord) {
ans = min(ans, dp[x] + dv[x]);
for (auto [y, w] : g[x]) {
if (dt[x] + w == dt[y] && dt[x] + w + ds[y] == ds[t]) {
dp[y] = min(dp[y], dp[x]);
}
}
}
cout << ans << '\n';
}
int main() {
BlueCrowner;
ll t = 1;
//cin >> t;
while (t--) {
solve();
}
return 0;
}
