//#pragma GCC optimize("Ofast")
//#pragma GCC target("avx,avx2,sse,sse2,sse3,ssse3,sse4,abm,popcnt,mmx")
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef double db;
typedef long double ldb;
typedef complex<double> cd;
constexpr ll INF64 = 9'000'000'000'000'000'000, INF32 = 2'000'000'000, MOD = 1'000'000'007;
constexpr db PI = acos(-1);
constexpr bool IS_FILE = false, IS_TEST_CASES = false;
random_device rd;
mt19937 rnd32(rd());
mt19937_64 rnd64(rd());
template<typename T>
bool assign_max(T& a, T b) {
if (b > a) {
a = b;
return true;
}
return false;
}
template<typename T>
bool assign_min(T& a, T b) {
if (b < a) {
a = b;
return true;
}
return false;
}
template<typename T>
T square(T a) {
return a * a;
}
template<>
struct std::hash<pair<ll, ll>> {
ll operator() (pair<ll, ll> p) const {
return ((__int128)p.first * MOD + p.second) % INF64;
}
};
vector<ll> dist(ll v, vector<vector<pair<ll, ll>>>& arr) {
vector<ll> d(arr.size(), INF64);
priority_queue<pair<ll, ll>, vector<pair<ll, ll>>, greater<pair<ll, ll>>> pq;
pq.emplace(0, v);
d[v] = 0;
while (!pq.empty()) {
auto[nd, u] = pq.top();
pq.pop();
if (nd != d[u]) {
continue;
}
for (auto[i, di] : arr[u]) {
if (assign_min(d[i], nd + di)) {
pq.emplace(d[i], i);
}
}
}
return d;
}
void dfs(ll v, vector<bool>& used, vector<vector<ll>>& tree, vector<ll>& ts) {
used[v] = true;
for (auto i : tree[v]) {
if (!used[i]) {
dfs(i, used, tree, ts);
}
}
ts.push_back(v);
}
void solve() {
ll n, m, s, t, u, v;
cin >> n >> m >> s >> t >> u >> v;
s--;
t--;
u--;
v--;
vector<vector<pair<ll, ll>>> arr(n);
for (ll i = 0; i < m; i++) {
ll a, b, c;
cin >> a >> b >> c;
a--;
b--;
arr[a].emplace_back(b, c);
arr[b].emplace_back(a, c);
}
vector<ll> ds = dist(s, arr), dt = dist(t, arr), du = dist(u, arr), dv = dist(v, arr);
ll dst = ds[t];
vector<vector<ll>> narr(n);
for (ll i = 0; i < n; i++) {
for (auto[j, c] : arr[i]) {
if (ds[i] + c + dt[j] == dst) {
narr[i].push_back(j);
}
}
}
vector<ll> ts;
vector<bool> used(n, false);
for (ll i = 0; i < n; i++) {
if (!used[i]) {
dfs(i, used, narr, ts);
}
}
ll ans = du[v];
vector<ll> dp = du;
for (auto i : ts) {
for (auto j : narr[i]) {
assign_min(dp[i], dp[j]);
}
assign_min(ans, dp[i] + dv[i]);
}
dp = dv;
for (auto i : ts) {
for (auto j : narr[i]) {
assign_min(dp[i], dp[j]);
}
assign_min(ans, dp[i] + du[i]);
}
cout << ans << '\n';
}
int main() {
if (IS_FILE) {
freopen("", "r", stdin);
freopen("", "w", stdout);
}
ios_base::sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
ll t = 1;
if (IS_TEST_CASES) {
cin >> t;
}
for (ll i = 0; i < t; i++) {
solve();
}
}
