#include<bits/stdc++.h>
using namespace std;
using ll = long long;
using pii = pair<int,long long>;
#define el cout << '\n'
#define fi first
#define se second
#define pb push_back
#define all(x) x.begin(), x.end()
#define FOR(i, a, b) for (int i = (a); i <= (b); i++)
#define FOD(i, a, b) for (int i = (a); i >= (b); i--)
#define REP(i, n) for (int i = 0; i < (n); i++)
template <class T1, class T2>bool chmax(T1 &a, T2 b){return a < b ? a = b, 1 : 0;}
template <class T1, class T2>bool chmin(T1 &a, T2 b){return a > b ? a = b, 1 : 0;}
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
const ll mod = 1e9 + 7;
const int maxn = 1e5 + 5;
void solve(){
int n, m, s1, e1, s2, e2;
cin >> n >> m >> s1 >> e1 >> s2 >> e2;
vector<vector<pii>> ad(n + 1);
REP(i, m){
int u, v;
ll w;
cin >> u >> v >> w;
ad[u].pb({v, w});
ad[v].pb({u, w});
}
using T = pair<long long, int>;
vector<vector<int>> dag(n + 1);
vector<ll> d(n + 1, 1e18);
priority_queue<T, vector<T>, greater<T>> pq;
pq.push({0, s1});
d[s1] = 0;
while(pq.size()){
auto [val, u] = pq.top();
pq.pop();
if (val != d[u]) continue;
for (auto [v, w] : ad[u]){
if (val + w < d[v]){
d[v] = val + w;
dag[v] = {u};
pq.push({d[v], v});
}
else if (val + w == d[v]){
dag[v].pb(u);
}
}
}
vector<vector<ll>> dis(n + 1, vector<ll> (2, 1e18));
for (int cnt = 0; cnt < 2; cnt++){
int cur = (cnt == 0 ? s2 : e2);
dis[cur][cnt] = 0;
pq.push({0, cur});
while(pq.size()){
auto [val, u] = pq.top();
pq.pop();
if (val != dis[u][cnt]) continue;
for (auto [v, w] : ad[u]){
if (val + w < dis[v][cnt]){
dis[v][cnt] = val + w;
pq.push({dis[v][cnt], v});
}
}
}
}
const ll INF = 1e18;
ll res = dis[e2][0];
using pll = array<long long, 2>;
vector<pll> dp(n + 1, {INF, INF});
vector<bool> vis(n + 1);
function<void(int)> dfs = [&](int u) {
if (vis[u]) return;
vis[u] = true;
dp[u] = {dis[u][0], dis[u][1]};
for (int v : dag[u]) {
dfs(v);
for (int id = 0; id < 2; id++) {
chmin(dp[u][id], dp[v][id]);
}
}
for (int id = 0; id < 2; id++) {
chmin(res, dis[u][id] + dp[u][!id]);
}
};
dfs(e1);
cout << res;
}
int32_t main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
int tests = 1;
// cin >> tests;
for (int _ = 1; _ <= tests; _++){
cerr << "- Case #" << _ << ": \n";
solve();
el;
}
return 0;
}
