#include <cassert>
#include <iostream>
#include <vector>
using namespace std;
#define rep(i, a, b) for (auto i = (a); i < (b); ++i)
#define trav(x, v) for (auto &x : v)
#define eb(x...) emplace_back(x)
#define ff first
#define ss second
using ll = long long;
using vi = vector<int>;
using vl = vector<ll>;
using pii = pair<int, int>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
template<class T> bool ckmin(T& a, const T& b) { return a > b ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) { return a < b ? a = b, 1 : 0; }
const int N = 1 << 17;
const ll inf = 1e18;
vector<pii> g[N];
#include <ext/pb_ds/priority_queue.hpp>
using namespace __gnu_pbds;
using pq = __gnu_pbds::priority_queue<pli, greater<pli>, thin_heap_tag>;
int n;
vl dij(int s) {
vl dist(n, inf); dist[s] = 0;
pq q;
vector<pq::point_iterator> it(n);
rep(i, 0, n) it[i] = q.push({dist[i], i});
while (!q.empty()) {
int u = q.top().ss;
q.pop();
it[u] = nullptr;
trav(e, g[u]) {
if (ckmin(dist[e.ff], dist[u] + e.ss)) {
assert(it[e.ff] != nullptr);
q.modify(it[e.ff], {dist[e.ff], e.ff});
}
}
}
return dist;
}
ll dp[2][N];
vl sd, dist[2];
pll dfs(int u) {
if (dp[0][u] == inf) {
assert(dp[1][u] == inf);
dp[0][u] = dist[0][u];
dp[1][u] = dist[1][u];
trav(e, g[u]) {
if (sd[u] < sd[e.ff] + e.ss) continue;
assert(sd[u] == sd[e.ff] + e.ss);
auto nxt = dfs(e.ff);
if (dist[0][u] + nxt.ss < dp[0][u] + dp[1][u])
dp[0][u] = dist[0][u], dp[1][u] = nxt.ss;
if (dist[1][u] + nxt.ff < dp[0][u] + dp[1][u])
dp[1][u] = dist[1][u], dp[0][u] = nxt.ff;
if (nxt.ff + nxt.ss < dp[0][u] + dp[1][u])
dp[0][u] = nxt.ff, dp[1][u] = nxt.ss;
}
}
assert(dp[1][u] != inf);
return {dp[0][u], dp[1][u]};
}
signed main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int m;
cin >> n >> m;
int s, t; cin >> s >> t; --s, --t;
int x, y; cin >> x >> y; --x, --y;
rep(i, 0, m) {
int a, b, c; cin >> a >> b >> c;
--a; --b;
g[a].eb(b, c);
g[b].eb(a, c);
}
sd = dij(s);
dist[0] = dij(x);
dist[1] = dij(y);
assert(dist[0][y] == dist[1][x]);
ll ans = dist[0][y];
rep(u, 0, n) dp[0][u] = dp[1][u] = inf;
auto tmp = dfs(t);
ckmin(ans, tmp.ff + tmp.ss);
cout << ans;
}
