#include <bits/stdc++.h>
using namespace std;
#define fastio ios::sync_with_stdio(false); cin.tie(NULL);
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define sz(x) ((long long)(x).size())
#define rep(i,a,b) for(long long i = a; i < b; ++i)
#define rrep(i,a,b) for(long long i = a; i >= b; --i)
using ll = long long;
using pii = pair<ll,ll>;
using vi = vector<ll>;
using vvi = vector<vector<pair<ll,ll>>>;
const ll INF = 1e18;
template<typename T> using minpq = priority_queue<T, vector<T>, greater<T>>;
struct DSU {
vi p, sz, mn;
void init(ll n) {
p.resize(n);
sz.assign(n, 1);
mn.resize(n);
iota(all(p), 0);
iota(all(mn), 0);
}
ll find(ll x) {
return x == p[x] ? x : p[x] = find(p[x]);
}
bool same(ll x, ll y) {
return find(x) == find(y);
}
ll size(ll x) {
return sz[find(x)];
}
ll get_min(ll x) {
return mn[find(x)];
}
bool join(ll x, ll y) {
x = find(x);
y = find(y);
if (x == y) return false;
if (sz[x] < sz[y]) swap(x, y);
p[y] = x;
sz[x] += sz[y];
mn[x] = min(mn[x], mn[y]);
return true;
}
};
ll distt = 0;
set<pii> dijskra(ll v, ll t, vvi &adj, ll src) {
vi p(v+1, -1);
vi dist(v+1, INF);
minpq<pii> pq;
dist[src] = 0;
pq.push({0, src});
while (!pq.empty()) {
auto [d, u] = pq.top(); pq.pop();
if (d > dist[u]) continue;
for (auto [nxt, wt] : adj[u]) {
if (dist[nxt] > dist[u] + wt) {
dist[nxt] = dist[u] + wt;
p[nxt] = u;
pq.push({dist[nxt], nxt});
}
}
}
distt = abs(dist[src] - dist[t]);
set<pii> pass;
for (ll cur = t; cur != -1; cur = p[cur]) {
ll a = cur, b = p[cur];
if (b == -1) continue; // skip the source's parent
if (a > b) swap(a, b);
pass.insert({a, b});
}
return pass;
}
ll digi2(ll v, vvi &adj, ll src, set<pii> pass, ll end) {
for (auto [a, b] : pass) {
for (auto &pr : adj[a]) if (pr.first == b) pr.second = 0;
for (auto &pr : adj[b]) if (pr.first == a) pr.second = 0;
}
vi dist(v+1, INF);
minpq<pii> pq;
dist[src] = 0;
pq.push({0, src});
while (!pq.empty()) {
auto [d, u] = pq.top(); pq.pop();
if (d > dist[u]) continue;
for (auto [nxt, wt] : adj[u]) {
if (dist[nxt] > dist[u] + wt) {
dist[nxt] = dist[u] + wt;
pq.push({dist[nxt], nxt});
}
}
}
distt = dist[end];
return distt;
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
ll n, m; cin >> n >> m;
ll s, t; cin >> s >> t;
ll u, v; cin >> u >> v;
vvi adj(n+1);
for (ll i = 0; i < m; i++) {
ll a, b, c; cin >> a >> b >> c;
adj[a].push_back({b, c});
adj[b].push_back({a, c});
}
set<pii> commuter_pass = dijskra(n, t, adj, s);
ll res = digi2(n, adj, u, commuter_pass, v);
cout << res << endl;
return 0;
}
