This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using vi = vector<int>;
using vl = vector<ll>;
#define pb push_back
#define rsz resize
#define all(x) begin(x), end(x)
#define sz(x) (int)(x).size()
using pi = pair<int,int>;
#define f first
#define s second
#define mp make_pair
const int MX = 100005;
const int MOD = (int) (1e9 + 7);
const ll INF = (ll) 1e18;
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
template <class T> using Tree = tree<T, null_type, less<T>,
rb_tree_tag, tree_order_statistics_node_update>;
#define ook order_of_key
#define fbo find_by_order
int n;
ll a[MX];
bool blocked[MX];
vector<pair<ll, int>> adj[MX];
ll ans = 0;
Tree<pair<ll, int>> fin;
ll dist[MX];
ll mdist[MX];
int sz[MX];
void dfs(int v, int p) {
if (p != -1 && mdist[v] >= 0) ++ans;
dist[v] += a[v];
for (pi to : adj[v]) {
if (blocked[to.f]) continue;
if (to.f != p) {
dist[to.f] = dist[v] - to.s;
mdist[to.f] = min(mdist[v], dist[to.f]);
dfs(to.f, v);
}
}
}
multiset<ll> curr;
void dfs2(int v, int p) {
curr.insert(dist[v]);
for (pi to : adj[v]) {
if (blocked[to.f]) continue;
if (to.f != p) {
dfs2(to.f, v);
}
}
if (dist[v] == (*--curr.end())) {
if (p != -1) fin.insert(mp(dist[v], v));
}
curr.erase(curr.find(dist[v]));
}
vi order;
void dfs3(int v, int p) {
for (pi to : adj[v]) {
if (blocked[to.f]) continue;
if (to.f != p) {
dfs3(to.f, v);
}
}
order.pb(v);
}
void solve(int root) {
dfs3(root, -1);
for (int x : order) mdist[x] = INF;
mdist[root] = 0;
dist[root] = 0;
dfs(root, -1);
dfs2(root, -1);
vector<bool> ok(n);
for (auto &x : fin) {
ok[x.s] = true;
}
ans += sz(fin);
order.clear();
for (pi to : adj[root]) {
if (blocked[to.f]) continue;
dfs3(to.f, root);
for (int x : order) {
if (ok[x]) {
fin.erase(mp(dist[x], x));
}
}
for (int x : order) {
ll cdist = mdist[x];
ans += sz(fin) - fin.order_of_key(mp(-cdist + a[root], INT_MIN));
}
for (int x : order) {
if(ok[x]) fin.insert(mp(dist[x], x));
}
order.clear();
}
fin.clear();
}
void dfs4(int v, int p) {
sz[v] = 1;
for (pi to : adj[v]) {
if (blocked[to.f]) continue;
if (to.f != p) {
dfs4(to.f, v);
sz[v] += sz[to.f];
}
}
}
int find(int v, int p, int root) {
for (pi to : adj[v]) {
if (blocked[to.f]) continue;
if (to.f != p) {
if (sz[to.f] > sz[root] / 2) {
return find(to.f, v, root);
}
}
}
return v;
}
void go(int root) {
dfs4(root, -1);
int cc = find(root, -1, root);
solve(cc);
blocked[cc] = true;
for (pi to : adj[cc]) {
if (!blocked[to.f]) {
go(to.f);
}
}
}
int main(){
ios::sync_with_stdio(false);
cin.tie(0);
cin >> n;
for (int i = 0; i < n; i++) cin >> a[i];
for (int i = 0; i < n - 1; i++) {
int u, v, w; cin >> u >> v >> w;
u--, v--;
adj[u].pb(mp(v, w)), adj[v].pb(mp(u, w));
}
go(0);
cout << ans << '\n';
}
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