#include <bits/stdc++.h>

using namespace std;

int a[200005], lis[200005];

vector<int> g[200005], v;

void dfs(int u, int parant = -87) {
	bool type = 0;
	int i, boook;
	if(v.empty() || v.back() < a[u]) {
		v.push_back(a[u]);
	}
	else {
		i = lower_bound(v.begin(), v.end(), a[u]) - v.begin();
		boook = v[i];
		v[i] = a[u];
		type = 1;
	}
	lis[u] = v.size();
	for(int child:g[u]) if(child != parant)
		dfs(child, u);
	if(type) {
		v[i] = boook;
	} else {
		v.pop_back();
	}
}

int main() {	
	int n;
	cin >> n;
	for(int i = 1; i <= n; i++) {
		cin >> a[i];
	}
	for(int i = 1; i < n; i++) {
		int u, v;
		cin >> u >> v;
		g[u].push_back(v);
		g[v].push_back(u);
	}
	dfs(1);
	for(int i = 1; i <= n; i++) {
		cout << lis[i] << endl;
	}

}