#include <iostream>
#include <string>
#include <vector>
#include <set>
#include <stack>
#include <queue>
#include <map>
#include <algorithm>
#include <iomanip>
#include <math.h>
#include <string.h>
#include <cstdio>
#include <tuple>
using namespace std; using ll = long long; using ld = long double;  using pll = pair<ll, ll>;
using vl = vector<ll>; using vll = vector<vl>; using vpll = vector<pll>;
const ld PI = 3.1415926535897932;
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#define rep1(n) for(ll i=0;i<n;++i)
#define rep2(i,n) for(ll i=0;i<n;++i)
#define rep3(i,a,b) for(ll i=a;i<b;++i)
#define rep4(i,a,b,c) for(ll i=a;i<b;i+=c)
#define rep(...) overload4(__VA_ARGS__,rep4,rep3,rep2,rep1)(__VA_ARGS__)
#define mp make_pair
#define mt make_tuple
#define INT(...) int __VA_ARGS__;in(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__;in(__VA_ARGS__)
#define ULL(...) ull __VA_ARGS__;in(__VA_ARGS__)
#define STR(...) string __VA_ARGS__;in(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__;in(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__;in(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__;in(__VA_ARGS__)
void in() {}
void debug_out() { cerr << endl; }
template<typename Head, typename... Tail>
void debug_out(Head h, Tail... t) {
	cerr << " " << h;
	if (sizeof...(t) > 0) cerr << " :";
	debug_out(t...);
}
template <typename T>
ostream& operator<<(ostream& os, vector<T> vec) {
	for (size_t i = 0; i < vec.size(); i++)os << vec[i] << (i + 1 == vec.size() ? "" : " ");
	return os;
}
ll ctoi(char c) {
	switch (c) {
	case '0': return 0; case '1': return 1; case '2': return 2;
	case '3': return 3; case '4': return 4; case '5': return 5;
	case '6': return 6; case '7': return 7; case '8': return 8;
	case '9': return 9;  default: return 0;
	}
}
void vout(vl V) {
	for (ll i = 0; i < (ll)V.size(); i++) cout << V[i] << " ";
	cout << endl;
}
bool pairCompare(const pll firstElof, pll secondElof)
{
	return firstElof.first > secondElof.first;
}
//**Snippetリスト**//
//rep, vin, all, iteLoop//
//bitSearch, bitList, nod, gcdlcm, isPrime, primeFactorize, Npow, divisor, modinv, dfs, bfs, eratos//
//dijkstra, WarshallFloyd, BellmanFord, UnionFind, COM, digitDP ,RMQ//
ll i, j, k, l; ll N, M, K, H, W, L, X, Y, Z, R, Q;
ll MOD = 1000000007; ll INF = 1LL << 62; ll ans = 0; ll z = 0, o = 1;
vl flag, color; vll path; vl A; vl dp; vl Ans;

void dfs(ll now) {
	stack<ll> S; S.push(now);	
	//dp[id]は初めて末尾の要素の最小値がA[now]以上になるような長さid+1
	ll id = lower_bound(dp.begin(), dp.end(), A[now]) - dp.begin();
	//==>dp[id-1]はA[now]未満なので長さidのLISにA[now]を足して長さid+1のLISに出来る！
	//古い値を記録しておく(後で戻す)
	ll prev = dp[id];
	//長さid+1のLISはA[now]を末尾に出来る！
	dp[id] = A[now];
	//始めて作成不可能なインデックスが返るが、添字の関係でこれでぴったりLISの解答となる
	Ans[now] = lower_bound(dp.begin(), dp.end(), INF) - dp.begin();
	flag[now] = 1;
	while (!S.empty()) {
		ll u = S.top(); S.pop();
		for (ll i = 0; i < path[u].size(); i++) {
			ll v = path[u][i];
			if (flag[v] == 0) dfs(v);
		}
	}
	//もとに戻す
	dp[id] = prev;
}
int main() {
	cin >> N;
	A.resize(N);
	flag.resize(N);
	path.resize(N);
	Ans.resize(N);
	dp.resize(N);
	for (i = 0; i < N; i++) cin >> A[i];
	for (i = 0; i < N-1; i++) {
		ll u, v;
		cin >> u >> v;
		u--; v--;
		path[u].push_back(v);
		path[v].push_back(u);
	}
	//初期値はINF(作成不可能)
	for (i = 0; i < N; i++) dp[i] = INF;
	//dp[i]：長さi+1の部分増加列の末尾の要素の最小値
	//長さ1の部分増加列の末尾の要素の最小値はとりあえずA[0]
	dp[0] = A[0];
	dfs(0);
	for (i = 0; i < N; i++) cout << Ans[i] << endl;
}

Measured memory_bytes: 161420