#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <sstream>
#include <iostream>
#include <math.h>
#include <time.h>
#include <unistd.h>
#include <algorithm>
#include <map>
#include <list>
#include <queue>
#include <stack>
#include <vector>
#include <set>
#include <string>
 
#ifndef ONLINE_JUDGE
	#define DEBUG(x) cout << '>' << #x << ':' << x << endl;
#else
	#define DEBUG(x) do {} while(0);
#endif
 
#define pb push_back
#define mp make_pair
#define ALL(x) (x).begin(), (x).end()
#define PER(i, N) for(int (i) = (N)-1; (i) >= 0; (i)--)
#define REP(i, N) for(int (i) = 0; (i) < (int)(N); (i)++)
 #include <iomanip>
using namespace std;
typedef long long ll;
inline bool EQ(double a, double b) { return fabs(a-b) < 1e-9; }

template <typename T, typename U> std::istream&operator>>(std::istream&i, pair<T,U>&p) {i >> p.x >> p.y; return i;}
template<typename T>std::istream&operator>>(std::istream&i,vector<T>&t) {for(auto&v:t){i>>v;}return i;}
template <typename T, typename U> std::ostream&operator<<(std::ostream&o, const pair<T,U>&p) {o << p.x << ' ' << p.y; return o;}
template<typename T>std::ostream&operator<<(std::ostream&o,const vector<T>&t) {if(t.empty())o<<'\n';for(size_t i=0;i<t.size();++i){o<<t[i]<<" \n"[i == t.size()-1];}return o;}
template<typename T> using minheap = priority_queue<T, vector<T>, greater<T>>;
template<typename T> using maxheap = priority_queue<T, vector<T>, less<T>>;
template<typename T> T gcd(T a,T b) { if (a<b) swap(a,b); return b?gcd(b,a%b):a; }

int n;
vector<int> nxt[222222];
int A[222222];
int ans[222222];



const int inf = 1e9;
struct Node {
	Node *l = 0, *r = 0;
	int lo, hi, mset = inf, madd = 0, val = 0;
	Node(int lo,int hi):lo(lo),hi(hi){} // Large interval of -inf
	Node(vector<int>& v, int lo, int hi) : lo(lo), hi(hi) {
		if (lo + 1 < hi) {
			int mid = lo + (hi - lo)/2;
			l = new Node(v, lo, mid); r = new Node(v, mid, hi);
			val = max(l->val, r->val);
		}
		else val = v[lo];
	}
	int query(int L, int R) {
		if (R <= lo || hi <= L) return -inf;
		if (L <= lo && hi <= R) return val;
		push();
		return max(l->query(L, R), r->query(L, R));
	}
	void set(int L, int R, int x) {
		if (R <= lo || hi <= L) return;
		if (L <= lo && hi <= R) mset = val = x, madd = 0;
		else {
			push(), l->set(L, R, x), r->set(L, R, x);
			val = max(l->val, r->val);
		}
	}
	void add(int L, int R, int x) {
		if (R <= lo || hi <= L) return;
		if (L <= lo && hi <= R) {
			if (mset != inf) mset += x;
			else madd += x;
			val += x;
		}
		else {
			push(), l->add(L, R, x), r->add(L, R, x);
			val = max(l->val, r->val);
		}
	}
	void push() {
		if (!l) {
			int mid = lo + (hi - lo)/2;
			l = new Node(lo, mid); r = new Node(mid, hi);
		}
		if (mset != inf)
			l->set(lo,hi,mset), r->set(lo,hi,mset), mset = inf;
		else if (madd)
			l->add(lo,hi,madd), r->add(lo,hi,madd), madd = 0;
	}
};
Node* root;

void solve(int u, int p=-1) {
	int curr = root->query(1, A[u]);
	int prev = root->query(A[u], A[u]+1);
	root->set(A[u], A[u]+1, curr+1);
	ans[u] = max(curr+1, root->query(1, 9*n));
	for(int v: nxt[u]) {
		if(v==p)
			continue;
		solve(v, u);
	}
	root->set(A[u], A[u]+1, prev);
}

void solve(istream& cin, ostream& cout) {
	cin >> n;
	root = new Node(0, 10*n);
	vector<pair<int,int>> B;
	REP(i, n) {
		int a;
		cin >> a;
		B.pb({a,i});
	}
	REP(i, n-1) {
		int u,v;
		cin>>u>>v;
		u--;v--;
		nxt[u].pb(v);
		nxt[v].pb(u);
	}
	sort(ALL(B));
	int last = -1;
	int X = 2;
	REP(i, n) {
		if(B[i].first != last) {
			X++;
		}
		A[B[i].second] = X;
		last = B[i].first;
	}
//	REP(i, n) cout << A[i] << " ";
//	cout <<endl;
	solve(0);
	REP(i, n) cout << ans[i]<<endl;
}


int main() {
    ios_base::sync_with_stdio(false);
	cin.tie(nullptr); cout.tie(nullptr);
	solve(cin, cout);
	/*
	{
		istringstream instr("2\n2\n14");
		solve(instr, cout);
	}
 */
	return 0;
}


Measured memory_bytes: 43716