We have a tree with N vertices, whose i-th edge connects Vertex u_i and Vertex v_i. Vertex i has an integer a_i written on it. For every integer k from 1 through N, solve the following problem:

* We will make a sequence by lining up the integers written on the vertices along the shortest path from Vertex 1 to Vertex k, in the order they appear. Find the length of the longest increasing subsequence of this sequence.



Here, the longest increasing subsequence of a sequence A of length L is the subsequence A_{i_1} , A_{i_2} , ... , A_{i_M} with the greatest possible value of M such that 1 \leq i_1 < i_2 < ... < i_M \leq L and A_{i_1} < A_{i_2} < ... < A_{i_M}.

Constraints

* 2 \leq N \leq 2 \times 10^5
* 1 \leq a_i \leq 10^9
* 1 \leq u_i , v_i \leq N
* u_i \neq v_i
* The given graph is a tree.
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N
a_1 a_2 ... a_N
u_1 v_1
u_2 v_2
:
u_{N-1} v_{N-1}


Output

Print N lines. The k-th line, print the length of the longest increasing subsequence of the sequence obtained from the shortest path from Vertex 1 to Vertex k.

Example

Input

10
1 2 5 3 4 6 7 3 2 4
1 2
2 3
3 4
4 5
3 6
6 7
1 8
8 9
9 10


Output

1
2
3
3
4
4
5
2
2
3
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.math.BigDecimal;
import java.math.RoundingMode;
import java.util.*;
import java.util.concurrent.Delayed;
import java.util.logging.Logger;

import javax.transaction.xa.Xid;


public class Main {
	static final long MOD=998244353;
	static int[] an;
	public static void main(String[] args){
		PrintWriter out = new PrintWriter(System.out);
		InputReader sc=new InputReader(System.in);
		int N=sc.nextInt();
		int[] A=sc.nextIntArray(N);
		graph G=new graph(N);
		an=new int[N];
		for (int i = 0; i < N-1; i++) {
			int a=sc.nextInt()-1;
			int b=sc.nextInt()-1;
			G.addEdge(a, b, 1);
			G.addEdge(b, a, 1);
		}
		int[] dp=new int[N];
		Arrays.fill(dp, Integer.MAX_VALUE/2);
		G.Treedfs(0,-1,A,dp);
		for (int i = 0; i < A.length; i++) {
			out.println(an[i]);
		}
		out.flush();
	}
	static class Edge implements Comparable<Edge>{
		int to;
		long v;
		public Edge(int to,long v) {
			this.to=to;
			this.v=v;
		}
		@Override
    	public boolean equals(Object obj) {
    		if(obj instanceof Edge) {
    			Edge other = (Edge) obj;
    			return other.to==this.to && other.v==this.v;
    		}
    		return false;
    	}//同値の定義
    	@Override
    	public int hashCode() {
    		return Objects.hash(this.to,this.v);
    	}
    	@Override
		  public int compareTo( Edge p2 ){
			 if (this.v>p2.v) {
				return 1;
			}
			 else if (this.v<p2.v) {
				return -1;
			}
			 else {
				return 0;
			}
		  }
	} 
	static class graph{
		ArrayList<Edge>[] list;
		int size;
		long INF=Long.MAX_VALUE/2;
		int[] color;
		@SuppressWarnings("unchecked")
		public graph(int n) {
			size = n;
			list = new ArrayList[n];
			color =new int[n];
			for(int i=0;i<n;i++){
				list[i] = new ArrayList<Edge>();
			}
		}
		void addEdge(int from,int to,long w) {
			list[from].add(new Edge(to,w));
		}
		void Treedfs(int v, int p ,int[] A,int[] dp) {
			int k=lower_bound(dp, 0, dp.length-1, A[v]);
			int before=dp[k];
			dp[k]=A[v];
			int ans=lower_bound(dp, 0, dp.length-1, Integer.MAX_VALUE/2);
			an[v]=ans;
			for (Edge nv : list[v]) {
				if (nv.to == p) continue;  
				Treedfs(nv.to, v,A,dp);
			}
			dp[k]=before;
		}
	}
	public static int lower_bound(int[] a, int fromIndex, int toIndex, int val) {
		if (val > a[toIndex])
			return toIndex + 1;
		if (val <= a[fromIndex])
			return fromIndex;
		int lb = fromIndex - 1, ub = toIndex;
		while (ub - lb > 1) {
			int mid = (ub - lb)/2+lb;
			if (a[mid] >= val) {
				ub = mid;
			} else {
				lb = mid;
			}
		}
		return ub;
	}
	static class InputReader { 
		private InputStream in;
		private byte[] buffer = new byte[1024];
		private int curbuf;
		private int lenbuf;
		public InputReader(InputStream in) {
			this.in = in;
			this.curbuf = this.lenbuf = 0;
		}
 
		public boolean hasNextByte() {
			if (curbuf >= lenbuf) {
				curbuf = 0;
				try {
					lenbuf = in.read(buffer);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return false;
			}
			return true;
		}
 
		private int readByte() {
			if (hasNextByte())
				return buffer[curbuf++];
			else
				return -1;
		}
 
		private boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}
 
		private void skip() {
			while (hasNextByte() && isSpaceChar(buffer[curbuf]))
				curbuf++;
		}
 
		public boolean hasNext() {
			skip();
			return hasNextByte();
		}
 
		public String next() {
			if (!hasNext())
				throw new NoSuchElementException();
			StringBuilder sb = new StringBuilder();
			int b = readByte();
			while (!isSpaceChar(b)) {
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}
 
		public int nextInt() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}
 
		public long nextLong() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}
 
		public double nextDouble() {
			return Double.parseDouble(next());
		}
 
		public int[] nextIntArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}
 
		public long[] nextLongArray(int n) {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}
 
		public char[][] nextCharMap(int n, int m) {
			char[][] map = new char[n][m];
			for (int i = 0; i < n; i++)
				map[i] = next().toCharArray();
			return map;
		}
	}
}
