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.util.*;
public class Main {
	
	static int INF = Integer.MAX_VALUE;
	static int[] a, dp, ans;
	static List<Integer>[] list;
	static int max;
	
	static int lower_bound(int[] a, int key) {
		if(a[a.length-1] < key)
			return a.length;
		int lb = 0, ub = a.length-1, mid;
		do {
			mid = (ub+lb)/2;
			if(a[mid] < key)
				lb = mid + 1;
			else
				ub = mid;
		}while(lb < ub);
		return ub;
	}
	
	
	static void dfs(int v, int p) {
		int id = lower_bound(dp, a[v]);
		int p_id = id;
		int val = dp[id];
		int p_max = max;
		dp[id] = a[v];
		ans[v] = max = Math.max(max, id);
		for(int i : list[v])
			if(i != p)
				dfs(i, v);
		dp[p_id] = val;
		max = p_max;
	}
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		a = new int[N];
		list = new ArrayList[N];
		for(int i = 0; i < N; i++) {
			a[i] = sc.nextInt();
			list[i] = new ArrayList<>();
		}
		for(int i = 1; i < N; i++){
			int u = sc.nextInt()-1;
			int v = sc.nextInt()-1;
			list[u].add(v);
			list[v].add(u);
		}
		dp = new int[N+1];
		Arrays.fill(dp, INF);
		dp[0] = 0;
		ans = new int[N];
		dfs(0, 0);
		StringBuilder out = new StringBuilder();
		for(int i = 0; i < N; i++)
			out.append(ans[i] + "\n");
		System.out.print(out);
	}

}
