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
#設定
import sys
input = sys.stdin.buffer.readline
sys.setrecursionlimit(10 ** 7)

#ライブラリインポート
from collections import defaultdict
import bisect
INF = float("inf")

#入力受け取り
def getlist():
	return list(map(int, input().split()))


class Graph(object):
	def __init__(self):
		self.graph = defaultdict(list)

	def __len__(self):
		return len(self.graph)

	def add_edge(self, a, b):
		self.graph[a].append(b)

	def get_nodes(self):
		return self.graph.keys()

def Euler_tour(G, node, visit, DP, prev, ans, A):
	for i in G.graph[node]:
		if visit[i] != "Yes":
			visit[i] = "Yes"
			#LIS更新
			x = bisect.bisect_left(DP, A[i])
			prev.append([x, DP[x]])
			DP[x] = A[i]
			ans[i] = bisect.bisect_left(DP, INF)
			# print(DP, i)
			# print(prev)
			Euler_tour(G, i, visit, DP, prev, ans, A)

	#LIS戻す
	x, val = prev.pop()
	DP[x] = val

#処理内容
def main():
	N = int(input())
	A = getlist()
	G = Graph()
	for i in range(N - 1):
		a, b = getlist()
		a -= 1; b -= 1
		G.add_edge(a, b)
		G.add_edge(b, a)

	#DFS初期化
	DP = [INF] * N
	DP[0] = A[0]
	prev = [[0, A[0]]]
	ans = [None] * N
	ans[0] = 1
	visit = ["No"] * N
	visit[0] = "Yes"
	Euler_tour(G, 0, visit, DP, prev, ans, A)
	for i in range(N):
		print(ans[i])


if __name__ == '__main__':
	main()