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
N = int(input())
A = list(map(int,input().split()))
e_list = [[] for i in range(N)]
for i in range(N-1):
    a,b = list(map(int,input().split()))
    a,b = a-1,b-1
    e_list[a].append(b)
    e_list[b].append(a)

from collections import deque

vi = 0  #change
INF = float('inf')

Q = deque([vi])

DP = [INF]*(N+1)
ans = [-1]*(N)
l = [0]

def bisect(DP,a,l):
    if DP[0] >= a:
        if DP[0]==INF:
            l[0]+=1
        b = DP[0]
        DP[0] = a        
        return (0,b) 
    ok = 0
    ng = N
    while ng-ok>1:
        if DP[(ok+ng)//2]>=a:
            ng = (ok+ng)//2
        else:
            ok = (ok+ng)//2
    if DP[ng]==INF:
        l[0]+=1
    b = DP[ng]
    DP[ng] = a
    return (ng,b)


checked_list = [False]*N
checked_list[vi]=True

while len(Q)>0:
    v = Q.pop()
    if type(v)==type(0):
        Q.append(bisect(DP, A[v], l))
        ans[v] = l[0]
        for v1 in e_list[v]:
            if not checked_list[v1]:
                checked_list[v1]=True
                Q.append(v1)
    else:
        i,a = v
        DP[i] = a
        if a==INF:
            l[0]-=1
        
print(*ans, sep = "\n")