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 sys,bisect
input = sys.stdin.readline

n = int(input())
a = list(map(int,input().split()))

ans = [1]*n

edge = [[] for i in range(n)]
for i in range(n-1):
    u,v = map(int,input().split())
    edge[u-1].append(v-1)
    edge[v-1].append(u-1)

root = 0
chi = [[] for i in range(n)]
par = [-1]*n
used = [False]*n
tank = [0]

while tank:
    q = tank.pop()
    used[q] = True
    for e in edge[q]:
        if not used[e]:
            chi[q].append(e)
            tank.append(e)
            par[e] = q

tank = [root]

idx = dict()
val = dict()
dp = [10**10]*n

eulerNum = -1

while tank:
    q = tank.pop()
    if q >= 0:
        #first time
        num = a[q]
        kk = bisect.bisect_left(dp,num)
        
        val[q] = dp[kk]
        idx[q] = kk
        dp[kk] = num
        ans[q] = bisect.bisect_left(dp,10**10)

        eulerNum += 1
        tank.append(~q)
        for ch in chi[q]:
            tank.append(ch)
    else:
        if ~q != root:
            if dp[idx[~q]] == a[~q]:
                dp[idx[~q]] = val[~q]
                eulerNum += 1

print(*ans,sep = "\n")