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()))
peer = [[] for _ in range(n)]
for _ in range(n-1):
  a,b = map(int,input().split())
  a -= 1
  b -= 1
  peer[a].append(b)
  peer[b].append(a)
inf = 10**12
minf = 10**11
pre = [inf for _ in range(n)]
pst = [[] for _ in range(n)]
right = [inf for _ in range(n)]
seen = [0 for _ in range(n)]
seen[0] = 1
now = [0]
while now:
  last = now
  now = []
  for x in last:
    for y in peer[x]:
      if seen[y] == 0:
        now.append(y)
        seen[y] = 1
        pre[y] = x
        right[y] = x
        if pst[x]:
          right[pst[x][-1]] = y
        pst[x].append(y)
down = [i for i in range(n)]
for i in range(n):
  if pst[i]:
    down[i] = pst[i][0]
#print(pre)
#print(right)
#print(pst)
#print(down)
seen = [0 for _ in range(n)]
import bisect
lis = [inf for _ in range(n)]
rec = [[] for _ in range(n)]
now = 0
ans = [0 for _ in range(n)]
while True:
  if seen[now] == 0:
    seen[now] += 1
    #print(A[now],lis)
    b = bisect.bisect_left(lis,A[now])
    rec[now] = [b,lis[b]]
    lis[b] = A[now]
    ans[now] = bisect.bisect_left(lis,minf)
    now = down[now]
  else:
    seen[now] += 1
    b,c = rec[now]
    lis[b] = c
    if now == 0:
      break
    now = right[now]
for x in ans:
  print(x)