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 = [int(a) for a in input().split()]
X = [[] for i in range(N)]
for i in range(N-1):
    x, y = map(int, input().split())
    x, y = x-1, y-1
    X[x].append(y)
    X[y].append(x)

def EulerTour(n, X, i0):
    def bl(k):
        l, r = -1, n
        while r - l > 1:
            m = (l + r) // 2
            if L[m][-1] < k:
                l = m
            else:
                r = m
        return l + 1

    inf = 1 << 30
    P = [-1] * n
    Q = [~i0, i0]
    ANS = [0] * n
    L = [[inf] for _ in range(n)]
    I = [0] * n
    while Q:
        i = Q.pop()
        if i < 0:
            i = ~i
            L[I[i]].pop()
            continue
        if i >= 0:
            k = A[i]
            b = bl(k)
            L[b].append(k)
            I[i] = b
            ANS[i] = bl(inf)
        for a in X[i][::-1]:
            if a != P[i]:
                P[a] = i
                for k in range(len(X[a])):
                    if X[a][k] == i:
                        del X[a][k]
                        break
                Q.append(~a)
                Q.append(a)
    return ANS

print("\n".join(map(str, EulerTour(N, X, 0))))