Distinct Colors

You are given a rooted tree consisting of n nodes. The nodes are numbered 1,2,\ldots,n, and node 1 is the root. Each node has a color. Your task is to determine for each node the number of distinct colors in the subtree of the node.

Input

The first input line contains an integer n: the number of nodes. The nodes are numbered 1,2,\ldots,n. The next line consists of n integers c_1,c_2,\ldots,c_n: the color of each node. Then there are n-1 lines describing the edges. Each line contains two integers a and b: there is an edge between nodes a and b.

Output

Print n integers: for each node 1,2,\ldots,n, the number of distinct colors.

Constraints

$1 \le n \le 2$ \cdot 10^5$

$1 \le a,b \le n$

$1 \le c_i \le 10^9$

Example

Input

5
2 3 2 2 1
1 2
1 3
3 4
3 5

Output

3 1 2 1 1