Distinct Colors

• Time limit: 1.00 s
• Memory limit: 512 MB

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