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CSES Problem Set

Distinct Colors


Task | Statistics


CSES - Distinct Colors

Time limit:1.00 s Memory limit:512 MB

You are given a rooted tree that consists 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 that describe 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
Example

Input:
5
2 3 2 2 1
1 2
1 3
3 4
3 5


Output:
3 1 2 1 1