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**Task** | Statistics

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.

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 $b$.

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

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

- $1 \le a,b \le n$

- $1 \le c_i \le 10^9$

Input:

`5`

2 3 2 2 1

1 2

1 3

3 4

3 5

Output:

`3 1 2 1 1`