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

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`