Problem Statement

We have a tree with $N$ vertices numbered $1$ to $N$. The $i$-th edge in this tree connects Vertex $a_i$ and $b_i$. Additionally, each vertex is painted in a color, and the color of Vertex $i$ is $c_i$. Here, the color of each vertex is represented by an integer between $1$ and $N$ (inclusive). The same integer corresponds to the same color; different integers correspond to different colors.

For each $k=1, 2, ..., N$, solve the following problem:

• Find the number of simple paths that visit a vertex painted in the color $k$ one or more times.

Note: The simple paths from Vertex $u$ to $v$ and from $v$ to $u$ are not distinguished.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $1 \leq c_i \leq N$
• $1 \leq a_i,b_i \leq N$
• The given graph is a tree.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
c_1 c_2 ... c_N
a_1 b_1
:
a_{N-1} b_{N-1}

Output

Print the answers for $k = 1, 2, ..., N$ in order, each in its own line.