Problem:
Score : 600 points

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.

Sample Input 1

3
1 2 1
1 2
2 3

Sample Output 1

5
4
0

Let P_{i,j} denote the simple path connecting Vertex i and j.

There are 5 simple paths that visit a vertex painted in the color 1 one or more times:

P_{1,1}\,,\,
P_{1,2}\,,\,
P_{1,3}\,,\,
P_{2,3}\,,\,
P_{3,3}

There are 4 simple paths that visit a vertex painted in the color 2 one or more times:

P_{1,2}\,,\,
P_{1,3}\,,\,
P_{2,2}\,,\,
P_{2,3}

There are no simple paths that visit a vertex painted in the color 3 one or more times.

Sample Input 2

1
1

Sample Output 2

1

Sample Input 3

2
1 2
1 2

Sample Output 3

2
2

Sample Input 4

5
1 2 3 4 5
1 2
2 3
3 4
3 5

Sample Output 4

5
8
10
5
5

Sample Input 5

8
2 7 2 5 4 1 7 5
3 1
1 2
2 7
4 5
5 6
6 8
7 8

Sample Output 5

18
15
0
14
23
0
23
0

Solution in Rust (1.42.0) (judge verdict: Time Limit Exceeded)

use std::io::{self, BufRead};
use std::collections::HashSet;

fn create_tree(tree: &mut Vec<HashSet<usize>>, edges: &Vec<HashSet<usize>>, r: usize) {
  let children: HashSet<usize> = edges[r].iter().filter(|e| tree[**e].is_empty()).map(|e| *e).collect();
  tree[r] = children.clone();
  for c in children {
    create_tree(tree, edges, c);
  }
}

fn count_color(counts: &mut Vec<usize>, passed: &mut Vec<bool>, colors: &mut Vec<usize>, tree: &Vec<HashSet<usize>>, cs: &Vec<usize>, r: usize, l: usize) {
  let c = cs[l];
  if passed[c] {
    for i in 0..colors.len() {
      if r <= l {
        counts[colors[i]] += 1;
      }
    }
    for child in &tree[l] {
      count_color(counts, passed, colors, tree, cs, r, *child);
    }
  } else {
    passed[c] = true;
    colors.push(c);
    for i in 0..colors.len() {
      if r <= l {
        counts[colors[i]] += 1;
      }
    }
    for child in &tree[l] {
      count_color(counts, passed, colors, tree, cs, r, *child);
    }
    colors.pop();
    passed[c] = false;
  }
}

fn main() {
  let stdin = io::stdin();
  let mut lines = stdin.lock().lines();
  let line = lines.next().unwrap().unwrap();
  let n: usize = line.parse().unwrap();
  let line = lines.next().unwrap().unwrap();
  let cs: Vec<usize> = line.split(' ').map(|x| x.parse().unwrap()).map(|c: usize| c - 1).collect();
  let mut es: Vec<HashSet<usize>> = vec![HashSet::new(); n];
  for _ in 0..(n-1) {
    let line = lines.next().unwrap().unwrap();
    let xs: Vec<usize> = line.split(' ').map(|x| x.parse().unwrap()).collect();
    let x = xs[0] - 1;
    let y = xs[1] - 1;
    es[x].insert(y);
    es[y].insert(x);
  }

  let mut counts: Vec<usize> = vec![0; n];
  for r in 0..n {
    let mut tree: Vec<HashSet<usize>> = vec![HashSet::new(); n];
    create_tree(&mut tree, &es, r);
    let mut passed: Vec<bool> = vec![false; n];
    let mut colors: Vec<usize> = Vec::new();
    count_color(&mut counts, &mut passed, &mut colors, &tree, &cs, r, r);
  }

  for c in counts {
    println!("{}", c);
  }
}