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: Accepted)

#![allow(unused_imports)]
use std::cmp;
use std::collections::*;

pub struct Scanner {
    line: Vec<String>,
    idx: usize,
}

#[allow(dead_code)]
impl Scanner {
    fn new() -> Scanner {
        return Scanner {
            line: vec![],
            idx: 0,
        };
    }
    fn next<T: std::str::FromStr>(&mut self) -> T {
        if self.idx == self.line.len() {
            let mut buffer = String::new();
            std::io::stdin().read_line(&mut buffer).ok();
            let a: Vec<&str> = buffer.trim().split(' ').collect();
            self.line = a.iter().map(|&s| String::from(s)).collect();
            self.idx = 0;
        }
        let ret: T = self.line[self.idx].parse::<T>().ok().expect("Parse error.");
        self.idx += 1;
        ret
    }
    fn next_string(&mut self) -> Vec<char> {
        let s: String = self.next();
        return s.chars().collect::<Vec<char>>();
    }
    fn next_vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        let mut v: Vec<T> = Vec::with_capacity(n);
        for _i in 0..n {
            v.push(self.next());
        }
        v
    }
}

fn merge(a: HashMap<usize, u64>, b: HashMap<usize, u64>) -> HashMap<usize, u64> {
    let (c, mut d) = if a.len() < b.len() { (a, b) } else { (b, a) };
    for (k, v) in c {
        let p = d.entry(k).or_insert(0);
        *p += v;
    }
    d
}

fn dfs(
    u: usize,
    p: usize,
    c: &Vec<usize>,
    edge: &Vec<Vec<usize>>,
    ans: &mut Vec<u64>,
) -> (u64, u64, HashMap<usize, u64>) {
    let mut hm: HashMap<usize, u64> = HashMap::new();
    let mut cnt = 0;
    let mut si = 1;
    for v in edge[u].iter().cloned() {
        if v == p {
            continue;
        }
        let (cn, s, h) = dfs(v, u, c, edge, ans);
        cnt += cn;
        si += s;

        match h.get(&c[u]) {
            Some(x) => {
                let si = s - x;           
                ans[c[u]] -= (si + 1) * si / 2;
            }
            None => {
                ans[c[u]] -= (s + 1) * s / 2;
            }
        }
        hm = merge(hm, h);
        
    }
    *hm.entry(c[u]).or_insert(0) = si;

    if u == 0 {
        for i in 1..ans.len() {
            match hm.get(&i) {
                Some(x) => {
                    let si = si - x;
                    ans[i] -= (si + 1) * si / 2;
                }
                None => {
                    ans[i] -= (si + 1) * si / 2;
                }
            }
        }
    }
    return (cnt, si, hm);
}

fn main() {
    let mut scan = Scanner::new();
    let n: usize = scan.next();
    let c: Vec<usize> = scan.next_vec(n);
    let mut edge: Vec<Vec<usize>> = vec![vec![]; n];
    for _i in 0..n - 1 {
        let a: usize = scan.next();
        let b: usize = scan.next();
        let (a, b) = (a - 1, b - 1);
        edge[a].push(b);
        edge[b].push(a);
    }
    let mut ans = vec![n as u64 * (n as u64 + 1) / 2; n + 1];
    dfs(0, 0, &c, &edge, &mut ans);
    for i in 1..ans.len() {
        println!("{}", ans[i]);
    }
}