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)]

use kyoproio::*;
use std::{
    collections::*,
    io::{self, prelude::*},
    iter,
    mem::{replace, swap},
};

fn main() -> io::Result<()> {
    std::thread::Builder::new()
        .stack_size(64 * 1024 * 1024)
        .spawn(solve)?
        .join()
        .unwrap();
    Ok(())
}

fn solve() {
    let stdin = io::stdin();
    let mut kin = KInput::new(stdin.lock());
    let stdout = io::stdout();
    let mut out = io::BufWriter::new(stdout.lock());
    macro_rules! output {($($args:expr),+) => { write!(&mut out, $($args),+) }; }
    macro_rules! outputln {
        ($($args:expr),+) => { output!($($args),+); outputln!(); };
        () => { output!("\n"); if cfg!(debug_assertions) { out.flush(); } }
    }

    let n: usize = kin.input();
    let mut c = vec![0];
    c.extend(kin.iter::<usize>().take(n));
    let mut g = vec![vec![]; n + 1];
    for _ in 0..n - 1 {
        let (a, b): (usize, usize) = kin.input();
        g[a].push(b);
        g[b].push(a);
    }
    let m = (n * (n + 1) / 2) as isize;
    let mut sub = vec![1; n + 1];
    let mut comp = vec![n as isize; n + 1];
    let mut ans = vec![m; n + 1];
    let mut dfs = Dfs {
        c, sub, comp, ans
    };
    dfs.dfs(&g, 1, 0);
    for i in 1..=n {
        dfs.ans[i] -= dfs.comp[i] * (dfs.comp[i] + 1) / 2;
    }
    for i in 1..=n {
        outputln!("{}", dfs.ans[i]);
    }
}

struct Dfs {
    c: Vec<usize>,
    sub: Vec<isize>,
    comp: Vec<isize>,
    ans: Vec<isize>,
}
impl Dfs {
    fn dfs(&mut self, g: &[Vec<usize>], u: usize, p: usize) {
        let col = self.c[u];
        let comp_temp = self.comp[col];
        for &v in g[u].iter().filter(|&&v| v != p) {
            self.comp[col] = 0;
            self.dfs(g, v, u);
            self.comp[col] += self.sub[v];
            self.ans[col] -= self.comp[col] * (self.comp[col] + 1) / 2;
            self.sub[u] += self.sub[v];
        }
        self.comp[col] = comp_temp - self.sub[u];
    }
}


// -----------------------------------------------------------------------------
pub mod kyoproio {
    #![warn(unused)]
    use std::io::prelude::*;
    pub trait Input {
        fn str(&mut self) -> &str;
        fn bytes(&mut self) -> &[u8] {
            self.str().as_ref()
        }
        fn input<T: InputParse>(&mut self) -> T {
            T::input(self)
        }
        fn iter<T: InputParse>(&mut self) -> Iter<T, Self> {
            Iter(self, std::marker::PhantomData)
        }
        fn seq<T: InputParse, B: std::iter::FromIterator<T>>(&mut self, n: usize) -> B {
            self.iter().take(n).collect()
        }
    }
    pub struct KInput<R> {
        src: R,
        buf: String,
        pos: usize,
    }
    impl<R: BufRead> KInput<R> {
        pub fn new(src: R) -> Self {
            Self {
                src,
                buf: String::with_capacity(1024),
                pos: 0,
            }
        }
    }
    impl<R: BufRead> Input for KInput<R> {
        fn str(&mut self) -> &str {
            loop {
                if self.pos >= self.buf.len() {
                    self.pos = 0;
                    self.buf.clear();
                    if self.src.read_line(&mut self.buf).expect("io error") == 0 {
                        return &self.buf;
                    }
                }
                let range = self.pos
                    ..self.buf[self.pos..]
                        .find(|c: char| c.is_ascii_whitespace())
                        .map(|i| i + self.pos)
                        .unwrap_or_else(|| self.buf.len());
                self.pos = range.end + 1;
                if range.end > range.start {
                    return &self.buf[range];
                }
            }
        }
    }
    pub struct Iter<'a, T, I: ?Sized>(&'a mut I, std::marker::PhantomData<*const T>);
    impl<'a, T: InputParse, I: Input + ?Sized> Iterator for Iter<'a, T, I> {
        type Item = T;
        fn next(&mut self) -> Option<Self::Item> {
            Some(self.0.input())
        }
    }
    pub trait InputParse: Sized {
        fn input<I: Input + ?Sized>(input: &mut I) -> Self;
    }
    impl InputParse for Vec<u8> {
        fn input<I: Input + ?Sized>(input: &mut I) -> Self {
            input.bytes().to_owned()
        }
    }
    macro_rules! from_str_impl {
        { $($T:ty)* } => {
            $(impl InputParse for $T {
                fn input<I: Input + ?Sized>(input: &mut I) -> Self {
                    input.str().parse::<$T>().expect("parse error")
                }
            })*
        };
    }
    from_str_impl! {
        String char bool f32 f64 isize i8 i16 i32 i64 i128 usize u8 u16 u32 u64 u128
    }
    macro_rules! tuple_impl {
        ($H:ident $($T:ident)*) => {
            impl<$H: InputParse, $($T: InputParse),*> InputParse for ($H, $($T),*) {
                fn input<I: Input + ?Sized>(input: &mut I) -> Self {
                    ($H::input(input), $($T::input(input)),*)
                }
            }
            tuple_impl!($($T)*);
        };
        () => {};
    }
    tuple_impl!(A B C D E F G);
}