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 C# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using CompLib.Util;

public class Program
{
    private int N;
    private int[] C;
    private List<int>[] E;

    private long[] Ans;
    private long[] Cnt;

    public void Solve()
    {
        var sc = new Scanner();
        N = sc.NextInt();
        C = new int[N];
        for (int i = 0; i < N; i++)
        {
            C[i] = sc.NextInt() - 1;
        }

        E = new List<int>[N];
        for (int i = 0; i < N; i++)
        {
            E[i] = new List<int>();
        }

        for (int i = 0; i < N - 1; i++)
        {
            int a = sc.NextInt() - 1;
            int b = sc.NextInt() - 1;
            E[a].Add(b);
            E[b].Add(a);
        }

        Ans = new long[N];
        for (int i = 0; i < N; i++)
        {
            Ans[i] = (long) N * (N + 1) / 2;
        }

        Cnt = new long[N];

        Go(0, -1);
        for (int i = 0; i < N; i++)
        {
            Ans[i] -= (N - Cnt[i]) * (N - Cnt[i] + 1) / 2;
        }

        Console.WriteLine(string.Join("\n", Ans));
    }

    long Go(int cur, int par)
    {
        // cur以下の部分木のサイズ
        long subtree = 1;
        long tmp = Cnt[C[cur]];

        foreach (int to in E[cur])
        {
            if (to == par) continue;
            Cnt[C[cur]] = 0;
            subtree += Go(to, cur);
        }


        Cnt[C[cur]] += subtree;

        if (par != -1)
        {
            Ans[C[par]] -= (subtree - Cnt[C[par]]) * (subtree - Cnt[C[par]] + 1) / 2;
        }
        else
        {
        }

        Cnt[C[cur]] = tmp;
        Cnt[C[cur]] += subtree;
        return subtree;
    }


    public static void Main(string[] args) => new Program().Solve();
}

namespace CompLib.Util
{
    using System;
    using System.Linq;

    class Scanner
    {
        private string[] _line;
        private int _index;
        private const char Separator = ' ';

        public Scanner()
        {
            _line = new string[0];
            _index = 0;
        }

        public string Next()
        {
            while (_index >= _line.Length)
            {
                _line = Console.ReadLine().Split(Separator);
                _index = 0;
            }

            return _line[_index++];
        }

        public int NextInt() => int.Parse(Next());
        public long NextLong() => long.Parse(Next());
        public double NextDouble() => double.Parse(Next());
        public decimal NextDecimal() => decimal.Parse(Next());
        public char NextChar() => Next()[0];
        public char[] NextCharArray() => Next().ToCharArray();

        public string[] Array()
        {
            _line = Console.ReadLine().Split(Separator);
            _index = _line.Length;
            return _line;
        }

        public int[] IntArray() => Array().Select(int.Parse).ToArray();
        public long[] LongArray() => Array().Select(long.Parse).ToArray();
        public double[] DoubleArray() => Array().Select(double.Parse).ToArray();
        public decimal[] DecimalArray() => Array().Select(decimal.Parse).ToArray();
    }
}