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# (Mono-mcs 6.8.0.105) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using static System.Math;
using System.Text;
using System.Threading;
using System.Globalization;
using System.Runtime.CompilerServices;
using Library;

namespace Program
{
    public static class ABC163F
    {
        static bool SAIKI = false;
        static public int numberOfRandomCases = 0;
        static public void MakeTestCase(List<string> _input, List<string> _output, ref Func<string[], bool> _outputChecker)
        {
        }
        static public void Solve()
        {
            var N = NN;
            var cList = NNList(N).Select(e => e - 1).ToArray();
            var abList = Repeat(0, N - 1).Select(_ => new { a = NN - 1, b = NN - 1 }).ToArray();
            var tree = new LIB_Tree(N);
            foreach (var item in abList)
            {
                tree.AddPath(item.a, item.b);
            }
            var dic = new Dictionary<long, long>[N];
            var cnt = new long[N];
            var list = Repeat(0, N).Select(_ => new List<long>()).ToArray();
            foreach (var item in tree.BFSFromLeaf(0))
            {
                foreach (var item2 in tree.GetSurround(item.node).Where(e => e != item.parent))
                {
                    cnt[item.node] += cnt[item2];
                    if (dic[item.node] == null)
                    {
                        dic[item.node] = dic[item2];
                        if (dic[item2].ContainsKey(cList[item.node]))
                        {
                            list[cList[item.node]].Add(cnt[item2] - dic[item2][cList[item.node]]);
                        }
                        else
                        {
                            list[cList[item.node]].Add(cnt[item2]);
                        }
                    }
                    else
                    {
                        foreach (var item3 in dic[item2])
                        {
                            if (dic[item.node].ContainsKey(item3.Key))
                            {
                                dic[item.node][item3.Key] += item3.Value;
                            }
                            else
                            {
                                dic[item.node][item3.Key] = item3.Value;
                            }
                        }
                        if (dic[item2].ContainsKey(cList[item.node]))
                        {
                            list[cList[item.node]].Add(cnt[item2] - dic[item2][cList[item.node]]);
                        }
                        else
                        {
                            list[cList[item.node]].Add(cnt[item2]);
                        }
                    }
                }
                if (dic[item.node] == null)
                {
                    dic[item.node] = new Dictionary<long, long>();
                }
                cnt[item.node]++;
                dic[item.node][cList[item.node]] = cnt[item.node];
            }
            for (var i = 0; i < N; i++)
            {
                var v = 0L;
                if (dic[0].ContainsKey(i)) v = dic[0][i];
                list[i].Add(cnt[0] - v);
            }
            var basenum = N * (N + 1) / 2;
            for (var i = 0; i < N; i++)
            {
                var ans = 0L;
                foreach (var item in list[i])
                {
                    ans += item * (item + 1) / 2;
                }
                Console.WriteLine(basenum - ans);
            }
        }
        class Printer : StreamWriter
        {
            public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } }
            public Printer(Stream stream) : base(stream, new UTF8Encoding(false, true)) { base.AutoFlush = false; }
            public Printer(Stream stream, Encoding encoding) : base(stream, encoding) { base.AutoFlush = false; }
        }
        static LIB_FastIO fastio = new LIB_FastIODebug();
        static public void Main(string[] args) { if (args.Length == 0) { fastio = new LIB_FastIO(); Console.SetOut(new Printer(Console.OpenStandardOutput())); } if (SAIKI) { var t = new Thread(Solve, 134217728); t.Start(); t.Join(); } else Solve(); Console.Out.Flush(); }
        static long NN => fastio.Long();
        static double ND => fastio.Double();
        static string NS => fastio.Scan();
        static long[] NNList(long N) => Repeat(0, N).Select(_ => NN).ToArray();
        static double[] NDList(long N) => Repeat(0, N).Select(_ => ND).ToArray();
        static string[] NSList(long N) => Repeat(0, N).Select(_ => NS).ToArray();
        static long Count<T>(this IEnumerable<T> x, Func<T, bool> pred) => Enumerable.Count(x, pred);
        static IEnumerable<T> Repeat<T>(T v, long n) => Enumerable.Repeat<T>(v, (int)n);
        static IEnumerable<int> Range(long s, long c) => Enumerable.Range((int)s, (int)c);
        static IOrderedEnumerable<T> OrderByRand<T>(this IEnumerable<T> x) => Enumerable.OrderBy(x, _ => xorshift);
        static IOrderedEnumerable<T> OrderBy<T>(this IEnumerable<T> x) => Enumerable.OrderBy(x.OrderByRand(), e => e);
        static IOrderedEnumerable<T1> OrderBy<T1, T2>(this IEnumerable<T1> x, Func<T1, T2> selector) => Enumerable.OrderBy(x.OrderByRand(), selector);
        static IOrderedEnumerable<T> OrderByDescending<T>(this IEnumerable<T> x) => Enumerable.OrderByDescending(x.OrderByRand(), e => e);
        static IOrderedEnumerable<T1> OrderByDescending<T1, T2>(this IEnumerable<T1> x, Func<T1, T2> selector) => Enumerable.OrderByDescending(x.OrderByRand(), selector);
        static IOrderedEnumerable<string> OrderBy(this IEnumerable<string> x) => x.OrderByRand().OrderBy(e => e, StringComparer.OrdinalIgnoreCase);
        static IOrderedEnumerable<T> OrderBy<T>(this IEnumerable<T> x, Func<T, string> selector) => x.OrderByRand().OrderBy(selector, StringComparer.OrdinalIgnoreCase);
        static IOrderedEnumerable<string> OrderByDescending(this IEnumerable<string> x) => x.OrderByRand().OrderByDescending(e => e, StringComparer.OrdinalIgnoreCase);
        static IOrderedEnumerable<T> OrderByDescending<T>(this IEnumerable<T> x, Func<T, string> selector) => x.OrderByRand().OrderByDescending(selector, StringComparer.OrdinalIgnoreCase);
        static uint xorshift { get { _xsi.MoveNext(); return _xsi.Current; } }
        static IEnumerator<uint> _xsi = _xsc();
        static IEnumerator<uint> _xsc() { uint x = 123456789, y = 362436069, z = 521288629, w = (uint)(DateTime.Now.Ticks & 0xffffffff); while (true) { var t = x ^ (x << 11); x = y; y = z; z = w; w = (w ^ (w >> 19)) ^ (t ^ (t >> 8)); yield return w; } }
    }
}
namespace Library {
    partial class LIB_Tree
    {
        int N;
        List<int>[] path;
        public struct EulerRes
        {
            public long node;
            public long parent;
            public long direction;
        }
        public struct BFSRes
        {
            public long node;
            public long parent;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public LIB_Tree(long n)
        {
            N = (int)n;
            path = Enumerable.Repeat(0, N).Select(_ => new List<int>()).ToArray();
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public void AddPath(long u, long v)
        {
            if (u >= N || v >= N) throw new Exception();
            path[u].Add((int)v);
            path[v].Add((int)u);
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public int[] GetSurround(long u) => path[u].ToArray();
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public List<BFSRes> BFSFromRoot(long root)
        {
            var bfsList = new List<BFSRes>();
            var q = new Queue<int>();
            var done = new bool[N];
            bfsList.Add(new BFSRes { node = root, parent = -1 });
            done[root] = true;
            q.Enqueue((int)root);
            while (q.Count > 0)
            {
                var w = q.Dequeue();
                foreach (var i in path[w])
                {
                    if (done[i]) continue;
                    done[i] = true;
                    q.Enqueue(i);
                    bfsList.Add(new BFSRes { node = i, parent = w });
                }
            }
            return bfsList;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public List<BFSRes> BFSFromLeaf(long root) => BFSFromRoot(root).ToArray().Reverse().ToList();
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public List<EulerRes> EulerTour(long root)
        {
            var eulerList = new List<EulerRes>();
            var s = new Stack<Tuple<int, int>>();
            var done = new bool[N];
            done[root] = true;
            s.Push(Tuple.Create((int)root, -1));
            while (s.Count > 0)
            {
                var w = s.Peek();
                var ad = true;
                foreach (var i in path[w.Item1])
                {
                    if (done[i]) continue;
                    done[i] = true;
                    ad = false;
                    s.Push(Tuple.Create(i, w.Item1));
                }
                if (!ad || path[w.Item1].Count == 1) eulerList.Add(new EulerRes { node = w.Item1, parent = w.Item2, direction = 1 });
                if (ad)
                {
                    s.Pop();
                    eulerList.Add(new EulerRes { node = w.Item1, parent = w.Item2, direction = -1 });
                }
            }
            return eulerList;
        }
    }
    class LIB_FastIO
    {
        public LIB_FastIO() { str = Console.OpenStandardInput(); }
        readonly Stream str;
        readonly byte[] buf = new byte[1024];
        int len, ptr;
        public bool isEof = false;
        public bool IsEndOfStream { get { return isEof; } }
        byte read()
        {
            if (isEof) throw new EndOfStreamException();
            if (ptr >= len)
            {
                ptr = 0;
                if ((len = str.Read(buf, 0, 1024)) <= 0)
                {
                    isEof = true;
                    return 0;
                }
            }
            return buf[ptr++];
        }
        char Char()
        {
            byte b = 0;
            do b = read();
            while (b < 33 || 126 < b);
            return (char)b;
        }
        virtual public string Scan()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
                sb.Append(b);
            return sb.ToString();
        }
        virtual public long Long()
        {
            long ret = 0; byte b = 0; var ng = false;
            do b = read();
            while (b != '-' && (b < '0' || '9' < b));
            if (b == '-') { ng = true; b = read(); }
            for (; true; b = read())
            {
                if (b < '0' || '9' < b)
                    return ng ? -ret : ret;
                else ret = ret * 10 + b - '0';
            }
        }
        virtual public double Double() { return double.Parse(Scan(), CultureInfo.InvariantCulture); }
    }
    class LIB_FastIODebug : LIB_FastIO
    {
        Queue<string> param = new Queue<string>();
        string NextString() { if (param.Count == 0) foreach (var item in Console.ReadLine().Split(' ')) param.Enqueue(item); return param.Dequeue(); }
        public LIB_FastIODebug() { }
        public override string Scan() => NextString();
        public override long Long() => long.Parse(NextString());
        public override double Double() => double.Parse(NextString());
    }
}