Problem:
Score : 400 points

Problem Statement

We have N balls. The i-th ball has an integer A_i written on it.

For each k=1, 2, ..., N, solve the following problem and print the answer.

Find the number of ways to choose two distinct balls (disregarding order) from the N-1 balls other than the k-th ball so that the integers written on them are equal.

Constraints

3 \leq N \leq 2 \times 10^5

1 \leq A_i \leq N

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

For each k=1,2,...,N, print a line containing the answer.

Sample Input 1

5
1 1 2 1 2

Sample Output 1

2
2
3
2
3

Consider the case k=1 for example. The numbers written on the remaining balls are 1,2,1,2.

From these balls, there are two ways to choose two distinct balls so that the integers written on them are equal.

Thus, the answer for k=1 is 2.

Sample Input 2

4
1 2 3 4

Sample Output 2

0
0
0
0

No two balls have equal numbers written on them.

Sample Input 3

5
3 3 3 3 3

Sample Output 3

6
6
6
6
6

Any two balls have equal numbers written on them.

Sample Input 4

8
1 2 1 4 2 1 4 1

Sample Output 4

5
7
5
7
7
5
7
5

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using Yorukatsu024.Questions;
using Yorukatsu024.Extensions;
using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;

namespace Yorukatsu024.Questions
{
    /// <summary>
    /// ABC159 D
    /// </summary>
    public class QuestionC : AtCoderQuestionBase
    {
        public override IEnumerable<object> Solve(TextReader inputStream)
        {
            int n = inputStream.ReadInt();
            var a = inputStream.ReadIntArray();
            var integerCount= new Dictionary<int, int>();

            foreach (var ai in a)
            {
                if (integerCount.ContainsKey(ai))
                {
                    integerCount[ai]++;
                }
                else
                {
                    integerCount.Add(ai, 1);
                }
            }

            var count = 0L;
            foreach (var pair in integerCount)
            {
                if (pair.Value >= 2)
                {
                    count += Combination(pair.Value, 2);
                }
            }

            foreach (var ai in a)
            {
                if (integerCount[ai] >= 3)
                {
                    yield return count - Combination(integerCount[ai], 2) + Combination(integerCount[ai] - 1, 2);
                }
                else if (integerCount[ai] == 2)
                {
                    yield return count - Combination(integerCount[ai], 2);
                }
                else
                {
                    yield return count;
                }
            }
        }

        public static long Combination(int n, int r)
        {
            CheckNR(n, r);
            r = Math.Min(r, n - r);

            // See https://stackoverflow.com/questions/1838368/calculating-the-amount-of-combinations
            long result = 1;
            for (int i = 1; i <= r; i++)
            {
                result *= n--;
                result /= i;
            }
            return result;
        }

        private static void CheckNR(int n, int r)
        {
            if (n <= 0)
            {
                throw new ArgumentOutOfRangeException(nameof(n), $"{nameof(n)}は正の整数でなければなりません。");
            }
            if (r < 0)
            {
                throw new ArgumentOutOfRangeException(nameof(r), $"{nameof(r)}は0以上の整数でなければなりません。");
            }
            if (n < r)
            {
                throw new ArgumentOutOfRangeException($"{nameof(n)},{nameof(r)}", $"{nameof(r)}は{nameof(n)}以下でなければなりません。");
            }
        }
    }
}


namespace Yorukatsu024
{
    class Program
    {
        static void Main(string[] args)
        {
            IAtCoderQuestion question = new QuestionC();    // 問題に合わせて書き換え
            var answers = question.Solve(Console.In);
            foreach (var answer in answers)
            {
                Console.WriteLine(answer);
            }
        }
    }
}

#region Base Classes

namespace Yorukatsu024.Questions
{

    public interface IAtCoderQuestion
    {
        IEnumerable<object> Solve(string input);
        IEnumerable<object> Solve(TextReader inputStream);
    }

    public abstract class AtCoderQuestionBase : IAtCoderQuestion
    {
        public IEnumerable<object> Solve(string input)
        {
            var stream = new MemoryStream(Encoding.Unicode.GetBytes(input));
            var reader = new StreamReader(stream, Encoding.Unicode);

            return Solve(reader);
        }

        public abstract IEnumerable<object> Solve(TextReader inputStream);
    }

}

#endregion

#region Extensions

namespace Yorukatsu024.Extensions
{
    internal static class TextReaderExtensions
    {
        internal static int ReadInt(this TextReader reader) => int.Parse(ReadString(reader));
        internal static long ReadLong(this TextReader reader) => long.Parse(ReadString(reader));
        internal static double ReadDouble(this TextReader reader) => double.Parse(ReadString(reader));
        internal static string ReadString(this TextReader reader) => reader.ReadLine();

        internal static int[] ReadIntArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(int.Parse).ToArray();
        internal static long[] ReadLongArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(long.Parse).ToArray();
        internal static double[] ReadDoubleArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(double.Parse).ToArray();
        internal static string[] ReadStringArray(this TextReader reader, char separator = ' ') => reader.ReadLine().Split(separator);
    }
}

#endregion