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: Time Limit Exceeded)

using System;
using System.Linq;
using System.Collections.Generic;

namespace AtCoder
{
	class Program
	{
		public static void Main()
		{
			var inputNum = IO.ReadInt();
			var numbers = IO.ReadIntArray();
			var numberCounts = numbers.GroupBy(iNumber => iNumber)
										   .ToDictionary(iGroup => iGroup.Key,
														 iGroup =>
			{
				var numberNum = iGroup.Count();
				if(numberNum < 2) { return new[] { 0L , 0L }; }

				return new[]
				{
					Util.CombinationNum(numberNum , 2),
					(numberNum == 2) ? 0 : Util.CombinationNum(numberNum - 1 , 2)
				};
			});

			foreach(var iIndex in Enumerable.Range(0 , inputNum))
			{
				var number = numbers[iIndex];
				var combinationNum = 0L;
				foreach(var iPair in numberCounts)
				{
					var index = (iPair.Key == number) ? 1 : 0;
					combinationNum += iPair.Value[index];
				}
				IO.Write(combinationNum);
			}
		}
	}

	public static class IO
	{
		public static string   Read()								 { return Console.ReadLine(); }
		public static string[] ReadArray(char iSplitter = ' ')		 { return Read().Split(iSplitter); }
		public static int	   ReadInt()							 { return int.Parse(Read()); }
		public static int[]	   ReadIntArray(char iSplitter = ' ')	 { return ReadArray().Select(iText => int.Parse(iText)).ToArray(); }
		public static long	   ReadLong()							 { return int.Parse(Read()); }
		public static long[]   ReadLongArray(char iSplitter = ' ')	 { return ReadArray().Select(iText => long.Parse(iText)).ToArray(); }
		public static double   ReadDouble()							 { return double.Parse(Read()); }
		public static double[] ReadDoubleArray(char iSplitter = ' ') { return ReadArray().Select(iText => double.Parse(iText)).ToArray(); }
		public static char[]   ReadCharArray()						 { return Read().ToCharArray(); }

		public static void Write(string iValue)									   { Console.WriteLine(iValue); }
		public static void Write(int iValue)									   { Console.WriteLine(iValue); }
		public static void Write(IEnumerable<int> iValue , string iJoinWord = " ") { Console.WriteLine(string.Join(iJoinWord , iValue)); }
		public static void Write(long iValue)									   { Console.WriteLine(iValue); }
		public static void Write(double iValue)									   { Console.WriteLine(iValue); }
		public static void Write(decimal iValue)								   { Console.WriteLine(iValue); }
		public static void Write(bool iValue)									   { Console.WriteLine(iValue ? "Yes" : "No"); }
	}

	public static class Util
	{
		public static long Gcd(long i0 , long i1) { return (i0 > i1) ? _Gcd(i0 , i1) : _Gcd(i1 , i0); }
		public static long Lcm(long i0 , long i1) { return (i0 * i1) / Gcd(i0 , i1); }
		public static long ModPow(long iBaseNumber , long iPow , long iModNumber)
		{
			var num = 1L;
			while(iPow != 0)
			{
				if((iPow & 0x1) != 0)
				{
					num = (num * iBaseNumber) % iModNumber;
				}
				iBaseNumber = (iBaseNumber * iBaseNumber) % iModNumber;
				iPow >>= 1;
			}
			return num;
		}
		public static long CombinationNum(int iLeftNumber , int iRightNumber)
		{
			if(iRightNumber == 0) { return 1; }
			if(iLeftNumber == 0)  { return 0; }
			return iLeftNumber * CombinationNum(iLeftNumber - 1 , iRightNumber - 1) / iRightNumber;
		}

		private static long _Gcd(long i0 , long i1)	{ return (i1 == 0) ? i0 : _Gcd(i1 , i0 % i1); }
	}
}