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)

/*******************************************c#
* 20.04.16 AtCoder Beginner Contest 159. C - Maximum Volume
*
*
*********************************************/
/*********************************************

::test input::

*********************************************/
using System; //Console, IComparable
using System.IO; //StreamWriter 
using System.Linq; //Select(), Where(), OrderBy(), Count()
using System.Collections.Generic; //List<T>
using System.Reflection; //PropertyInfo[], GetProperties[]
using static System.Console; using static IOmacro.CInput;

namespace Nalgo {
    public class combination {
        public long combs(int n, int r) {
            if (n == r || r == 0) return 1L;
            else return (combs(n-1, r-1) + combs(n-1, r));
        }
    }
    
}


namespace tempName {
    public class CRun{
        private static class gv{
            public static int N;
            public static int[] A;
            public static int[] H;
        }
    
        public void build(){            
            gv.N = _int;
            gv.A = _inta;
            gv.H = new int[gv.N +2]; Array.Clear(gv.H, 0, gv.H.Length);
            foreach (var x in gv.A) {
                gv.H[x]++;
            }
        }
    
        public void solve(){
            var algo = new Nalgo.combination();
            
            long ans = 0;
            
            foreach (int x in gv.H) {
                ans += (long)(x >= 2 ? algo.combs((int)x, 2) : 0);
            }
            
            foreach (var x in gv.A) {
                long ans_buf = ans;
                int H_now = gv.H[x];
                
                ans_buf -= (H_now >= 2 ? (long)(H_now -1) : 0L);
                Console.WriteLine(ans_buf);
            }
            //_writer.Close();
            
            
        }
    }

    class Program { 
        static void Main() { 
            var run = new CRun();
            run.build();
            run.solve();
            
            
        } 
    }
}

namespace IOmacro {
    public static class CInput {
        public static StreamWriter _writer = new StreamWriter(Console.OpenStandardOutput());
        public static string _string{get{return Console.ReadLine();}}
        public static string[] _stringa{get{return (Console.ReadLine().Split());}}
        public static int _int{get{return int.Parse(Console.ReadLine());}}
        public static int[] _inta{get{return Console.ReadLine().Split().Select(x=>int.Parse(x)).ToArray();}}
        public static long _long{get{return long.Parse(Console.ReadLine());}}
        public static long[] _longa{get{return Console.ReadLine().Split().Select(x=>long.Parse(x)).ToArray();}}    
    }
}