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.

Examples

Input

5
1 1 2 1 2


Output

2
2
3
2
3


Input

4
1 2 3 4


Output

0
0
0
0


Input

5
3 3 3 3 3


Output

6
6
6
6
6


Input

8
1 2 1 4 2 1 4 1


Output

5
7
5
7
7
5
7
5
import java.util.*;

public class Main{
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);

		int N = sc.nextInt();
		int[] A = new int[N];
		long[] countA = new long[N+1];
		long[] plus = new long[N+1];
		long[] minus = new long[N+1];
		for( int i=0; i<N; i++ ){
			A[i] = sc.nextInt();
			countA[ A[i] ]++;
		}
		long total = 0;      
		for( int i=1; i<=N; i++ ){
			if( countA[i]>1 ){
				plus[i] = countA[i]*(countA[i]-1)/2;
				minus[i] = (countA[i]-1)*(countA[i]-2)/2;
				total += plus[i];
			}
		}     
		for( int i=0; i<N; i++ ){
			System.out.println( total - plus[A[i]] + minus[A[i]] );
		}    
	}
}
