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.*;
import java.io.*;
public class Main{
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		PrintWriter ou = new PrintWriter(System.out);
		int n = Integer.parseInt(sc.next());
		int[] a = new int[n];
		long[] b = new long[n];
		for(int i = 0 ; i < n ; i++){
			a[i] = Integer.parseInt(sc.next()) - 1;
			b[a[i]]++;
		}
		sc.close();
		long yono = 0;
		for(int i = 0 ; i < n ; i++){
			yono += b[i] * (b[i] - 1) / 2;
		}
		for(int i = 0 ; i < n ; i++){
			ou.print(yono - b[a[i]] + 1 + "\n");
		}
		ou.flush();
	}
}