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.Scanner;
public class Main {

	@SuppressWarnings("resource")
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		int N=sc.nextInt();
		int A[]=new int[N];
		int B[]=new int[N];
		for(int i=0;i<N;i++) {
			A[i]=sc.nextInt();
			B[A[i]-1]++;
		}
		long ans=0;
		for(int i=0;i<N;i++) {
			ans+=calcNumOfCombination(B[i],2);
		}
		for(int i=0;i<N;i++) {
			System.out.println(ans-calcNumOfCombination(B[A[i]-1], 2)+calcNumOfCombination(B[A[i]-1]-1, 2));
		}

	}
	public static long calcNumOfCombination(int n, int r){
		if(n==0||n==1) {
			return 0;
		}else {
        long num = 1;
        for(int i = 1; i <= r; i++){
            num = num * (n - i + 1) / i;
        }
        return num;}
    }
}
