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];
		int[] B = new int[N];
		long buf = 0;
		for(int i = 0;i < N;i++){
			A[i] = sc.nextInt() - 1;
			B[i] = A[i];
		}
		Arrays.sort(A);
		int count = 1;
		int[] num = new int[N];
		num[A[0]] = 1;
		for(int i = 1;i < N;i++){
			if(A[i - 1] == A[i]){
				count++;
				if(i == N-1){
					num[A[i]] = count;
				}
			}else{
				num[A[i - 1]] = count;
				count = 1;
				if(i == N-1){
					num[A[i]] = 1;
				}
			}
		}
		for(int i = 0;i < N;i++){
			if(num[i] > 1){
				buf += (long)((long)num[i] * (long)(num[i] - 1) / 2);
			}
		}
		for(int i = 0;i < N;i++){
			long ans = buf;
			if(num[B[i]] > 1){
				ans -= (num[B[i]] - 1);
			}
			System.out.println(ans);
		}
	}
}