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 {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		long H[] = new long[N];
		int A[] = new int[N];
		for(int i = 0 ; i < N ; ++i){
			A[i] = sc.nextInt();
			A[i] = A[i] - 1;
			H[A[i]]++;
		}
		long T = 0;
		for(long h : H){
			T += h * (h - 1) / 2;
		}
		
		for(int i = 0 ; i < N ; ++i){
			int a = A[i];
			if(H[a] == 1){
				System.out.println(T);
			}else{
				long h = H[a];
				long h1 = h * (h - 1) / 2;
				long h2 = (h - 1) * (h - 2) / 2;
				System.out.println(T - h1 + h2);				
			}
		}
	}
}
