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.io.PrintWriter;
import java.util.*;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		
		int N = sc.nextInt();
		int[] A = new int[N];
		int[] cnt = new int[N];
		for(int i=0; i<N; i++) {
			A[i] = sc.nextInt()-1;
			cnt[A[i]]++;
		}
		
		long total = 0;
		for(int i=0; i<N; i++) {
			if(cnt[i]>=2) {
				total += (long)cnt[i]*(cnt[i]-1)/2;
			}
		}
		
		for(int i=0; i<N; i++) {
			long ans = total - (cnt[A[i]]>=2 ? cnt[A[i]]-1 : 0);
			pw.println(ans);
		}
		
		pw.close();
		sc.close();
	}
}
