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 long fu(int n){
		if(n>0){
			return (long)n*(long)(n-1)/2;
		}else{return (long)0;}
	}
	
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
  	int n=sc.nextInt();
  	long f=0;
  	int[] a=new int[n],b=new int[n];
  	long[] c=new long[n];
  	for(int i=0;i<n;i++){
  		b[i]=0;
  		c[i]=0;
  	}
  	for(int i=0;i<n;i++){
  		a[i]=sc.nextInt();
  		b[a[i]-1]++;
  		c[a[i]-1]=fu(b[a[i]-1]);
  	}
  	for(int i=0;i<n;i++){
  		f+=c[i];
  	}
  	for(int i=0;i<n;i++){
  		long e=f;
  		if(b[a[i]-1]>1){
  			e=(e-c[a[i]-1])+fu(b[a[i]-1]-1);
  		}else{e=e;}
  		System.out.println(e);
  	}
  }
}