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.*;
import java.util.Map.Entry;
 
class Main {
	 static int mod =  (int) (Math.pow(10,9)+7);
//	 static int mod = 998244353;
	 public static void main(String[] args) {
	        Scanner sc = new Scanner(System.in);
	        int N = sc.nextInt();
	        long[] m = new long[N+1];
	        int[] a = new int[N];
	        for (int i=0 ; i<N; i++) {
	            a[i] = Integer.parseInt(sc.next());
	            m[a[i]]++;
	        }
	        long sum=0;
	        for(int i=0;i<N+1;i++) {
	        	if(m[i]>1) {
	        		sum=sum+((m[i]*(m[i]-1))/2l);
	        	}
	        }
	        for(int i=0;i<N;i++) {
	        	if(m[a[i]]>1) {
	        		System.out.println((long)sum-m[a[i]]+1);
	        	} else {
	        		System.out.println(sum);
	        	}
	        }
	        
	 }
}
