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.BufferedInputStream;
import java.math.BigInteger;
import java.util.Scanner;
public class Main {
    public static long combination(int n,int k){
        if(n==0)
            return 0;
        if(k==0)
            return 1;
        else
            return combination(n,k-1)*(n-k+1)/k;

    }
    public static void main(String[] args) {
        Scanner sc = new Scanner(new BufferedInputStream(System.in));
        int n=sc.nextInt();
        int a[]=new int[n];
        int b[]=new int[201001];
        int c[]=new int[n];
        for(int i=0;i<n;i++){
            a[i]=sc.nextInt();
            b[a[i]]++;
        }
        long m=0;
        for(int i=0;i<b.length;i++) {
            m += Main.combination(b[i],2);
        }
        for(int i=0;i<n;i++){
            long v=m-Main.combination(b[a[i]],2)+Main.combination(b[a[i]]-1,2);
            System.out.println(v);

        }

    }
}