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 {

    static final int MOD = 1000000007;

    public static void main(String[] args) {

        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int a[] = new int[n]; //数列
        long count[] = new long[n]; //各値の出現回数
        long sum=0; //Nから選ぶときのパターン

        for(int i=0;i<n;i++)count[i]=0;

        for(int i=0;i<n;i++){
            a[i]=sc.nextInt()-1;
            count[a[i]]++;
        }

        for(int i=0;i<n;i++){
            if(count[i]>1){
                sum += (count[i]*(count[i]-1))/2;
            }
        }

        for(int i=0;i<n;i++){
            int num = a[i]; //numのボールが一個減る
            long dif = 0;
            if(count[num]>1){
                dif = count[num]-1;
            }
            System.out.println(sum-dif);
        }

    }
}
