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.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        long[] A = new long[n + 1];
        int[] Aa = new int[n];
        long result = 0;
        for(int i = 0; i < n; i++) {
            Aa[i] = sc.nextInt();
            A[Aa[i]]++;
        }
        for(int i = 0; i < n + 1; i++) {
            result += A[i] * (A[i] - 1) / 2;
        }
        for(int i = 0; i < n; i++) {
            System.out.println(result - (A[Aa[i]] > 1 ? A[Aa[i]] - 1 : 0));
        }
    }
}
