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.Random;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        //int n = 200000;
        int[] a = new int[n];
        long[] fq = new long[n + 1];
        //Random rnd = new Random(12313);
        for (int i = 0; i < n; ++i) {
            a[i] = sc.nextInt();
            //a[i] = rnd.nextInt(2) + 1; //rnd.nextInt(n + 1) + 1;
            fq[a[i]]++;
        }
        long c = 0;
        for (int i = 1; i <= n; ++i) {
            c += (fq[i] >= 2) ? (fq[i] * (fq[i] - 1)) / 2 : 0;
        }
        for (int i = 0; i < n; ++i) {
            if (fq[a[i]] >= 2) {
                System.out.println(c - (fq[a[i]] - 1));
            }
            else {
                System.out.println(c);
            }
        }
    }
}
