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 {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int[] A = new int[N];
        int[] count = new int[N+1];
        for (int i = 0; i < N; i++) {
            A[i] = sc.nextInt();
            count[A[i]]++;
        }

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

        StringBuilder ans = new StringBuilder();
        for (int i = 0; i < N; i++) {
            long tmp = count[A[i]] == 2 ? sum-1 : sum-(count[A[i]]-1);
            ans.append(tmp).append('\n');
        }

        System.out.print(ans);
    }
}

