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+1];
        int[] b = new int[n];
        for (int i = 0; i < n; i++) {
            int x = sc.nextInt();
            b[i] = x;
            a[x]++;
        }
        long[] s = new long[n+1];
        long sum = 0L;
        for (int i = 0; i < n; i++) {
            if(a[b[i]] < 2 || 0 < s[b[i]])continue;
            long x = (long)a[b[i]]*(a[b[i]]-1L)/2L;
            long y = (long)(a[b[i]]-1L)*(a[b[i]]-2L)/2L;
            sum += x;
            s[b[i]] = x-y;
        }
        StringBuilder sb = new StringBuilder();
        for (int i = 0; i < n; i++) {
            long t = sum - s[b[i]];
            sb.append(t + "\n");
        }
        System.out.print(sb.toString());
        sc.close();

    }

}
