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.*;
import java.io.BufferedInputStream;

public class Main {
  public static void main(String[] args){
    Scanner sc = new Scanner (new BufferedInputStream(System.in));
    int n = sc.nextInt();
    int[] num = new int[n];
    long[] count = new long[n + 1];
    for(int i = 0; i < n; ++i) {
      num[i] = sc.nextInt();
      count[num[i]]++;
    }
    long res = 0;
    for(int i = 0; i <= n; ++i) {
        if(count[i] > 1) res += count[i] * (count[i] - 1) / 2;
    }
    for(int i = 0; i < n; ++i) {
        if(count[num[i]] < 2) System.out.println(res);
        else System.out.println(res - count[num[i]] * (count[num[i]] - 1) / 2 + (count[num[i]] - 1)* (count[num[i]] - 2) / 2);
    }
  }
}