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.math.*;
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];
    for (int i = 0; i < N; i++)
      A[i] = sc.nextInt();
    sc.close();

    int[] n = new int[N + 1];
    for (int i = 0; i < N; i++) n[A[i]]++;

    long sum = 0;
    long[] c = new long[N + 1];
    for (int i = 0; i < N + 1; i++)
      if (1 < n[i]) {
        c[i] = combination(n[i], 2);
        sum += c[i];
      }

    for (int i = 0; i < N; i++) {
      int a = A[i];
      long na = n[a];
      long ans = sum - c[a];
      if (2L < na) {
        ans += c[a] * (na- 2) / na;
      }
      System.out.println(ans);
    }
  }

  private static long combination(int n, int k) {
    int closer = Integer.min(n - k, k);
    long result = 1;
    for (int i = 1; i <= closer; i++)
      result = result * (n - closer + i) / i;
    return result;
  }
}