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();
    long x[] = new long[N+1];//iが書かれたボールが何個入っているかを管理する配列(i番目がiのボール)
    int A[] = new int[N];//ボールを管理
    for(int i=0;i<N;i++){
      A[i]=sc.nextInt();
      x[A[i]]++;
    }
    //選び方の総数(どれも削らない場合)を算出
    long allCnt=0;
    for(int i=1;i<=N;i++){
      if(x[i]<=1){
        //一個以下なら何もしない
        allCnt=allCnt;
      }else{
        allCnt=allCnt+(x[i]*(x[i]-1))/2;
      }
    }
    
    //あとは総数からそのボールに書かれている数字を引いた数をそれぞれ出力(具体的にはx[A[i]]個減らす)
    for(int i=0;i<N;i++){
      
      System.out.println(Math.max(0,allCnt-x[A[i]]+1));
      

    }
    
  }
  

  
}
