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.math.*;

class Main{
public static void main(String args[]){
   Scanner sc = new Scanner(System.in);
   int n = sc.nextInt();
   long[] count = new long[200005];
   for(int i=0;i<200005;i++){
     count[i] = 0;
   }
   int[] a = new int[n];
   for(int i=0;i<n;i++) {     
   int t = sc.nextInt();
   a[i] = t;
   count[t] += 1;
            }
   long ret = 0;
   for(int i=0;i<200005;i++){
     ret += count[i]*(count[i]-1);
   }
   ret /= 2;
   for(int i=0;i<n;i++) { 
   int t = a[i];
   long remove = count[t]*(count[t]-1) - (count[t]-1)*(count[t]-2);
   remove /= 2;
   System.out.println(ret-remove);
   }
}
}
