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];
        int mx = 0;
        for(int i=0;i<n;i++){ a[i] = sc.nextInt(); mx = Math.max(mx,a[i]);}
        int[] dp = new int[mx+1];
        for(int i=0;i<n;i++){
            dp[a[i]]++;
        }
        long ans = 0;
        for(int i=1;i<=mx;i++){
            long x = dp[i];
            x *= (x-1);
            x/=2;
            ans +=x;
        }
        for(int i=0;i<n;i++){
            int y = dp[a[i]];
            System.out.println(ans-y+1);
        }
     }
}