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 a = sc.nextInt();
		long [] in = new long [a];
        long [] in2 = new long [a];
        long b = 0;
        long c;
        int d,e;
        for(int i=0;i<a;i++){in[i] = sc.nextLong();
                             d = (int)in[i];
                             in2[d-1]++;
                            }
        for(int i=0;i<a;i++){b+=in2[i]*(in2[i]-1)/2;                                                 
                            }
        for(int i=0;i<a;i++){e = (int)in[i];
                             c = in2[e-1];
                             System.out.println(b-c+1);
                            }	
	}
}
