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.io.*;
public class Main
{
    public static void main(String args[])throws Exception
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in)); 
        PrintWriter pw=new PrintWriter(System.out);
        int n=Integer.parseInt(br.readLine());
        int cntr[]=new int[200001];
        int arr[]=new int[n];
        long sum=0;
        String str[]=br.readLine().split(" ");
        for(int i=0;i<n;i++)
        {
            arr[i]=Integer.parseInt(str[i]);
            cntr[arr[i]]++;
        }
        for(int i=1;i<=200000;i++)
        sum+=(long)(cntr[i]-1)*cntr[i]/2;
        for(int i=0;i<n;i++)
        pw.println(sum-cntr[arr[i]]+1);
        pw.flush();
        pw.close();
    }
}
