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.*;
class Main {
  public static void main(String[] args) {
    Scanner sc = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
		
		int n= sc.nextInt();
		int arr[] = new int[n+1];
		for(int i=1;i<=n;i++)
			arr[i] = sc.nextInt();
		long occ[] = new long[(int)2e5+1];
		HashMap<Integer,Long> hm = new HashMap<>();
		for(int i=1;i<=n;i++){
			occ[arr[i]]+=1;
			hm.put(arr[i],0l);
		}
		
		ArrayList<Integer> al = new ArrayList<>(hm.keySet());
		long total =0;
		int len = al.size();
		for(int i=0;i<len;i++){
			int val = al.get(i);
			long oc = occ[val];
			long temp = ((oc)*(oc-1))/2;
			hm.put(val,temp);
			total+=temp;
		}
		StringBuilder sb = new StringBuilder();
		for(int i=1;i<=n;i++){
			int val = arr[i];
			long gh =total-(occ[val]-1);
			sb.append(gh+"\n");
		}
		System.out.print(sb.toString());
	}
}