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.math.BigInteger;
import java.util.HashMap;
import java.util.Map;
import java.util.Scanner;

public class Main {

	public static final MyScanner in = new MyScanner();

	public static void main(String[] args) {

		long all=0;
		Map<Integer,Integer> map = new HashMap<>();
		int N = in.nextInt();
		int[] A = new int[N];
		for(int i=0;i<N;i++) {
			A[i] = in.nextInt();
			int a = map.getOrDefault(A[i], -1) + 1;
			all+=a;
			map.put(A[i], a);
		}

		for(int a: A) {
			System.out.println(all - map.get(a));
		}
	}


	public static class MyScanner {
		Scanner sc = new Scanner(System.in);
		String next() { return sc.next();}
		int nextInt() { return Integer.valueOf(sc.next());}
		long nextLong() { return Long.valueOf(sc.next()); }
	}
}