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.Scanner;

class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int[] A = new int[N];
		for(int i =0;  i<N; i++){
			A[i] = sc.nextInt();
		}
		int[] count = new int[N];

		for(int a : A) {
			count[a-1] ++;
		}

		long sum = 0;
		for(int c : count) {
			sum += combination(c, 2);
		}
		
		for(int k=0; k < N; k++) {
			System.out.println(sum - (count[A[k]-1] -1 ));
		}

	}
	//組み合わせの数nCrを計算
	static long combination(long n, long r){
		if(n < r) return 0;
		long num = 1;
		for(long i = 1; i <= r; i++){
			num = num * (n - i + 1) / i;
		}
		return num;
	}
}





