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 IOException{
    	// Solution sol = new Solution();
    	BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    	StringTokenizer st = new StringTokenizer(br.readLine());
    	int N = Integer.parseInt(st.nextToken());
    	st = new StringTokenizer(br.readLine());
    	HashMap<Integer, Integer> hm = new HashMap();
    	int[] arr = new int[N];
    	long[][] count = new long[N+1][3];
    	for(int i=0; i<N; i++){
    		arr[i]=Integer.parseInt(st.nextToken());
    		count[arr[i]][0]++;
    	}
    	long sum=0;
    	for(int i=1; i<=N; i++){
    		count[i][1]=count[i][0]*(count[i][0]-1)/2;
    		count[i][2]=(count[i][0]-1)*(count[i][0]-2)/2;
    		sum+=count[i][1];
    	}
    	for(int i=0; i<N; i++){
    		System.out.println(sum-count[arr[i]][1]+count[arr[i]][2]);
    	}

    }
}