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.math.*;
public class Main {
    static final int MOD = 1_000_000_007; // 10^9+7
    //static final int MAX = 2_147_483_646; // intの最大値
    static final int INF = 1_000_000_000; // 10^9
    static final int MAX = 10_000_000;
    public static void main(String args[]) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] ary = new int[n];
        int[] count = new int[n+1];
        for(int i = 0;i < n;i++){
            ary[i] = sc.nextInt();
            count[ary[i]]++;
        }
        long ans = 0;
        for(int i = 0;i < n+1;i++){
            long tmp = count[i];
            tmp *= count[i]-1;
            tmp /=2;
            ans+= tmp;
        }
        for(int i = 0;i < n;i++){
            System.out.println(ans-count[ary[i]]+1);
        }

    }       
}




