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.*;

class Main {

    static public long[] solve(int N, int[] A) {
        int[] d = new int[N+1];
        for (int n : A) d[n]++;
        
        long sum = 0;
        for (long v : d) {
            sum += v*(v-1)/2;
        }

        long[] res = new long[N];
        int i = 0;
        for (int n : A) {
            res[i++] = (d[n]==1) ? sum : (sum-d[n]+1);
        }
        return res;
    }

    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();
        }
        sc.close();

        for (long n : solve(N, A))
            System.out.println(n);
    }
}