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
// package app;

import java.math.BigDecimal;
import java.util.Arrays;
import java.util.HashMap;
import java.util.Map;
import java.util.Objects;
import java.util.Scanner;
import java.util.stream.Stream;

public class Main {

    public static void main(final String[] args) throws Exception {

        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int a[] = new int[n];

        Map<Integer, Long> map = new HashMap<>();

        for (int i = 0; i < n; i++) {
            a[i] = sc.nextInt();

            if (!map.containsKey(a[i])) {
                map.put(a[i], (long) 1);
            } else {
                map.put(a[i], map.get(a[i]) + 1);
            }
        }

        long all = 0;

        for (int key : map.keySet()) {
            all += map.get(key) * (map.get(key) - 1) / 2;
        }

        for (int i = 0; i < n; i++) {
            long tmp = map.get(a[i]);
            System.out.println(all - (tmp - 1));
        }
    }
}