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.io.*;
import java.util.*;


class Main {
    public static void main(String[] args) {
        Scanner scr = new Scanner(System.in);
//        int t = scr.nextInt();
//        while (t-- > 0)
        solve(scr);
    }


    static void solve(Scanner scr) {
        int n = scr.nextInt();
        int[] a = new int[n];
        long[] b = new long[n + 1];

        for (int i = 0; i < n; i++) {
            a[i] = scr.nextInt();
            b[a[i]]++;
        }
        long s = 0;
        for (int i = 0; i < n+1; i++) {
            s += (b[i] * (b[i] - 1)) / 2;
        }

        for (int i = 0; i < n; i++) {
            long c = (b[a[i]] - 1) * (b[a[i]] - 2) / 2;
            long d = (b[a[i]]) * (b[a[i]] - 1) / 2;
            System.out.println(s - d + c);
        }


    }



}



