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.*;
import java.lang.Math;

public class Main {
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        long[] a = new long[n];
        Map<Long, Long> mp = new HashMap<>();
        for(int i = 0; i < n; ++i){
            a[i] = sc.nextLong();
            long v = mp.getOrDefault(a[i], 0L);
            mp.put(a[i], v+1);
        }
      
        long sum = 0;
        for(long v : mp.values()){
            sum += v * (v-1) / 2L;
        }

      for(int i = 0; i < n; ++i){
            long v = mp.get(a[i]);
            long ans = sum;
            ans -= v*(v-1)/2L;
            ans += (v-1)*(v-2)/2L;
            System.out.println(ans);
        }
    }
}
