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.*;
 
public class Main {
 
    public static void main(String[] args) {
        Scanner stdIn = new Scanner(System.in);
        int N = stdIn.nextInt();
        int[] A = new int[N];
        for (int i = 0; i < N; i++) {
            A[i] = stdIn.nextInt();
        }
        stdIn.close();
        int[] cnt = new int[N];
        for (int i = 0; i < N; i++) {
            cnt[i] = 0;
            A[i]--;
        }
        for (int i = 0; i < N; i++) {
            cnt[A[i]]++;
        }

        // 消さないとき
        long total = 0;
        for (int i = 0; i < N; i++) {
            total += choose2(cnt[i]);
        }
        // i番目を消したとき
        for (int i = 0; i < N; i++) {
            long ans = total;
            ans -= choose2(cnt[A[i]]);
            ans += choose2(cnt[A[i]] - 1);
            System.out.println(ans);
        }
    }

    // n個の中から2個選ぶ関数
    public static long choose2(long n) {
        return n * (n - 1) / 2;
    }
}