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

见题面

见题面