Score : $400$ points

Problem Statement

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.

5
1 1 2 1 2

2
2
3
2
3

Consider the case $k=1$ for example. The numbers written on the remaining balls are $1,2,1,2$. From these balls, there are two ways to choose two distinct balls so that the integers written on them are equal. Thus, the answer for $k=1$ is $2$.

4
1 2 3 4

0
0
0
0

No two balls have equal numbers written on them.

5
3 3 3 3 3

6
6
6
6
6

Any two balls have equal numbers written on them.

8
1 2 1 4 2 1 4 1

5
7
5
7
7
5
7
5