Banned K

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

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

N A_1 A_2 ... A_N

outputFormat

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

样例

8
1 2 1 4 2 1 4 1

5
7
5
7
7
5
7
5

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