F - Shift and Inversions

Score : $600$ points

Problem Statement

Given is a sequence $A = [a_0, a_1, a_2, \dots, a_{N-1}]$ that is a permutation of $0, 1, 2, \dots, N - 1$.
For each $k = 0, 1, 2, \dots, N - 1$, find the inversion number of the sequence $B = [b_0, b_1, b_2, \dots, b_{N-1}]$ defined as $b_i = a_{i+k \bmod N}$.

Constraints

• All values in input are integers.
• $2 ≤ N ≤ 3 \times 10^5$
• $a_0, a_1, a_2, \dots, a_{N-1}$ is a permutation of $0, 1, 2, \dots, N - 1$.

Input

Input is given from Standard Input in the following format:

$N$

$a_0$ $a_1$ $a_2$ $\cdots$ $a_{N-1}$

Output

Print $N$ lines.
The $(i + 1)$-th line should contain the answer for the case $k = i$.

4
0 1 2 3

0
3
4
3

We have $A = [0, 1, 2, 3]$.

For $k = 0$, the inversion number of $B = [0, 1, 2, 3]$ is $0$.
For $k = 1$, the inversion number of $B = [1, 2, 3, 0]$ is $3$.
For $k = 2$, the inversion number of $B = [2, 3, 0, 1]$ is $4$.
For $k = 3$, the inversion number of $B = [3, 0, 1, 2]$ is $3$.

10
0 3 1 5 4 2 9 6 8 7

9
18
21
28
27
28
33
24
21
14