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 $b_i = a_{i+k \bmod N}$.

What is inversion number? The inversion number of a sequence $A = [a_0, a_1, a_2, \dots, a_{N-1}]$ is the number of pairs of indices $(i, j)$ such that $i < j$ and $a_i > a_j$.

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 $k = i$.