Problem Statement

You are given a permutation $P = (P_1, P_2, \ldots, P_N)$ of $(1, 2, \ldots, N)$. Takahashi can repeatedly perform the following operation on $P$ (possibly zero times):

• Choose an integer $i$ satisfying $1 \leq i \leq N-1$. Pay a cost of $i$, and swap $P_i$ and $P_{i+1}$.

Find the minimum total cost required to sort $P$ in ascending order.

Constraints

• $2 \leq N \leq 2 \times 10^5$
• $(P_1, P_2, \ldots, P_N)$ is a permutation of $(1, 2, \ldots, N)$.
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N
P_1 P_2 \ldots P_N

Output

Print the minimum total cost required to sort $P$ in ascending order.