Jeff and Furik

题意翻译

有一个长度为n的排列p,Jeff每次操作选两个相邻元素交换，Furik每次操作随机执行下列操作之一： 1.对于所有p[i]<p[i+1],随机取一对p[i]与p[i+1]交换 2.对于所有p[i]>p[i+1],随机取一对p[i]与p[i+1]交换 两个操作被选中的概率均为0.5。如果一个操作无法进行，那么furik必定会进行可以进行的操作。 两人轮流操作，Jeff先手。当排列为升序时，游戏结束。 Jeff希望游戏尽早结束，那么在Jeff每次操作最优的情况下，游戏结束时两人操作次数的期望值是多少？。

题目描述

Jeff has become friends with Furik. Now these two are going to play one quite amusing game. At the beginning of the game Jeff takes a piece of paper and writes down a permutation consisting of $ n $ numbers: $ p_{1} $ , $ p_{2} $ , $ ... $ , $ p_{n} $ . Then the guys take turns to make moves, Jeff moves first. During his move, Jeff chooses two adjacent permutation elements and then the boy swaps them. During his move, Furic tosses a coin and if the coin shows "heads" he chooses a random pair of adjacent elements with indexes $ i $ and $ i+1 $ , for which an inequality $ p_{i}&gt;p_{i+1} $ holds, and swaps them. But if the coin shows "tails", Furik chooses a random pair of adjacent elements with indexes $ i $ and $ i+1 $ , for which the inequality $ p_{i}&lt;p_{i+1} $ holds, and swaps them. If the coin shows "heads" or "tails" and Furik has multiple ways of adjacent pairs to take, then he uniformly takes one of the pairs. If Furik doesn't have any pair to take, he tosses a coin one more time. The game ends when the permutation is sorted in the increasing order. Jeff wants the game to finish as quickly as possible (that is, he wants both players to make as few moves as possible). Help Jeff find the minimum mathematical expectation of the number of moves in the game if he moves optimally well. You can consider that the coin shows the heads (or tails) with the probability of $ 50 $ percent.

输入输出格式

输入格式

The first line contains integer $ n $ $ (1<=n<=3000) $ . The next line contains $ n $ distinct integers $ p_{1} $ , $ p_{2} $ , $ ... $ , $ p_{n} $ $ (1<=p_{i}<=n) $ — the permutation $ p $ . The numbers are separated by spaces.

输出格式

In a single line print a single real value — the answer to the problem. The answer will be considered correct if the absolute or relative error doesn't exceed $ 10^{-6} $ .

输入输出样例

输入样例 #1

2
1 2

输出样例 #1

0.000000

输入样例 #2

5
3 5 2 4 1

输出样例 #2

13.000000

说明

In the first test the sequence is already sorted, so the answer is $ 0 $ .