Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

B. Jeff and Furik

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputJeff 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} > *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} < *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.

Input

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.

Output

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}.

Examples

Input

2

1 2

Output

0.000000

Input

5

3 5 2 4 1

Output

13.000000

Note

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

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Mar/19/2019 11:55:38 (f2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|