ReverseSort

A permutation of N numbers from 1 to N A1, A2, ……, AN is given. You can perform the operation reverse (i, j) to reverse the order of the numbers in the interval [i, j] (1 ≤ i ≤ j ≤ N) for this permutation. For example, if reverse (2, 4) is applied to [1, 2, 3, 4, 5], it becomes [1, 4, 3, 2, 5]. Calculate how many operations you need to do at a minimum to get the permutation sorted in ascending order.

Constraints

• N is an integer

• 2 ≤ N ≤ 10

Input

The input is given in the following format.

N A1 A2 …… AN

Output

Print the solution to the problem on one line.

Examples

Input

5 1 4 3 5 2

Output

2

Input

5 3 1 5 2 4

Output

4

Input

3 1 2 3

Output

0

Input

10 3 1 5 2 7 4 9 6 10 8

Output

9

inputFormat

Input

The input is given in the following format.

N A1 A2 …… AN

outputFormat

Output

Print the solution to the problem on one line.

Examples

Input

5 1 4 3 5 2

Output

2

Input

5 3 1 5 2 4

Output

4

Input

3 1 2 3

Output

0

Input

10 3 1 5 2 7 4 9 6 10 8

Output

9

样例

3
1 2 3

0