COCI '14 Contest 7 #6 Police

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Points: 30 (partial)
Time limit: 0.6s
Memory limit: 64M

Problem types

Librarian Jurica has shelves in his library, and each shelf can contain books. Jurica is a good librarian so he decided to make an inventory in the library and, if it's necessary, return the books that aren't in their place to the right place. He moves the books in the following way:

• moving the books one place to the left or to the right on a shelf if the place to the left or to the right is available,
• taking a book from a shelf and placing it to an available place on that or any other shelf.

Careful Jurica can't move books if he has a book in his hands. Additionally, he can't take more than one book at once.

Jurica has been having back pains ever since he had to move all the volumes of the printed edition of Wikipedia from the first to the second floor so now he wants to put all the books in place with as little lifting as possible because his back is hurting. What is the minimal number of lifting he needs?

Input

The first line of input contains the integers and .

Each of the following lines contain integers, the line describing the current state of the shelf.

Number denotes an empty place on the shelf, and a number different than denotes that there is a book in that place denoted with that number. All books are denoted with different numbers from to , where is the total number of books on the shelves. After that, an additional lines follow, each containing integers, the line describing the wanted state of the shelf.

In the initial and final state of the shelves, the same books will appear.

Output

The first and only line of output must contain the required minimal number of lifting or if it is impossible to arrange the books in the aforementioned way.

Scoring

In test cases worth of points in total, each book will be on the same shelf in the initial and final state.

Sample Input 1

2 4
1 0 2 0
3 5 4 0
2 1 0 0
3 0 4 5

Sample Output 1

2

Explanation for Sample Output 1

Jurica will move book 1 one place to the right, then lift book 2 and move it over to the first place of the first shelf. He lifts book 5 and places it on the fourth place on the second shelf.

Sample Input 2

3 3
1 2 3
4 5 6
7 8 0
4 2 3
6 5 1
0 7 8

Sample Output 2

4

Sample Input 3

2 2
1 2
3 4
2 3
4 1

Sample Output 3

-1