Swap and Flip

We have N cards numbered 1, 2, ..., N. Card i (1 \leq i \leq N) has an integer A_i written in red ink on one side and an integer B_i written in blue ink on the other side. Initially, these cards are arranged from left to right in the order from Card 1 to Card N, with the red numbers facing up.

Determine whether it is possible to have a non-decreasing sequence facing up from left to right (that is, for each i (1 \leq i \leq N - 1), the integer facing up on the (i+1)-th card from the left is not less than the integer facing up on the i-th card from the left) by repeating the operation below. If the answer is yes, find the minimum number of operations required to achieve it.

• Choose an integer i (1 \leq i \leq N - 1). Swap the i-th and (i+1)-th cards from the left, then flip these two cards.

Constraints

• 1 \leq N \leq 18
• 1 \leq A_i, B_i \leq 50 (1 \leq i \leq N)
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N A_1 A_2 ... A_N B_1 B_2 ... B_N

Output

If it is impossible to have a non-decreasing sequence, print -1. If it is possible, print the minimum number of operations required to achieve it.

Examples

Input

3 3 4 3 3 2 3

Output

1

Input

2 2 1 1 2

Output

-1

Input

4 1 2 3 4 5 6 7 8

Output

0

Input

5 28 15 22 43 31 20 22 43 33 32

Output

-1

Input

5 4 46 6 38 43 33 15 18 27 37

Output

3

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

N A_1 A_2 ... A_N B_1 B_2 ... B_N

outputFormat

Output

If it is impossible to have a non-decreasing sequence, print -1. If it is possible, print the minimum number of operations required to achieve it.

Examples

Input

3 3 4 3 3 2 3

Output

1

Input

2 2 1 1 2

Output

-1

Input

4 1 2 3 4 5 6 7 8

Output

0

Input

5 28 15 22 43 31 20 22 43 33 32

Output

-1

Input

5 4 46 6 38 43 33 15 18 27 37

Output

3

样例

5
28 15 22 43 31
20 22 43 33 32

-1