Alice was given two $4$ x $4$ binary grids, $A$ and $B$. She wants to convert grid $A$ to $B$. She can perform any of the following operations any number of times on grid $A$ (she can't modify $B$): 

1. Rotate grid $A$ clockwise by $90$ degrees. 
2. Flip a row in grid $A$ i.e. change all 0's in the chosen row to 1's, and 1's to 0's. 
3. Flip a column in grid $A$ i.e. change all 0's in the chosen column to 1's, and 1's to 0's. 

Output the minimum number of moves that Alice needs to convert $A$ to $B$, or $-1$ if it is impossible to make both grids equal. 

INPUT FORMAT

The first $4$ lines of the input each contain a string of length $4$ - denoting the rows in grid $A$, each character in the string is either $0$ or $1$. 

The next line is an empty line. 

The remaining $4$ lines of the input each contain a string of length $4$ - denoting the rows in grid $B$, each character in the string is either $0$ or $1$.

OUTPUT FORMAT 

The first and only line of the output should contain the minimum number of operations Alice needs to convert grid $A$ to $B$, or $-1$ if it's impossible to do so, using the operations in the statement.