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 \(B\)):

Rotate grid \(A\) clockwise by \(90\) degrees.
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.
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.