Rotation Game

You have a board with height two and width W. The board is divided into 1x1 cells. Each row of the board is numbered 1 and 2 from top to bottom and each column is numbered 1 to W from left to right. We denote a cell at the i-th row in the j-th column by (i, j). Initially, some checkers are placed on some cells of the board. Here we assume that each checker looks the same. So we do not distinguish each checker. You are allowed to perform the following operations on the board:

1. Square rotation: Choose a 2x2 square on the board. Then move checkers in the 2x2 square such that the checkers rotate their position in the square by 90 degrees in either clockwise or counterclockwise direction.

   

2. Triangular rotation: Choose a set of cells on the board that form a triangle. Here, we call a set of cells triangle if it is formed by removing exactly one cell from a 2x2 square. In the similar manner with the square rotation, rotate checkers in the chosen triangle in either clockwise or counterclockwise direction.

   

The objective in this problem is to transform the arrangement of the checkers into desired arrangement by performing a sequence of rotation operations. The information of the initial arrangement and the target arrangement are given as the input. For the desired arrangement, one of the following is specified for each cell (i, j): i. cell (i,j) must contain a checker, ii. cell (i,j) must not contain a checker, or iii. there is no constraint for cell (i, j). Compute the minimum required number of operations to move the checkers so the arrangement satisfies the constraints and output it.

The input is formatted as follows.

W
s11s11...s1W
s21s21...s2W

t11t11...t1W
t21t21...t2W

The first line of the input contains an integer W (2 ≤ W ≤ 2,000), the width of the board. The following two lines contain the information of the initial arrangement. If a cell (i, j) contains a checker in the initial arrangement, sij is o. Otherwise, sij is .. Then an empty line follows. The following two lines contain the information of the desired arrangement. Similarly, if a cell (i, j) must contain a checker at last, tij is o. If a cell (i, j) must not contain a checker at last, tij is .. If there is no condition for a cell (i, j), tij is *. You may assume that a solution always exists.

Output the minimum required number of operations in one line.