Poster

JOI made a poster to advertise his class's presentation at the school festival. The poster is an N by N grid of cells, and each cell is painted one of red, green, or blue. The color of the cell in row i from the top and column j from the left (1 ≦ i ≦ N, 1 ≦ j ≦ N) of the poster is red when Si,j= R, green when Si,j= G, and blue when Si,j= B.

His classmates were not satisfied with this poster. After some discussion, they decided to make a new poster with the same grid shape but a different arrangement of colors. The color of the cell in row i from the top and column j from the left (1 ≦ i ≦ N, 1 ≦ j ≦ N) of the new poster will be red when Ti,j= R, green when Ti,j= G, and blue when Ti,j= B.

JOI decided to make the new poster by repeatedly applying one of the following operations to the current poster.

• Choose one cell and repaint it any color he likes.
• Rotate the whole poster 90° clockwise. A cell that was in row i from the top and column j from the left (1 ≦ i ≦ N, 1 ≦ j ≦ N) moves to row j from the top and column N-i+1 from the left.
• Rotate the whole poster 90° counterclockwise. A cell that was in row i from the top and column j from the left (1 ≦ i ≦ N, 1 ≦ j ≦ N) moves to row N-j+1 from the top and column i from the left.

Each operation takes JOI 1 minute. Given the poster he made and the new poster, write a program to find the minimum number of minutes JOI needs to make the new poster.

The input is given from standard input in the following format.

N
S1,1 … S1,N
:
SN,1 … SN,N
T1,1 … T1,N
:
TN,1 … TN,N

Print the minimum number of minutes needed to make the new poster on 1 line.

• 1 ≦ N ≦ 500.
• Si,j is one of R, G, B.
• Ti,j is one of R, G, B.