A kind of grid is sometimes used for encoding messages. Our naval fleet officials decide to use this kind of encoding messages for communication with their ship captains. The encoding grid is a square sheet of paper divided into 2N x 2N little squares. N^2 of little squares are cut out (see figure 1).

Let us briefly describe the encoding process. Take text of message of length 4N^2. Then put an encoding grid onto a blank sheet of paper and begin to write first N^2 letters of message into the cut little squares (one letter per square, write letters in all cut squares in the first line from left to right, then in the second line etc.). See example on figure 2 for message "HELLOYELLOWWORLD". After finishing the first step rotate the encoding grid 90 degrees clockwise and continue similarly writing letters. After two more steps all letters should be written (see example on figure 3).

                     O###                H###                 HOOY
                     ##O#                ##E#                 LREO
                     O##O                L##L                 LWEL
                     ####                ####                 LLDW

                    (fig.1)             (fig.2)              (fig.3)

It is necessary to have a correctly constructed grid. It means that when it is used in the way described above after each rotation new N^2 blank squares will appear under cut squares of the grid.

The naval fleet officials encoded thousands of messages with their grid and then they wanted to send them to ships. Unfortunately they lost the grid. Fortunately the naval admiral remembered the original text of one of the messages.

Your task is to get this original message text and encoded text and find one possible correctly constructed encoding grid with which the message text could have been encoded.

Input

The first line of input file contains an integer N (1<=N<=10). The second line contains 4N^2 capital letters representing the original message. The next 2N lines contain the encoded text (each line 2N capital letters).

Output

The output file contains a correctly constructed grid with which given message could have been encoded. In each of 2N lines one line of grid (2N characters) will be displayed where "O" (capital letter 'O' represents cut square and "#" uncut square.

Sample Input

2
HELLOYELLOWWORLD
HOOY
LREO
LWEL
LLDW

Sample Output

O###
##O#
O##O
####