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. N² of little squares are cut out (see figure
1).

Let us briefly describe the encoding process. Take text of message of length
4N². Then put an encoding grid onto a blank sheet of paper and begin
to write first N² 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 N² 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 remembe"#008DDC" 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.