Magic Square#2554
Numbers from to are written in a 3 \times 3 square in arbitrary order. You are allowed to make a cyclic shift by one element of any row (to the left or to the right) or any column (up or down). The objective is to write a program that transforms the square into a magic square using the minimal number of such operations.
An example of such a transformation is shown in the picture:
The input file consists of three lines. Each line contains the numbers of a single row of the square—three integers separated by spaces.
Note that any square can be converted into a magic square using some number of cyclic shifts.
The first line of the output file should contain an integer —the minimal number of cyclic shift operations needed to transform the given square into a magic square. The next lines should describe one shift per line. Shifts are encoded as follows:
Dx—shift column down;
Ux—shift column up;
Lx—shift row left;
Rx—shift row right.
Row or column number (1 \le x \le 3) is written after the letter without space. Rows are numbered from top to bottom, columns from left to right.
Example 1