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The king of Byteland has received a gift, a jigsaw puzzle. The puzzle consists of a board of size . The field in the -th row and -th column () has coordinates and contains a piece with the number , . Each of the numbers appears on exactly one of the pieces.
Coordinates of the fields
To solve the puzzle, you have to put the pieces in order, so that for each the field contains the piece with number .
The following moves are allowed to solve the puzzle:
The king of Byteland managed to solve his puzzle, but he is not sure if he would be able to solve it starting from a different initial configuration. Help him to solve this problem.
Write a program that:
In the first line of the standard input there is one integer - the size of the board side (). The following lines contain the description of the initial configuration. The line contains integers separated by single spaces.
If there is no solution, the program should write to the standard output only one line containing only one word NO.
If a solution exists, the first line should contain one integer - the number of moves leading to the solution of the puzzle. The number of moves in your solution must not exceed . The following lines should contain the descriptions of the moves, one move per line.
Each such line should consist of a letter R (for shifting a row to the right) or C (for shifting a column down), a space, and two integers: and separated by a space; , . A line containing R describes a cyclic shift of the -th row fields to the right. Such a move leads to the following board configuration:
If there are several possible solutions, your program should output anyone of them.
For the input data:
4 4 6 2 3 5 10 7 8 9 14 11 12 13 1 15 16
the correct result is:
2 C 2 1 R 1 3
The above sequence of moves gives the following sequence of
Task author: Rafał Rusin.