Nita and Bruce are making a splash at the beach! With so many waves, Nita wants to make sure that the beach is safe for everyone to swim in.

Currently, the beach is a ~H~ by ~W~ grid with the water level in each cell being either ~0~ or ~1~. Whenever a cell of the grid is splashed, the water level at that cell changes to ~1~ if it was ~0~ or to ~0~ if it was ~1~.

Nita wants to calm the entire area of the beach to level ~0~, but she can only perform two types of operations:

1. Rupture: Nita splashes all the cells in an entire row or column.
2. Bear Paws: Bruce splashes any ~2~ by ~2~ subgrid of the beach.

Help Nita and Bruce to convert the water level of every cell of the beach to 0!

Input Specification

First line: ~H~ and ~W~ (the height and width of the beach respectively).

An ~H \times W~ grid of ~0~s and ~1~s follows, describing the initial state of the beach.

Output Specification

There are two parts for the output:

Part 1: If it is solvable, print Y. Otherwise, print N. (Producing a correct answer for Part 1 in any subtask earns you 75% of the marks for that subtask).

Part 2: If it is solvable, print an integer ~K~ stating the number of operations in your proposed solution.

On the next ~K~ lines, list the operations you used to solve the puzzle. More specifically,

• R x splashes all cells in row x
• C x splashes all cells in column x
• G x y splashes the ~2 \times 2~ grid with the top left corner at row x column y.

If multiple valid solutions exist, any one of them will be accepted. ~K~ does not need to be minimal but should not exceed ~10^6~.

Constraints

In all test cases, ~2 \le H, W \le 1000~

Subtask 1 [20%]

~2 \le H, W \le 3~

Subtask 4 [80%]

No additional constraints.

Remember: for all subtasks, you will be awarded 75% of the available points for producing a correct answer for Part 1 of the output specification, regardless of your output for Part 2.

Sample Input 1

3 3
1 0 1
1 1 0
0 0 1

Sample Output 1

Y
4
C 1
C 3
R 3
G 2 2

Explanation for Sample Case 1

Nita splashes column ~1~, which results in

0 0 1
0 1 0
1 0 1

Then splash column ~3~, which results in

0 0 0
0 1 1
1 0 0

Then splash row ~3~, which results in

0 0 0
0 1 1
0 1 1

Finally, splash the ~2 \times 2~ subgrid with a top-left corner at ~(2, 2)~, which results in

0 0 0
0 0 0
0 0 0

Sample Input 2

2 2
1 0
1 1

Output for Sample Input 2

N

Explanation for Sample Case 2

No matter what Nita and Bruce do, there's no way to convert the entire grid to all ~0~s.