Problem Statement

We have a canvas represented as a grid with H rows and W columns. Let (i, j) denote the square at the i-th row from the top $(1 \leq i \leq H)$ and j-th column from the left $(1 \leq j \leq W). Initially, (i, j)$ is painted red if s_{i, j}= R and blue if s_{i, j}= B.
For any number of times, you can choose one of the two operations below and do it.

Operation X: Choose a square painted red, and repaint all squares in the row containing that square (including itself) white.
Operation Y: Choose a square painted red, and repaint all squares in the column containing that square (including itself) white.

Show one way that maximizes the number of squares painted white in the end.

Input

Input is given from Standard Input in the following format:
H W
$s_{1, 1}s_{1, 2}s_{1, 3}\cdotss_{1, W}$
$s_{2, 1}s_{2, 2}s_{2, 3}\cdotss_{2, W}$
$s_{3, 1}s_{3, 2}s_{3, 3}\cdotss_{3, W}$
$\vdots$
$s_{H, 1}s_{H, 2}s_{H, 3}\cdotss_{H, W}$

Output

Print the following to Standard Output:
n
t_1 r_1 c_1
t_2 r_2 c_2
t_3 r_3 c_3
$\vdots$
t_n r_n c_n

Here, n is the number of operations you do, and t_i, r_i, c_i means that your i-th operation is Operation t_i with (r_i, c_i) being chosen, where t_i is X or Y.
If there are multiple possible solutions, you may print any of them.

Constraints

• $1 \leq H \leq 2500$
• $1 \leq W \leq 2500$
• s_{i, j} is R or $B. (1 \leq i \leq H, 1 \leq j \leq W)$
• H and W are integers.

Sample Input 1

4 4
RBBB
BBBB
BBBB
RBRB

Sample Output 1

3
X 1 1
Y 4 3
X 4 1

Here is one sequence of operations that makes 10 squares white:

• First, do Operation X choosing (1, 1).
• Then, do Operation Y choosing (4, 3).
• Then, do Operation X choosing (4, 1).

There is no way to make 11 or more squares white.

Sample Input 2

1 119
BBBRBBBBBBRBBBBBBRBBBBBBRBBBBBBRBBBBBBRBBBBBBRBBBBBBRBBBBBBRBBBBBBRBBBBBBRBBBBBBRBBBBBBRBBBBBBRBBBBBBRBBBBBBRBBBBBBRBBB

Sample Output 2

4
Y 1 60
Y 1 109
Y 1 46
X 1 11

We can repaint all squares white.

Sample Input 3

10 10
BBBBBBBBBB
BBBBBBBBBB
BBBBBBBBBB
BBBBBBBBBB
BBBBBBBBBB
BBBBBBBBBB
BBBBBBBBBB
BBBBBBBBBB
BBBBBBBBBB
BBBBBBBBBB

Sample Output 3

0

Since there is no red square, we cannot do the operations at all.

见题面 Input 部分

见题面 Output 部分