Problem Statement

AtCoDeer is thinking of painting an infinite two-dimensional grid in a checked pattern of side $K$. Here, a checked pattern of side $K$ is a pattern where each square is painted black or white so that each connected component of each color is a $K$ $×$ $K$ square. Below is an example of a checked pattern of side $3$:

AtCoDeer has $N$ desires. The $i$-th desire is represented by $x_i$, $y_i$ and $c_i$. If $c_i$ is B, it means that he wants to paint the square $(x_i,y_i)$ black; if $c_i$ is W, he wants to paint the square $(x_i,y_i)$ white. At most how many desires can he satisfy at the same time?

Constraints

• $1$ $≤$ $N$ $≤$ $10^5$
• $1$ $≤$ $K$ $≤$ $1000$
• $0$ $≤$ $x_i$ $≤$ $10^9$
• $0$ $≤$ $y_i$ $≤$ $10^9$
• If $i$ $≠$ $j$, then $(x_i,y_i)$ $≠$ $(x_j,y_j)$.
• $c_i$ is B or W.
• $N$, $K$, $x_i$ and $y_i$ are integers.

Input

Input is given from Standard Input in the following format:

N K
x_1 y_1 c_1
x_2 y_2 c_2
:
x_N y_N c_N

Output

Print the maximum number of desires that can be satisfied at the same time.