Problem Description

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 xi, yi and ci. If ci is B, it means that he wants to paint the square (xi,yi) black; if ci is W, he wants to paint the square (xi,yi) white. At most how many desires can he satisfy at the same time?

Constraints

• 1 ≤ N ≤ 105
• 1 ≤ K ≤ 1000
• 0 ≤ xi ≤ 109
• 0 ≤ yi ≤ 109
• If i ≠ j, then (xi,yi) ≠ (xj,yj).
• ci is B or W.
• N, K, xi and yi are integers.

Input

Input is given from Standard Input in the following format:

N K
x1 y1 c1
x2 y2 c2
:
xN yN cN

Output

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

Example

Sample Input 1

4 3
0 1 W
1 2 W
5 3 B
5 4 B

Sample Output 1

4
He can satisfy all his desires by painting as shown in the example above.

Sample Input 2

2 1000
0 0 B
0 1 W

Sample Output 2

2

Sample Input 3

6 2
1 2 B
2 1 W
2 2 B
1 0 B
0 6 W
4 5 W

Sample Output 3

4

题意：

思路：

Source Program

标签：yi,AtCoder,ci,xi,3876,Sample,Checker,square,Input
来源： https://blog.csdn.net/u011815404/article/details/95998357