Problem:
Score : 500 points

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.

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

Solution in C (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
int MAX(int a,int b){return a<b?b:a;}
int n,m,i,j,max=0,s[2010][3010],d[2010][3010];
int main(){
	char c;
	scanf("%d %d",&n,&m);
	while(n--){
		scanf("%d %d %c",&j,&i,&c);
		if(c=='B')j+=m;
		if(i%(2*m)/m)j+=m;
		d[i%m][j%(m*2)]++;
	}
	for(i=0;i<m;i++){
		for(j=0;j<2*m;j++)d[i+m][(j+m)%(2*m)]=d[i][j];
	}
  	for(i=0;i<2*m;i++){
      	for(j=0;j<m;j++)d[i][j+2*m]=d[i][j];
    }
	for(i=0;i<2*m;i++){
		for(j=0;j<3*m;j++)s[i+1][j+1]=d[i][j]+s[i+1][j]+s[i][j+1]-s[i][j];
	}
	for(i=0;i<=m;i++){
		for(j=0;j<2*m;j++)max=MAX(max,s[i][j]+s[i+m][j+m]-s[i+m][j]-s[i][j+m]);
	}
	printf("%d\n",max);
	return 0;
}