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: Runtime Error)

#include <stdio.h>

int check_BW(int x,int y,int K,char c,int i,int j){
    x = x % (2*K);
    y = y % K;
    char color;
    
    if(x>=j && x>j+K){
        if(y>=i){
            color = 'B';
        }else{
            color = 'W';
        }
    }else{
        if(y>=i){
            color = 'W';
        }else{
            color = 'B';
        }
    }
    
    if(c == color){
        return 1;
    }else{
        return 0;
    }
}

int main(void){
    int N,K;
    scanf("%d %d",&N,&K);
    int i,j,k;
    int x[N],y[N];
    char c[N];
    for(i=0; i<N; i++){
        scanf("%d %d %c",&x[i],&y[i],&c[i]);
    }
    int check = 0, max = 0;
    for(i=0; i<K; i++){
        for(j=0; j<2*K; j++){
            for(k=0; k<K; k++){
                check += check_BW(x[k],y[k],K,c[k],i,j);
            }
            if(max<check){
                max = check;
            }
            check = 0;
        }
    }
    printf("%d",max);
}