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: Wrong Answer)

#include<stdio.h>
#include<stdlib.h>
int main()
{
  int N, K;
  int x, y;
  char c[2];
  int i, j;
  int Check[1000 * 1000];
  int max;
  
  scanf("%d %d", &N, &K);
  
  for(i = 0; i < K * K; i++){
    Check[i] = 0;
  }
  
  for(i = 0; i < N; i++){
    scanf("%d %d %s",&x, &y, c);
    for(j = 0; j < K * K; j++){
      if(((x <= j % K && y <= j / K) && c[0] == 'B') || (((x > j % K || y > j / K) && c[0] == 'W'))){
        Check[j]++;
      }
    }
  }
  
  max = 0;
  for(i = 0; i < K * K; i++){
    if(Check[i] < N / 2){
      Check[i] = N - Check[i];
    }
    if(max < Check[i]){
      max = Check[i];
    }
  }
  
  // 出力
  printf("%d\n", max);

  return 0;
}