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: Time Limit Exceeded)

#include<stdio.h>

long ma(long a ,long b){
  if(a>b) return a;
  else return b;
}

int main(){
  int n,k,i,j,l;
  long x[100000],y[100000],cnt=0,max=0;
  char c[100000];
  scanf("%d %d",&n,&k);
  for(i=0;i<n;i++){
    scanf("%ld %ld %c",&x[i],&y[i],&c[i]);
  }
  for(i=0;i<k;i++){
    for(j=0;j<k;j++){
      cnt=0;
      for(l=0;l<n;l++){
        if(((x[l]+i)%(2*k)<k&&(y[l]+j)%(2*k)<k)||((x[l]+i)%(2*k)>=k&&(y[l]+j)%(2*k)>=k)){
          if(c[l]=='W') cnt++;
        }
        else{
          if(c[l]=='B') cnt++;
        }
      }
      cnt=ma(cnt,n-cnt);
      max=ma(max,cnt);
    }
  }  
  printf("%ld\n",max);
}