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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;

int main(){
  long n,k;
  cin >> n >> k;
  int b[4*k][4*k],w[4*k][4*k];
  for(int i = 0;i < 4*k;i++){
    for(int j = 0;j < 4*k;j++){
      b[i][j] = 0;
      w[i][j] = 0;
    }
  }
  for(long i = 0;i < n;i++){
    long x,y;
    char c;
    cin >> x >> y >> c;
    x %= 2*k;y %= 2*k;
    if(c == 'W'){
      w[x][y]++;
      w[x][y+2*k]++;
      w[x+2*k][y]++;
      w[x+2*k][y+2*k]++;
    }
    else{
      b[x][y]++;
      b[x+2*k][y]++;
      b[x][y+2*k]++;
      b[x+2*k][y+2*k]++;
    }
  }
  int bsum[4*k][4*k],wsum[4*k][4*k];
  for(long i = 0;i < 4*k;i++){
    bsum[0][i] = 0;bsum[i][0] = 0;
    wsum[0][i] = 0;wsum[i][0] = 0;
  }
  for(long i = 0;i < 4*k-1;i++){
    for(long j = 0;j < 4*k-1;j++){
      bsum[i+1][j+1] = bsum[i][j+1] + bsum[i+1][j] - bsum[i][j] + b[i][j];
      wsum[i+1][j+1] = wsum[i][j+1] + wsum[i+1][j] - wsum[i][j] + w[i][j];
    }
  }
  int ans = 0;
  for(long i = 0;i < 2*k;i++){
    for(long j = 0;j < 2*k;j++){
      int cur = 0;
      cur += wsum[i+k][j+k] - wsum[i][j+k] - wsum[i+k][j] + wsum[i][j];
      cur += wsum[i+2*k][j+2*k] - wsum[i+k][j+2*k] - wsum[i+2*k][j+k] + wsum[i+k][j+k];
      cur += bsum[i+k][j+2*k] - bsum[i][j+2*k] - bsum[i+k][j+k] + bsum[i][j+k];
      cur += bsum[i+2*k][j+k] - bsum[i+k][j+k] - bsum[i+2*k][j] + bsum[i+k][j];
      ans = max(ans,cur);
    }
  }
  cout << ans << endl;
}