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: Time Limit Exceeded)

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

int OK[1001][1001], NG[1001][1001];

int main() {
  int N, K;
  cin >> N >> K;

  auto res = 0;

  for(auto i = 0; i < N; ++i) {
    int x, y; char c1;
    cin >> x >> y >> c1;
    x %= 2*K;
    y %= 2*K;
    auto c = (c1=='B') ? 0 : 1;
    for(auto i = 0; i < K; ++i) for(auto j = 0; j < K; ++j) {
      auto t = 0;
      if(y < i || i+K <= y) t ^= 1;
      if(x < j || j+K <= x) t ^= 1;
      if(t == c) ++OK[i][j];
      else       ++NG[i][j];
      res = max({res, OK[i][j], NG[i][j]});
    }
  }

  cout << res << endl;
}