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: Wrong Answer)

#include <iostream>
#include <algorithm>
#include <vector>
#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define repR(i, n) for(int i = (n) - 1; i > -1; i--)
#define rep1(i, n) for(int i = 1; i < (int)(n + 1); i++)
#define rep1R(i, n) for(int i = (n); i > 0; i--)
using namespace std;

int n, k;
vector<int> X, Y;
vector<char> C;
int max_x, max_y;
vector<int> results;

int main() {
  cin >> n >> k;
  X.resize(n);
  Y.resize(n);
  C.resize(n);
  rep(i, n) cin >> X[i] >> Y[i] >> C[i];
  rep(i, 2 * k) {
    rep(j, 2 * k) {
      int result = 0;
      rep(idx, n) {
        if (((X[idx] - i) % k == 1 || (X[idx] - i) % k == 2) && ((Y[idx] - j) % k == 1 || (Y[idx] - j) % k == 2)) {
          if (C[idx] == 'B') ++result;
        } else {
          if (C[idx] == 'W') ++result;
        }
      }
      results.push_back(result);
    }
  }
  cout << *max_element(results.begin(), results.end()) << endl;
  return 0;
}