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 <stdlib.h>
#include <stdio.h>
#include <math.h>

#define rep(n, i) for(int i = 0; i < n; i++)
#define MAX(a, b) ((a) > (b) ? (a) : (b))
#define MIN(a, b) ((a) < (b) ? (a) : (b))

void solve(void){
    int n, k;
    scanf("%d%d\n",&n, &k);
    int xs[n], ys[n];
    char cs[n];
    rep (n, i) scanf("%d %d %s\n", &xs[i], &ys[i], &cs[i]);

    int ans = 0;
    rep (k, x){
        if (ans == n) break;
        rep(k, y){
            int temp_ans = 0;
            rep(n, i){
                char temp_c;
                if (((xs[i] + x) / k + (ys[i] + y) / k) % 2 == 0) temp_c = 'B';
                else temp_c = 'W';
                if (temp_c == cs[i]) temp_ans++;
            }
            ans = MAX(ans, MAX(temp_ans, n-temp_ans));
            if (ans == n) break;
        }
    }
  printf("%d\n", ans);
}

int main(void){
  solve();
  return 0;
}