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: Runtime Error)

#include<bits/stdc++.h>
using namespace std;
int xx[10001];
int yy[10001];
char c0[10001];
int main () {
	int n,k,x,y;
	char c;
	cin>>n>>k;
	for(int i=0; i<n; i++) {
		scanf("%d %d %c",&xx[i],&yy[i],&c0[i]);
		xx[i]+=k;
		yy[i]+=k;
	}
	int ans=0,ct,ct2;
	for(int sx=0; sx<k; sx++) {
		for(int sy=0; sy<k; sy++) {
			ct=ct2=0;
			for(int i=0; i<n; i++) {
				int dx=abs(xx[i]-sx)%(2*k);
				int dy=abs(yy[i]-sy)%(2*k);
				if((((dx<k&&dy<k)||(dx>=k&&dy>=k))&&c0[i]=='W')||(((dx>=k&&dy<k)||(dx<k&&dy>=k))&&c0[i]=='B'))
				{
					ct++;
				}
				if((((dx<k&&dy<k)||(dx>=k&&dy>=k))&&c0[i]=='B')||(((dx>=k&&dy<k)||(dx<k&&dy>=k))&&c0[i]=='W'))
				{
					ct2++;
				}
			}
			ans=max(ans,max(ct,ct2));
		}
	}
	printf("%d\n",ans);
	return 0;
}