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 n,K;
int b[2002][2002];
int s[4002][4002];
int get(int x , int y){
	return s[x+K-1][y+K-1] + s[x-1][y-1] - s[x-1][y+K-1] - s[x+K-1][y-1];
}
int main(){
	cin >> n >> K;
	for (int i=0; i<n; i++){
		int x,y;
		char c;
		cin >> x >> y >> c;
		if(c=='W') y += K;
		++b[x%(2*K)+1][y%(2*K)+1];
	}
	for (int i=1; i<4*K+1; i++){
		for (int j=1; j<4*K+1; j++){
			s[i][j] = s[i][j-1] + b[(i-1)%(2*K)+1][(j-1)%(2*K)+1];
		}
	}
	for (int j=1; j<4*K+1; j++){
		for (int i=1; i<4*K+1; i++){
			s[i][j] += s[i-1][j];
		}
	}
	int ans = 0;
	for (int i=1; i<2*K+1; i++){
		for (int j=1; j<2*K+1; j++){
			ans = max(ans , get(i,j) + get(i+K,j+K));
		}
	}
	cout << ans << endl;
	return 0;
}