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 9.2.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
#define MOD (long long)(1e9+7)
using namespace std;
int n,k,a[100005],b[100005];
string c[100005];
int main()
{
	cin >> n >> k;
	for(int i=0; i<n; i++) cin >> a[i] >> b[i] >> c[i];
	int ans=0;
	for(int i=0; i<=k; i++)
		for(int j=0; j<=k; j++)
		{
			int cnt=0;
			for(int p=0; p<n; p++)
			{
				if(((a[p]+i)/k)%2 == ((b[p]+j))/k%2 && c[p]=="W") cnt++;
				else if(((a[p]+i)/k)%2 != ((b[p]+j)/k)%2 && c[p]=="B") cnt++;
			}//cout<<cnt<<'\n';
			ans=max(ans,cnt);
		}
	cout << ans;
	return 0;
}