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: Time Limit Exceeded)

#include <iostream>
#include <algorithm>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <iomanip>

using namespace std;
struct color
{
    int x,y,no;
}s[100000];
int n,k,m;
int check(int x,int y,int no)
{
    int wro = 0;
    for(int i = 0;i < n;i ++)
    {
        int d = abs((s[i].x - x) / k) % 2;
        int e = abs((s[i].y - y) / k) % 2;
        if((s[i].no ^ no) ^ (d ^ e))wro ++;
    }
    return n - wro > wro ? n - wro : wro;
}
int main()
{
    scanf("%d%d",&n,&k);
    char ch;
    for(int i = 0;i < n;i ++)
    {
        scanf("%d %d %c",&s[i].x,&s[i].y,&ch);
        s[i].no = (ch == 'W' ? 0 : 1);
    }
    for(int i = 0;i < k;i ++)
    {
        for(int j = 0;j < k;j ++)
        {
            int d = check(- i,- j,0);
            if(d > m)m = d;
        }
    }
    printf("%d",m);
}