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: Wrong Answer)

#include <iostream>
#include <string>
#include <vector>
#include <set>
#include <algorithm>
#include <cctype>
#include <cmath>
#include <queue>
#include <map>
#include <numeric>
#include <unordered_map>
#include <iomanip>
#include <functional>
#include <bitset>
#include <complex>
#include <stack>



#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define repi(i,a,b) for(int i=int(a);i<int(b);i++)
#define all(x) (x).begin(),(x).end()

template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }

typedef long long ll;

using namespace std;


int main()
{
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n;cin>>n;
  int k;cin>>k;
  vector<vector<vector<int>>>zeon(k,vector<vector<int>>(k,vector<int>(2,0)));
  rep(i,n)
  {
    int x,y;
    char c;
    cin>>x>>y>>c;
    x=x%(2*k);
    y=y%(2*k);
    int cc=c=='B';
    if((x>=k)^(y>=k))
    {
      cc=1-cc;
    }
    x%=k;
    y%=k;
    zeon[x][y][cc]++;
  }
  vector<vector<int>>sum1(k+1,vector<int>(k+1,0));
  auto sum2=sum1;
  rep(i,k)rep(j,k)sum1[i+1][j+1]=sum1[i+1][j]+zeon[i][j][0];
  rep(j,k)rep(i,k)sum1[i+1][j+1]+=sum1[i+1][j+1]+sum1[i][j+1];

  rep(i,k)rep(j,k)sum2[i+1][j+1]=sum2[i+1][j]+zeon[i][j][0];
  rep(j,k)rep(i,k)sum2[i+1][j+1]+=sum2[i+1][j+1]+sum2[i][j+1];
  int res=0;
  rep(i,k+1)rep(j,k+1)
  {
    int tres1=0,tres2=0;
    tres1=sum1[k][k]-sum1[k][j]-sum1[i][k]+2*sum1[i][j];
    tres1+=sum2[k][j]+sum2[i][k]-sum2[i][j];

    tres2=sum2[k][k]-sum2[k][j]-sum2[i][k]+2*sum2[i][j];
    tres2+=sum1[k][j]+sum1[i][k]-sum1[i][j];
    chmax(res,tres1);
    chmax(res,tres2);

  }
  cout<<res/2<<endl;


  return 0;

}