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 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <exception>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iosfwd>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <locale>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <stdexcept>
#include <streambuf>
#include <string>
#include <typeinfo>
#include <utility>
#include <valarray>
#include <vector>
#include <climits>

#define rep(i, m, n) for(int i=int(m);i<int(n);i++)
#define EACH(i, c) for (auto &(i): c)
#define all(c) begin(c),end(c)
#define EXIST(s, e) ((s).find(e)!=(s).end())
#define SORT(c) sort(begin(c),end(c))
#define pb emplace_back
#define MP make_pair
#define SZ(a) int((a).size())

//#define LOCAL 0
//#ifdef LOCAL
//#define DEBUG(s) cout << (s) << endl
//#define dump(x)  cerr << #x << " = " << (x) << endl
//#define BR cout << endl;
//#else
//#define DEBUG(s) do{}while(0)
//#define dump(x) do{}while(0)
//#define BR
//#endif


//改造
typedef long long int ll;
using namespace std;
#define INF (1 << 30)
#define INFl (ll)5e15
#define DEBUG 0 //デバッグする時1にしてね
#define dump(x)  cerr << #x << " = " << (x) << endl
#define MOD 1000000007
//ここから編集する
int sw[1001][1001];
int sb[1001][1001];

int cal_sw(int sx,int sy,int tx,int ty){
    if(sx == 0 && sy == 0){
        return sw[tx][ty];
    }
    if(sx == 0){
        return sw[tx][ty] - sw[tx][sy-1] ;
    }
    if(sy == 0){
        return sw[tx][ty] - sw[sx-1][ty];
    }
    return sw[tx][ty] + sw[sx-1][sy-1] - sw[tx][sy-1] - sw[sx-1][ty];
}

int cal_sb(int sx,int sy,int tx,int ty){
    if(sx == 0 && sy == 0){
        return sb[tx][ty];
    }
    if(sx == 0){
        return sb[tx][ty] - sb[tx][sy-1] ;
    }
    if(sy == 0){
        return sb[tx][ty] - sb[sx-1][ty];
    }
    return sb[tx][ty] + sb[sx-1][sy-1] - sb[tx][sy-1] - sb[sx-1][ty];
}


int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);

    int N,K;
    cin >> N >> K;




    rep(i,0,N){
        int x,y;
        char c;
        cin >> x >> y >> c;
        x %= 2*K;
        y %= 2*K;
        if(x < K){
            if(y < K){
                if(c == 'B'){
                    sb[x%K][y%K]++;
                    sb[K][K]++;
                    sb[x%K][K]--;
                    sb[K][y%K]--;
                }else{
                    sw[x%K][y%K]++;
                    sw[K][K]++;
                    sw[x%K][K]--;
                    sw[K][y%K]--;
                }
            }else{
                if(c == 'W'){
                    sb[x%K][y%K]++;
                    sb[K][K]++;
                    sb[x%K][K]--;
                    sb[K][y%K]--;
                }else{
                    sw[x%K][y%K]++;
                    sw[K][K]++;
                    sw[x%K][K]--;
                    sw[K][y%K]--;
                }
            }
        }else{
            if(y < K){
                if(c == 'W'){
                    sb[x%K][y%K]++;
                    sb[K][K]++;
                    sb[x%K][K]--;
                    sb[K][y%K]--;
                }else{
                    sw[x%K][y%K]++;
                    sw[K][K]++;
                    sw[x%K][K]--;
                    sw[K][y%K]--;
                }
            }else{
                if(c == 'B'){
                    sb[x%K][y%K]++;
                    sb[K][K]++;
                    sb[x%K][K]--;
                    sb[K][y%K]--;
                }else{
                    sw[x%K][y%K]++;
                    sw[K][K]++;
                    sw[x%K][K]--;
                    sw[K][y%K]--;
                }
            }
        }
    }
    rep(i,0,K){
        rep(j,0,K){
            sb[i][j+1] += sb[i][j];
            sw[i][j+1] += sw[i][j];
        }
    }
    rep(i,0,K){
        rep(j,0,K){
            sb[i+1][j] += sb[i][j];
            sw[i+1][j] += sw[i][j];
        }
    }

    int ans = 0;
    rep(i,0,K){
        rep(j,0,K){
            //(i,j)から(K-1,K-1)が白の場合
            int cnt = cal_sw(i,j,K-1,K-1);

            //(i,j)から(K-1,K-1)の白と全体からこれを引いた黒を求める
            cnt += cal_sb(0,0,K-1,K-1) - cal_sb(i,j,K-1,K-1);
            ans = max(ans,cnt);
        }
    }

    rep(i,0,K){
        rep(j,0,K){
            int cnt = cal_sb(i,j,K-1,K-1);
            cnt += cal_sw(0,0,K-1,K-1) - cal_sw(i,j,K-1,K-1);
            ans = max(ans,cnt);
        }
    }

    cout << ans << endl;


    return 0;
}