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 <cmath>
#include <iostream>
#include <vector>
#include <queue>
#include <deque>
#include <map>
#include <set>
#include <stack>
#include <tuple>
#include <algorithm>
#include <functional>
#include <utility>
#include <string>
#define typeof(x) __typeof__(x)
#define int long long int
#define double long double
#define mod(x) ((x % MOD) + MOD) % MOD
#define ceil(x,m) ((x)+(m)-1)/(m)
#define rep(i,a,b) for(int i=(a);i<(b);++i)
#define rrep(i,a,b) for(int i=(b)-1;i>=(a);--i)

#define ALL(c) (c).begin(),(c).end()
#define RALL(c) (c).rbegin(),(c).rend()
#define SZ(c) (int)((c).size())
#define EACH(i,c) for(typeof((c).begin()) i=(c).begin(); i!=(c).end(); ++i)
#define SORT(c) sort(ALL(c))
#define RSORT(c) sort(RALL(c))
#define LB(c,x) (int)(lower_bound(ALL(c),x)-(c).begin())
#define UB(c,x) (int)(upper_bound(ALL(c),x)-(c).begin())
#define COUNT(c,x) UB(c,x)-LB(c,x)
#define UNIQUE(c) SORT(c); (c).erase(unique(ALL(c)),(c).end());
#define COPY(c1,c2) copy(ALL(c1),(c2).begin())
#define EXIST(s,e) (s).find(e)!=(s).end()
#define PB push_back
#define MP make_pair
#define vec vector

#define dump(x)  cerr << #x << " = " << (x) << endl;
#define debug(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ")" << endl;

using namespace std;

typedef pair<int,int> P;
struct edge { int to, cost; };

const int INF = 1e18;
const int MOD = 1e9+7;

template<typename T> ostream& operator << (ostream& s, const vector<T>& v) {
   int len = v.size();
   s << "[";
   for (int i = 0; i < len; i++) { s << v[i]; if (i < len - 1) s << " "; }
   s << "]";
   return s;
}

signed main()
{
   int N, K; cin >> N >> K;
   vec<vec<int>> b(K+1, vec<int>(K+1,0)), w(K+1, vec<int>(K+1, 0));
   int x, y, flag; char c;
   rep(i, 0, N) {
      cin >> x >> y >> c;
      flag = ((x/K) + (y/K) + (c=='W')) & 1;
      x %= K; y %= K;
      if (flag) {
         w[x+1][y+1] += 1;
      } else {
         b[x+1][y+1] += 1;
      }
   }

   rep(i, 0, K) {
      rep(j, 0, K) {
         b[i+1][j+1] += b[i+1][j] + b[i][j+1] - b[i][j];
         w[i+1][j+1] += w[i+1][j] + w[i][j+1] - w[i][j];
      }
   }

   int MAX = 0;
   rep(i, 0, K) {
      rep(j, 0, K) {
         MAX = max(MAX,
               (b[K][K] - b[i+1][K] - b[K][j+1] + 2*b[i+1][j+1]) +
               (w[i+1][K] + w[K][j+1] - 2*w[i+1][j+1]) );
         MAX = max(MAX,
               (w[K][K] - w[i+1][K] - w[K][j+1] + 2*w[i+1][j+1]) +
               (b[i+1][K] + b[K][j+1] - 2*b[i+1][j+1]) );
      }
   }
   cout << MAX << endl;
   return 0;
}