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 <bits/stdc++.h>
using namespace std;
#define repd(i,a,b) for (int i=(a);i<(b);i++)
#define rep(i,n) repd(i,0,n)
typedef long long ll;
typedef long double lb;
#define int long long
#define double long double
typedef pair<int,int> P;
const int MOD = 1000000007;
const ll INF = 1e16;
const double EPS = 1e-10;
const double PI = 3.141592653589793;
template<class T> inline bool chmin(T& a, T b){if(a>b){a = b;return 1;}return 0;}
template<class T> inline bool chmax(T& a, T b){if(a<b){a = b;return 1;}return 0;}
const pair<int,int> fd[] = {make_pair(1,0),make_pair(-1,0),make_pair(0,1),make_pair(0,-1)}; 


////////////////////////////////////////////////////////////////////

int n,k,x[110000],y[110000],t[5100][5100];
signed main(){
  cin>>n>>k;
  rep(i,n){
    int xx,yy;char cc;cin>>xx>>yy>>cc;
    if(cc == 'W')yy += k;
    xx %= 2*k;yy %= 2*k;
    x[i] = xx;y[i] = yy;
  }
  rep(i,n){
    t[x[i]][y[i]]++;
    t[x[i]+k][y[i]+k]++;
    t[x[i]+k][y[i]]--;
    t[x[i]][y[i]+k]--;
  }
  rep(i,4*k){
    rep(j,4*k-1){
      t[i][j+1] += t[i][j];
    }
  }
  rep(i,4*k){
    rep(j,4*k-1){
      t[j+1][i] += t[j][i];
    }
  }
  int ans = -1;
  rep(i,2*k)rep(j,2*k){
    int sum = t[i][j] + t[i+2*k][j] + t[i+k][j+k] + t[i+k][j+3*k];
    sum += t[i][j+2*k] + t[i+2*k][j+2*k] + t[i+3*k][j+k] + t[i+3*k][j+3*k];
    chmax(ans, sum);
  }
  cout << ans << endl;
}