Problem: 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:

cba927b2484fad94fb5ff7473e9aadef.png

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.

Examples

Input

4 3
0 1 W
1 2 W
5 3 B
5 4 B


Output

4


Input

2 1000
0 0 B
0 1 W


Output

2


Input

6 2
1 2 B
2 1 W
2 2 B
1 0 B
0 6 W
4 5 W


Output

4

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;
int main(){
  int n,k;cin >> n >> k;
  vector<vector<int>> a(2*k,vector<int>(2*k)),b(2*k,vector<int>(2*k));
  for(int i=0;i<n;i++){
    int x,y;cin >> x >> y;
    char c;cin >> c;
    if(c=='W'){
      a[x%(2*k)][y%(2*k)]++;
    }
    else{
      a[x%(2*k)][(y+k)%(2*k)]++;
    }
  }
  for(int i=0;i<2*k;i++){
    for(int j=0;j<2*k;j++){
      if(i<k){
        a[i][j]+=a[i+k][(j+k)%(2*k)];
      }
      else{
        a[i][j]=a[(i+k)%(2*k)][(j+k)%(2*k)];
      }
      b[i][(j+k)%(2*k)]=a[i][j];
    }
  }
  int ans=0;
  for(int i=0;i<2*k;i++){
    for(int j=1;j<2*k;j++){
      a[i][j]+=a[i][j-1];
      b[i][j]+=b[i][j-1];
    }
  }
  for(int j=0;j<2*k;j++){
    for(int i=1;i<2*k;i++){
      a[i][j]+=a[i-1][j];
      b[i][j]+=b[i-1][j];
    }
  }
  for(int i=k;i<2*k;i++){
    for(int j=k;j<2*k;j++){
      ans=max(ans,a[i][j]-a[i-k][j]-a[i][j-k]+a[i-k][j-k]);
      ans=max(ans,b[i][j]-b[i-k][j]-b[i][j-k]+b[i-k][j-k]);
    }
  }
  cout << ans << endl;
}