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;
#define rep(i,n) for(int i=0;i<n;i++)
#define all(v) v.begin(), v.end()
typedef long long ll;
typedef pair<ll,ll> P;
typedef vector<ll> vec;
typedef vector<vec> mat;
int n,k,X[200001],Y[200001],C[200001];
int A[1001][1001][2],B[1001][1001][2]={0};
int main(){
    char c;
    cin>>n>>k;
    rep(i,n){
        cin>>X[i]>>Y[i]>>c;
        C[i]=(c=='B');
    }
    rep(i,n) C[i]=(X[i]/k+Y[i]/k+C[i])%2,X[i]%=k,Y[i]%=k;
    rep(i,n) A[X[i]][Y[i]][C[i]]++;
    rep(i,k)rep(j,k)rep(k,2) B[i+1][j+1][k]=B[i][j+1][k]+B[i+1][j][k]-B[i][j][k]+A[i][j][k];
    int ans=0;
    rep(i,k)rep(j,k){
        int a=B[i][j][0]-B[0][0][0];
        a+=B[k][k][0]-B[i][k][0]-B[k][j][0]+B[i][j][0];
        a+=B[i][k][1]-B[i][j][1];
        a+=B[k][j][1]-B[i][j][1];
        ans=max({ans,a,n-a});
    }
    cout<<ans<<"\n";
}