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  xx;
int  yy;
int lt[2050][2050];
int main () {
	memset(lt,0,sizeof(lt));
	int n,k,x,y;
	char c[10];
	cin>>n>>k;
	for(int i=0; i<n; i++) {
		scanf("%d %d %s",&xx,&yy,c);
		if(c[0]=='W') {
			yy+=k;
		}
		xx%=2*k;
		yy%=2*k;
		lt[xx][yy]++;
	}
	for(int i=0; i<=2*k; i++)
		for(int j=1; j<=2*k; j++)
			lt[i][j]+=lt[i][j-1];
	for(int i=1; i<=2*k; i++)
		for(int j=0; j<=2*k; j++)
			lt[i][j]+=lt[i-1][j];
	int  ans=0;
	for(int a=1; a<=k; a++) {
		for(int b=1; b<=k; b++) {
			int c1=lt[b-1][a-1];
			int c2=lt[b-1][2*k-1]-lt[b-1][k+a-1];
			int c3=lt[2*k-1][a-1]-lt[k+b-1][a-1];
			int c4=lt[2*k-1][2*k-1]-lt[k+b-1][2*k-1]-lt[2*k-1][k+a-1]+lt[k+b-1][a+k-1];
			int c5=lt[k+b-1][a+k-1]-lt[b-1][a+k-1]-lt[b+k-1][a-1]+lt[b-1][a-1];
			ans=max(ans,c1+c2+c3+c4+c5);
			ans=max(ans,n-(c1+c2+c3+c4+c5));
		}
	}
	printf("%d\n",ans);
	return 0;
}