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 PYTHON3):

Solution:
# -*- coding: utf-8 -*-
import sys
sys.setrecursionlimit(10**9)
INF=10**18
MOD=10**9+7
input=lambda: sys.stdin.readline().rstrip()
YesNo=lambda b: bool([print('Yes')] if b else print('No'))
YESNO=lambda b: bool([print('YES')] if b else print('NO'))
int1=lambda x:int(x)-1

def main():
    N,K=map(int,input().split())
    a=[[[0]*K*2 for _ in range(K*2)] for _ in range(2)]
    for _ in range(N):
        x,y,c=input().split()
        x,y=int(x)%(K*2),int(y)%(K*2)
        if c=='W':
            a[0][y][x]+=1
        else:
            a[1][y][x]+=1
    S=[[[0]*(K*2+1) for _ in range(K*2+1)] for _ in range(2)]
    for k in range(2):
        for i in range(K*2):
            for j in range(K*2):
                S[k][i+1][j+1]=S[k][i][j+1]+S[k][i+1][j]-S[k][i][j]+a[k][i][j]
    def getsum(k,y1,y2,x1,x2):
        return S[k][x2][y2]-S[k][x1][y2]-S[k][x2][y1]+S[k][x1][y1]
    ans=0
    for k in range(2):
        for i in range(K+1):
            for j in range(K+1):
                tmp=0
                tmp+=getsum(k,0,i,0,j)+getsum(k,i+K,K*2,0,j)+getsum(k,0,i,j+K,K*2)+getsum(k,i+K,K*2,j+K,K*2)+getsum(k,i,i+K,j,j+K)
                tmp+=getsum(not k,i,i+K,0,j)+getsum(not k,i,i+K,j+K,K*2)+getsum(not k,0,i,j,j+K)+getsum(not k,i+K,K*2,j,j+K)
                ans=max(ans,tmp)
    print(ans)

if __name__ == '__main__':
    main()