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:
import sys
input = sys.stdin.readline
N,K=map(int,input().split())
#x,y,c=[],[],[]
lis=[[[0]*K for _ in range(K)] for i in range(2)]
for i in range(N):
    x,y,c=input().split()
    x=int(x)
    y=int(y)
    """x.append(int(xx))
    y.append(int(yy))
    c.append(cc)"""
    if c=="B" :
        C=1
    if c=="W":
        C=0
    now=(x//K+y//K+C)%2
    lis[now][x%K][y%K]+=1
#print(lis)
for t in range(2):
    for i in range(K):
        for j in range(1,K):
            lis[t][i][j]+=lis[t][i][j-1]
    #print(lis)
    for i in range(1,K):
        for j in range(K):
            lis[t][i][j]+=lis[t][i-1][j]
            #print("A",lis)
"""for t in range(2):
    for i in range(K):
        for j in range(K):
            if i!=0 : lis[t][i][j]+=lis[t][i-1][j]
            if j!=0 : lis[t][i][j]+=lis[t][i][j-1]
            if i!=0 and j!=0:
                lis[t][i][j]-=lis[t][i-1][j-1]"""
#print(lis)
ans=0
for t in range(2):
    for i in range(K):
        for j in range(K):
            cnt=2*lis[t][i][j]+lis[t][-1][-1]-lis[t][i][-1]-lis[t][-1][j]\
            +lis[1-t][i][-1]+lis[1-t][-1][j]-2*lis[1-t][i][j]
            ans=max(ans,cnt)
"""
for i in range(K):
    for j in range(K):
        cnt=-2*lis[i][j]+lis[i][-1]+lis[-1][j]
        ans=max(ans,cnt)"""

print(ans)
#print(x,y,c)