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())
L=[[0 for i in range(K*2+1)]for j in range(K*2+1)]
for i in range(N):
    x,y,c=list(input().split())
    if c=="W":
        x=int(x)+K
        y=int(y)
    else:
        x=int(x)
        y=int(y)
    L[x%(2*K)+1][y%(2*K)+1]+=1
#print(L)

for h in range(1,2*K+1):
    for w in range(1,2*K+1):
        L[h][w]=L[h-1][w]+L[h][w]
#print(L)
for h in range(1,2*K+1):
    for w in range(1,2*K+1):
        L[h][w]=L[h][w-1]+L[h][w]
#print(L)

ans=0
for h in range(1,K+1):
    for w in range(1,K+1):
        cnt=0
        for a in range(3):
            for b in range(3):
                if (a+b)%2==0:
                    HH=h+a*K
                    if h+a*K>2*K:
                        HH=2*K
                    HL=h+a*K-K
                    if h+a*K-K<0:
                        HL=0
                    WH=w+b*K
                    if w+b*K>2*K:
                        WH=2*K
                    WL=w+b*K-K
                    if w+b*K-K<0:
                        WL=0
                    cnt+=L[HH][WH]+L[HL][WL]-L[HH][WL]-L[HL][WH]
        ans=max(ans,max(cnt,N-cnt))
print(ans)