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:
#from collections import deque,defaultdict
printn = lambda x: print(x,end='')
inn = lambda : int(input())
inl   = lambda: list(map(int, input().split()))
inm   = lambda:      map(int, input().split())
ins = lambda : input().strip()
DBG = True # and False
BIG = 10**18
R = 10**9 + 7
#R = 998244353

def ddprint(x):
  if DBG:
    print(x)

n,k = inm()
k2 = k*2
#ddprint(f"{n=} {k=} {k2=}")
a = [[0]*k2 for i in range(k2)]
for i in range(n):
    x,y,c = input().split()
    xx = int(x)%k2
    yy = (int(y)+(k if c=='B' else 0))%k2
    #ddprint(f"{x=} {y=} {c=} {xx=} {yy=}")
    a[xx][yy] += 1

#ddprint("loc1")
racc = [[0]*k2 for i in range(k2)]
rx = [[0]*k2 for i in range(k2)]
for i in range(k2):
    #if i%100==0:
    #    ddprint(i)
    for j in range(k2):
        racc[i][j] = (0 if j==0 else racc[i][j-1])+a[i][j]
    rsum = sum(a[i])
    for j in range(k):
        rx[i][j] = racc[i][j+k-1]-(0 if j==0 else racc[i][j-1])
    for j in range(k,k2):
        rx[i][j] = rsum-rx[i][j-k]

cacc = [[0]*k2 for i in range(k2)]
cx = [[0]*k2 for i in range(k2)]
for i in range(k2):
    #if i%100==0:
    #    ddprint(i)
    for j in range(k2):
        cacc[j][i] = (0 if j==0 else cacc[j-1][i])+rx[j][i]
if False and DBG:
    for i in range(k2):
        ddprint(a[i])
    ddprint('')
    for i in range(k2):
        ddprint(rx[i])
    ddprint('')
    for i in range(k2):
        ddprint(cacc[i])

mx = 0
for i in range(k2):
    #if i%100==0:
    #    ddprint(i)
    for j in range(k2):
        ii = (i+k)%k2
        if j<k:
            v1 = cacc[j+k-1][i]-(0 if j==0 else cacc[j-1][i])
            v2 = cacc[k2-1][ii] - (cacc[j+k-1][ii]- \
                   (0 if j==0 else cacc[j-1][ii]))
        else:
            jj = j-k
            v1 = cacc[k2-1][i] - (cacc[jj+k-1][i]- \
                   (0 if jj==0 else cacc[jj-1][i]))
            v2 = cacc[jj+k-1][ii]- \
                   (0 if jj==0 else cacc[jj-1][ii])
        mx = max(mx,v1+v2)
print(mx)