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:
def calc(lx,ly,rx,ry):
  if rx<0 or ry<0 or lx>rx or ly>ry:
    return 0
  ret=acum[ry*2*k+rx]
  if lx!=0:
    ret-=acum[ry*2*k+lx-1]
  if ly!=0:
    ret-=acum[(ly-1)*2*k+rx]
  if lx!=0 and ly!=0:
    ret+=acum[(ly-1)*2*k+lx-1]
  return ret

n,k=map(int,input().split())
board=[0]*(4*k*k)
acum=[0]*(4*k*k)
for _ in range(n):
  x,y,c=input().split()
  x,y=int(x)%(2*k),int(y)%(2*k)
  if c=='B':
    board[y*2*k+x]+=1
  if c=='W':
    y+=k
    y%=2*k
    board[y*2*k+x]+=1
for i in range(2*k):
  for j in range(2*k):
    acum[i*2*k+j]=board[i*2*k+j]
    if i!=0:
      acum[i*2*k+j]+=acum[(i-1)*2*k+j]
    if j!=0:
      acum[i*2*k+j]+=acum[i*2*k+j-1]
    if i!=0 and j!=0:
      acum[i*2*k+j]-=acum[(i-1)*2*k+j-1]
ans=0
for i in range(k):
  for j in range(k):
    tmp1=0
    lx,ly=i,j
    rx,ry=lx+k-1,ly+k-1
    #1個目のマス
    tmp1+=calc(lx,ly,rx,ry)
    #左上のマス
    tlx,tly=0,0
    trx,ttry=lx-1,ly-1
    tmp1+=calc(tlx,tly,trx,ttry)
    #右上のマス
    tlx,tly=rx+1,0
    trx,ttry=2*k-1,ly-1
    tmp1+=calc(tlx,tly,trx,ttry)
    #左下のマス
    tlx,tly=0,ry+1
    trx,ttry=lx-1,2*k-1
    tmp1+=calc(tlx,tly,trx,ttry)
    #右下のマス
    tlx,tly=rx+1,ry+1
    trx,ttry=2*k-1,2*k-1
    tmp1+=calc(tlx,tly,trx,ttry)
    tmp2=0
    #上のマス
    tlx,tly=lx,0
    trx,ttry=rx,ly-1
    tmp2+=calc(tlx,tly,trx,ttry)
    #左のマス
    tlx,tly=0,ly
    trx,ttry=lx-1,ry
    tmp2+=calc(tlx,tly,trx,ttry)
    #右のマス
    tlx,tly=rx+1,ly
    trx,ttry=2*k-1,ry
    tmp2+=calc(tlx,tly,trx,ttry)
    #下のマス
    tlx,tly=lx,ry+1
    trx,ttry=rx,2*k-1
    tmp2+=calc(tlx,tly,trx,ttry)
    ans=max(ans,tmp1,tmp2)
print(ans)