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

def accumrate(h,w,acc,A):
  for i in range(1,h+1):
    for j in range(1,w+1):
      acc[i][j] = acc[i][j-1] + A[i-1][j-1]
  for i in range(1,h+1):
    for j in range(1,w+1):
      acc[i][j] += acc[i-1][j]
      
def cal(i,j,g,r,acc):
  return acc[g][r] + acc[i][j] - acc[g][j] - acc[i][r]

n,k = map(int,input().split())
K = 2*k
cw = [[0]*K for i in range(K)]
cb = [[0]*K for i in range(K)]
sw = 0
sb = 0
for i in range(n):
  x,y,c = input().split()
  if c == 'B':
    cb[int(x)%K][int(y)%K] += 1
    sb += 1
  else:
    cw[int(x)%K][int(y)%K] += 1
    sw += 1
    
acw = [[0]*(K+1) for i in range(K+1)]
acb = [[0]*(K+1) for i in range(K+1)]
accumrate(K,K,acb,cb)
accumrate(K,K,acw,cw)

ans = 0
for i in range(k):
  for j in range(k):
    chk_b = cal(0,0,i,j,acb)+cal(i,j,i+k,j+k,acb)+cal(i+k,j+k,K,K,acb)+cal(0,j+k,i,K,acb)+cal(i+k,0,K,j,acb)
    chk_w = cal(0,0,i,j,acw)+cal(i,j,i+k,j+k,acw)+cal(i+k,j+k,K,K,acw)+cal(0,j+k,i,K,acw)+cal(i+k,0,K,j,acw)
    ans = max(ans,max(chk_b+sw-chk_w,chk_w+sb-chk_b))
    
print(ans)