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:
# coding: utf-8
# Your code here!
import sys
sys.setrecursionlimit(10**6)
readline = sys.stdin.readline
 
#n = int(input())
n,k = [int(i) for i in readline().split()]
xyc = []


B = [[0]*(k+1) for i in range(k+1)]
W = [[0]*(k+1) for i in range(k+1)]

for _ in range(n):
    x,y,c = [i for i in readline().split()] 
    x = int(x)
    y = int(y)
    sgn = 0
    sgn += x//k
    x %= k
    sgn += y//k
    y %= k
    if sgn&1:
        if c == "W": B[x+1][y+1] += 1
#            xyc.append((x,y,"B"))
        else: W[x+1][y+1] += 1
#            xyc.append((x,y,"W"))
    else:
        if c == "W": W[x+1][y+1] += 1
#            xyc.append((x,y,"B"))
        else: B[x+1][y+1] += 1
#            xyc.append((x,y,"W"))


for i in range(k):
    for j in range(k):
        B[i+1][j+1] += B[i+1][j] + B[i][j+1] - B[i][j]
        W[i+1][j+1] += W[i+1][j] + W[i][j+1] - W[i][j]

#print(B)
#print(W)

ans = 0
for i in range(k):
    for j in range(k):
        resb1 = B[i][j] + (B[-1][-1] - B[-1][j] - B[i][-1] + B[i][j])
        resw1 = W[i][j] + (W[-1][-1] - W[-1][j] - W[i][-1] + W[i][j])
        
        resb2 = (B[i][-1] - B[i][j]) + (B[-1][j] - B[i][j])
        resw2 = (W[i][-1] - W[i][j]) + (W[-1][j] - W[i][j])
        
#        print(i,j,"ij",resb1,resw2,resw1,resb2)
        ans = max(ans,resb1+resw2, resw1+resb2)


print(ans)