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:
N,K = list(map(int,input().split()))

B = [[0]*(2*K) for i in range(2*K)]
W = [[0]*(2*K) for i in range(2*K)]

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

BS = [[0]*(2*K+1) for i in range(2*K+1)]
WS = [[0]*(2*K+1) for i in range(2*K+1)]

for i in range(2*K):
    for j in range(2*K):
        BS[i+1][j+1] = BS[i][j+1] + BS[i+1][j] - BS[i][j] + B[i][j]
        WS[i+1][j+1] = WS[i][j+1] + WS[i+1][j] - WS[i][j] + W[i][j]

def BOX(x1,y1,x2,y2,S):
    return S[x2][y2]-S[x1][y2]-S[x2][y1]+S[x1][y1]

def smax(a,b):
    if a<b:
        return b
    else:
        return a

ans = 0
for i in range(K):
    for j in range(K):
        count = 0
        count += BOX(0,0,i,j,WS) + BOX(i,0,i+K,j,BS) + BOX(i+K,0,2*K,j,WS)
        count += BOX(0,j,i,j+K,BS) + BOX(i,j,i+K,j+K,WS) + BOX(i+K,j,2*K,j+K,BS)
        count += BOX(0,j+K,i,2*K,WS) + BOX(i,j+K,i+K,2*K,BS) + BOX(i+K,j+K,2*K,2*K,WS)
        ans = smax(smax(count,N-count),ans)
print(ans)