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:
# D - Checker

N, K = map(int, input().split())
g = [[0]*K for _ in range(K)] # PDF解説通り2K*2K範囲でやると市松模様の処理が大変なのでK*Kの範囲で計算

for _ in range(N):
    x, y, c = input().split()
    x = int(x)
    y = int(y)
    tmp = (x//K + y//K) % 2
    x %= K
    y %= K
    if (tmp == 0 and c == "B") or (tmp == 1 and c == "W"):
        g[x][y] += 1
    else:
        g[x][y] -= 1 # 白希望の点を-1で記録する

for i in range(K):
    for j in range(1,K):
        g[i][j] += g[i][j-1]

for i in range(1,K):
    for j in range(K):
        g[i][j] += g[i-1][j]

# [i,j]を黒範囲の左下の点とする。[0,i] * [0,j] の範囲または[i+1,K-1] * [j+1,K-1]の範囲にある黒希望点の個数を足し、白希望の点の個数を引く
# 上記範囲外にある白希望の点の個数を足し、黒希望の点の個数を引く
ans = 0
for i in range(K):
    for j in range(K):
        n_satisfied = g[-1][-1] -2*(g[-1][j] + g[i][-1]) + 4*g[i][j]
        ans = max(ans, (N + n_satisfied)//2, (N - n_satisfied)//2) # ((希望通りの点 + 希望通りでない点) + (希望通りの点 - 希望通りでない点))//2

print(ans)