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
from itertools import accumulate
input = sys.stdin.readline
def main():
    N, K = map( int ,input().split())
    TK = K*2
    B = [[0]*(K*2) for _ in range(TK)]
    for _ in range(N):
        x, y, c = input().split()
        x, y = int(x), int(y)
        if c == "B":
            B[x%TK][y%TK] += 1
        else:
            B[x%TK][(y+K)%TK] += 1
    C = [[0]*(TK+1)] + [[0] + list( accumulate(B[i])) for i in range(TK)]
    for i in range(TK):
        for j in range(TK+1):
            C[i+1][j] += C[i][j]
    def get(i1, j1, i2, j2):
        return C[i2][j2] - C[i1][j2] - C[i2][j1] + C[i1][j1]
    ans = 0
    for i in range(K+1):
        for j in range(K+1):
            if ans < get(0,0,i,j) + get(i+K, 0, TK, j) + get(i, j, i+K, j+K) + get(0, j+K, i, TK) + get(K+i, K+j, TK, TK):
                ans = get(0,0,i,j) + get(i+K, 0, TK, j) + get(i, j, i+K, j+K) + get(0, j+K, i, TK) + get(K+i, K+j, TK, TK)
            if ans < get(i, 0, i+K, j) + get(0, j, i, j+K) + get(i+K, j, TK, j+K) + get(i, j+K, i+K, TK):
                ans = get(i, 0, i+K, j) + get(0, j, i, j+K) + get(i+K, j, TK, j+K) + get(i, j+K, i+K, TK)
    print(ans)
if __name__ == '__main__':
    main()