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:
def main():
    from itertools import accumulate as ac
    n,k=map(int,input().split())
    kk=2*k
    xyc=[input().split() for _ in [0]*n]
    b=[[0]*(k+1) for _ in [0]*(kk+1)]
    for x,y,c in xyc:
        if c=="B":
            if int(y)%kk<k:
                b[int(x)%kk+1][int(y)%k+1]+=1
            else:
                b[(int(x)+k)%kk+1][int(y)%k+1]+=1
        else:
            if int(y)%kk<k:
                b[(int(x)+k)%kk+1][int(y)%k+1]+=1
            else:
                b[int(x)%kk+1][int(y)%k+1]+=1
    b=[list(ac(i)) for i in b]
    for i in range(1,kk+1):
        for j in range(k+1):
            b[i][j]+=b[i-1][j]
    ans=0
    for i in range(kk):
        if i==0:
            a_t=((i,i+k,0),(i+k,kk,1))
        elif i<k:
            a_t=((0,i,-1),(i,i+k,0),(i+k,kk,1))
        elif i==k:
            a_t=((0,i,-1),(i,kk,0))
        else:
            a_t=((0,i-k,-2),(i-k,i,-1),(i,kk,0))
        for j in range(k):
            if j==0:
                b_t=((0,k,0),)
            else:
                b_t=((0,j,-1),(j,k,0))
            black=[]
            for i,j,l in a_t:
                for x,y,z in b_t:
                    if (l+z)%2==0:
                        black.append((i,x,j,y))
            ret=0
            for tx1,ty1,tx2,ty2 in black:
                ret+=b[tx1][ty1]+b[tx2][ty2]-b[tx1][ty2]-b[tx2][ty1]
            ans=max(ans,ret)
    print(ans)
main()