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():
    import sys
    input = sys.stdin.readline
    
    N,K = map(int,input().split())
    BMAP = [[0]*(2*K) for j in range(2*K)]
    WMAP = [[0]*(2*K) for j in range(2*K)]
    
    for i in range(N):
        x,y,c = input().split()
        x = int(x)%(2*K)
        y = int(y)%(2*K)
        if c == "B":
            BMAP[y][x] += 1
        else:
            WMAP[y][x] += 1
    
    import copy
    Bruiseki =  copy.deepcopy(BMAP)
    Wruiseki =  copy.deepcopy(WMAP)
    
    for i in range(2*K):
        for j in range(1,2*K):
            Bruiseki[i][j] += Bruiseki[i][j-1]
            Wruiseki[i][j] += Wruiseki[i][j-1]
    
    for i in range(2*K):
        for j in range(1,2*K):
            Bruiseki[j][i] += Bruiseki[j-1][i]
            Wruiseki[j][i] += Wruiseki[j-1][i]
    
    ans = 0
    for i in range(K):
        for j in range(K):
            Bone = Bruiseki[i][j]
            Btwo = Bruiseki[i][j+K] - Bone
            Bthree = Bruiseki[i][2*K-1] - Bruiseki[i][j+K]
            Bfour = Bruiseki[i+K][j] - Bone
            Bfive = Bruiseki[i+K][j+K] - Bone - Btwo - Bfour
            Bsix = Bruiseki[i+K][2*K-1] - Bruiseki[i+K][j+K] - Bthree
            Bseven =  Bruiseki[2*K-1][j] - Bruiseki[i+K][j]
            Beight = Bruiseki[2*K-1][j+K] - Bruiseki[i+K][j+K] - Bseven
            Bnine = Bruiseki[2*K-1][2*K-1] - Bruiseki[2*K-1][j+K] - Bthree - Bsix
            
            Wone = Wruiseki[i][j]
            Wtwo = Wruiseki[i][j+K] - Wone
            Wthree = Wruiseki[i][2*K-1] - Wruiseki[i][j+K]
            Wfour = Wruiseki[i+K][j] - Wone
            Wfive = Wruiseki[i+K][j+K] - Wone - Wtwo - Wfour
            Wsix = Wruiseki[i+K][2*K-1] - Wruiseki[i+K][j+K] - Wthree
            Wseven =  Wruiseki[2*K-1][j] - Wruiseki[i+K][j]
            Weight = Wruiseki[2*K-1][j+K] - Wruiseki[i+K][j+K] - Wseven
            Wnine = Wruiseki[2*K-1][2*K-1] - Wruiseki[2*K-1][j+K] - Wthree - Wsix
            
            tmp1 = Wone+Wthree+Wfive+Wseven+Wnine + Btwo+Bfour+Bsix+Beight
            tmp2 = Bone+Bthree+Bfive+Bseven+Bnine + Wtwo+Wfour+Wsix+Weight
            
            if tmp1 > ans:
                ans = tmp1
            if tmp2 > ans:
                ans = tmp2
            
    print(ans)

    
    
main()