Problem:
Score : 500 points

Problem Statement

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:

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.

Sample Input 1

4 3
0 1 W
1 2 W
5 3 B
5 4 B

Sample Output 1

4

He can satisfy all his desires by painting as shown in the example above.

Sample Input 2

2 1000
0 0 B
0 1 W

Sample Output 2

2

Sample Input 3

6 2
1 2 B
2 1 W
2 2 B
1 0 B
0 6 W
4 5 W

Sample Output 3

4

Solution in Fortran (gfortran v4.8.4) (judge verdict: Wrong Answer)

implicit none

integer:: n,i,j,k,count,jj,count_max
character,allocatable,dimension(:) :: c*1
integer,allocatable,dimension(:):: x,y
read (5,*) n,k

allocate(x(n))
allocate(y(n))
allocate(c(n))

do i=1,n
    read(5,*) x(i),y(i),c(i)
enddo

do j=1,int(k/2)+1
    do jj=1,int(k/2)+1
    count=0
    do i=1,n
        if (mod(mod(x(i)-j+1,k),2)==1 .and. mod(mod(x(i)-jj+1,k),2)==1 .and. c(i)=="W" ) then
            count=count+1
        endif

enddo
enddo
        count_max=max(count,n-count)
enddo

!write(*,*) n,k
!write(*,*) x,y,c
write(*,*) count_max

stop
end