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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

# -*- coding: utf-8 -*-
# python template for atcoder1
import sys
sys.setrecursionlimit(10**9)
input = sys.stdin.readline


def solve():
    N, K = map(int, input().split())
    K2 = 2*K

    grid = [[0]*(K2+1) for _ in range(K2+1)]

    # handle input
    # 全てを2K*2Kに圧縮する
    for _ in range(N):
        x, y, s = input().split()
        # 2K * 2Kに収める
        x = int(x)
        y = int(y)
        if s == "W":
            y += K
        x %= K2
        y %= K2

        grid[x][y] += 1

    # 累積和をとる
    for row in range(1, K2+1):
        for col in range(1, K2+1):
            grid[row][col] += grid[row-1][col] + \
                grid[row][col-1] - grid[row-1][col-1]

    ans = 0
    for row in range(K2):
        for col in range(K2):
            down_lim = (row % K)+K
            left_lim = (col % K)+K
            upper_left = grid[row][col] - \
                grid[row][0]-grid[0][col]+grid[0][0]
            down_right = grid[-1][-1]-grid[down_lim][-1] - \
                grid[-1][left_lim]+grid[down_lim][left_lim]
            upper_right = grid[row][-1] - \
                grid[0][-1]-grid[row][left_lim]+grid[0][left_lim]
            down_left = grid[col][-1]-grid[row][-1] - \
                grid[row][-1]+grid[row][0]
            center = grid[down_lim][left_lim]-grid[down_lim][col] - \
                grid[row][left_lim]+grid[row][col]
            tmp = upper_left+down_right+center+down_left+upper_right
            if row < K and col < K or row <= K and col >= K:
                tmp = tmp
            else:
                tmp = N - tmp

            ans = max(ans, tmp)
    print(ans)


solve()