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 -*-
import sys
import copy
import collections
from bisect import bisect_left
from bisect import bisect_right
from collections import defaultdict
from heapq import heappop, heappush
import math

# NO, PAY-PAY
#import numpy as np
#import statistics
#from statistics import mean, median,variance,stdev
 
def main():
    N,K = map(int,input().split())
    maps = [[0 for _ in range(4*K)] for _ in range(4*K)]
    
    for i in range(N):
        inp = input().split(" ")
        tmp1 = int(inp[0])
        tmp2 = int(inp[1])
        if inp[2] == "W":
            tmp2 += K
        tmp1 = tmp1 % (2*K)
        tmp2 = tmp2 % (2*K)
        maps[tmp1][tmp2] += 1
        
        maps[tmp1+(2*K)][tmp2+(2*K)] += 1
        maps[tmp1][tmp2+(2*K)] += 1
        maps[tmp1+(2*K)][tmp2] += 1
        
    for i in range(4*K):
        for j in range(4*K):
            if i == 0:
                if j == 0:
                    continue
                maps[i][j] = maps[i][j] + maps[i][j-1]
                continue
            if j == 0:
                maps[i][j] = maps[i][j] + maps[i-1][j]
                continue
            maps[i][j] = maps[i][j] + maps[i][j-1] + maps[i-1][j] - maps[i-1][j-1]
            
    ans = 0
    for i in range(2*K):
        for j in range(2*K):
            tmp_i = i-1
            tmp_j = j-1
            tmptmp_i = i+K-1
            tmptmp_j = j+K-1
            
            hidari_ue = (tmp_i, tmp_j)
            migi_ue = (tmp_i, tmptmp_j)
            hidari_shita = (tmptmp_i, tmp_j)
            migi_shita = (tmptmp_i, tmptmp_j)
            
            tmp = 0
            if i == 0 and j == 0:
                tmp = maps[migi_shita[0]][migi_shita[1]]
            elif i == 0:
                tmp = maps[migi_shita[0]][migi_shita[1]] - maps[hidari_shita[0]][hidari_shita[1]]
            elif j == 0:
                tmp = maps[migi_shita[0]][migi_shita[1]] - maps[migi_ue[0]][migi_ue[1]]
            else:
                tmp = maps[migi_shita[0]][migi_shita[1]] - maps[migi_ue[0]][migi_ue[1]] - maps[hidari_shita[0]][hidari_shita[1]] + maps[hidari_ue[0]][hidari_ue[1]]
            if ans < tmp:
                ans = tmp
        
    print(ans)
	
if __name__ == "__main__":
	main()