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 C++14 (GCC 5.4.1) (judge verdict: Accepted)




#if 1
#include <iostream>
#include <fstream>
#include <string>
#include <vector>
#include <map>
#include <set>
#include <unordered_map>
#include <unordered_set>
#include <queue>
#include <stack>
#include <array>
#include <deque>
#include <algorithm>
#include <utility>
#include <cstdint>
#include <functional>
#include <iomanip>
#include <numeric>
#include <assert.h>
#include <bitset>
#include <list>

auto& in = std::cin;
auto& out = std::cout;
#define all(C) std::begin(C), std::end(C)

int32_t N,K;
int32_t memo[2001][2001];//黒の始点,x,y

void imos(int32_t x, int32_t y, int32_t x2, int32_t y2)
{
	++memo[x][y];
	--memo[x][y2];
	--memo[x2][y];
	++memo[x2][y2];
}

int main()
{
	using std::endl;
	in.sync_with_stdio(false);
	out.sync_with_stdio(false);
	in.tie(nullptr);
	out.tie(nullptr);

	in >> N>>K;
	for (size_t i = 0; i < N; i++)
	{
		int32_t x, y; char c;
		in >> x >> y>>c;
		x %= 2*K; y %= 2*K;

		if (((x < K && y < K) || (x >= K && y >= K)) == (c == 'B'))
		{
			auto x_ = x % K, y_ = y % K;
			//++memo[0][0]; --memo[x_ + 1][y_ + 1];
			imos(0, 0, x_ + 1, y_ + 1);
			imos(x_ + K + 1, 0, 2 * K, y_ + 1);

			imos(0, y_ + K + 1, x_ + 1, 2 * K);
			imos(x_ + K + 1, y_ + K + 1, 2 * K, 2 * K);

			imos(x_ + 1, y_ + 1, x_ + K + 1, y_ + K + 1);
		}
		else
		{
			auto x_ = x % K, y_ = y % K;
			//++memo[x_ + 1][y_ + 1]; --memo[x_ + K + 1][y_ + K + 1];

			imos(x_ + 1, 0, x_ + K + 1, y_ + 1);
			imos(x_ + 1, y_ + K + 1, x_ + K + 1, 2 * K);

			imos(0, y_ + 1, x_ + 1, y_ + K + 1);
			imos(x_ + K + 1, y_ + 1, 2 * K, y_ + K + 1);
		}
	}

	for (size_t i = 0; i < 2001; i++)
		for (size_t j = 1; j < 2001; j++)
	{
			memo[i][j] += memo[i][j - 1];
	}
	for (size_t i = 1; i < 2001; i++)
		for (size_t j = 0; j < 2001; j++)
	{
		memo[i][j] += memo[i - 1][j];
	}

	int32_t max = 0;
	for (size_t i = 0; i < 2 * K; i++)
		for (size_t j = 0; j < 2*K; j++)
		{
			max = std::max(max, memo[i][j]);
		}
	out << max << endl;

	return 0;
}
#endif