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: Wrong Answer)

#include <iostream>
#include <string>
#include <algorithm>
#include <cstdio>
#include <vector>
#include <queue>
#include <set>
#include <numeric>
#include <cmath>

using namespace std;

typedef long long int lld;

const lld mod = 1e9+7;
const lld INF = 1e9;
//const lld MAXN = 1e9;

struct node
{
    int x,y;
    char c;
    bool color;
    node()
    {
        x=0,y=0;
        color = false;
    }
};

int main()
{
    int n,k;

    cin >> n >> k;
    vector<node> v(n);

    for(int i = 0; i < n; i++)
    {
        cin >> v[i].x >> v[i].y >> v[i].c;
    }

    for(int i = 0; i < n; i++)
    {
        v[i].x %= 2*k;
        v[i].y %= 2*k;
    }

    pair<int,int> even,odd; //first = number of 'B' second = "W"

    for(int i = 0; i < n; i++)
    {
        if ((v[i].x < k && v[i].y < k) || (v[i].x >= k && v[i].y >= k))
        {
            v[i].color = true;
            if (v[i].c == 'B')
            {
                even.first++;
            }else
            {
                even.second++;
            }
        }else
        {
            if (v[i].c == 'B')
            {
                odd.first++;
            }else
            {
                odd.second++;
            }
        }
    }

    // cout << "even_B = " << even.first << " even_W = " << even.second;
    // cout << "  odd_B = " << odd.first << " odd_W = " << odd.second;
    // printf("\n");

    int sol = 0;

    if (max(even.first,even.second) >= max(odd.first,odd.second))
    {
        if (even.first >= even.second)
        {
            for(int i = 0; i < n; i++)
            {
                if (v[i].color && v[i].c == 'B')
                {
                    sol++;
                }

                if (!v[i].color && v[i].c == 'W')
                {
                    sol++;
                }
            }
        }else
        {
            for(int i = 0; i < n; i++)
            {
                if (v[i].color && v[i].c == 'W')
                {
                    sol++;
                }

                if (!v[i].color && v[i].c == 'B')
                {
                    sol++;
                }
            }
        }
    }else
    {
        if (odd.first >= odd.second)
        {
            for(int i = 0; i < n; i++)
            {
                if (v[i].color && v[i].c == 'W')
                {
                    sol++;
                }

                if (!v[i].color && v[i].c == 'B')
                {
                    sol++;
                }
            }
        }else
        {
            for(int i = 0; i < n; i++)
            {
                if (v[i].color && v[i].c == 'B')
                {
                    sol++;
                }

                if (!v[i].color && v[i].c == 'W')
                {
                    sol++;
                }
            }
        }
    }

    if (max(even.first,even.second) == 0)
    {
        sol = odd.first + odd.second;
    }else if (max(odd.first,odd.second) == 0)
    {
        sol = even.first + even.second;
    }

    cout << sol << endl;

    return 0;
}