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 <bits/stdc++.h>
using namespace std;
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }

#define COUT(x) cout << #x << " = " << (x) << " (L" << __LINE__ << ")" << endl
template<class T1, class T2> ostream& operator << (ostream &s, pair<T1,T2> P)
{ return s << '<' << P.first << ", " << P.second << '>'; }
template<class T> ostream& operator << (ostream &s, vector<T> P)
{ for (int i = 0; i < P.size(); ++i) { if (i > 0) { s << " "; } s << P[i]; } return s; }
template<class T> ostream& operator << (ostream &s, vector<vector<T> > P)
{ for (int i = 0; i < P.size(); ++i) { s << endl << P[i]; } return s << endl; }
template<class T> ostream& operator << (ostream &s, set<T> P)
{ for(auto it : P) { s << "<" << it << "> "; } return s << endl; }
template<class T1, class T2> ostream& operator << (ostream &s, map<T1,T2> P)
{ for(auto it : P) { s << "<" << it.first << "->" << it.second << "> "; } return s << endl; }


int main() {
    int N, K;
    while (cin >> N >> K) {
    vector<vector<int>> dp(K*5+1, vector<int>(K*5+1, 0));
    for (int i = 0; i < N; ++i) {
        int x, y; char c;
        cin >> x >> y >> c;
        int qx = x / K, qy = y / K;
        if (abs(qx - qy) % 2 == 0) x = x%K, y = y%K;
        else x = x%K, y = y%K+K;
        if (c == 'W') x += K;
        for (int d = 0; d < 3; ++d) {
            for (int e = 0; e < 3; ++e) {
                if (abs(d - e) % 2 == 0) {
                    dp[x + d*K][y + e*K]++;
                    dp[x + (d+1)*K][y + e*K]--;
                    dp[x + d*K][y + (e+1)*K]--;
                    dp[x + (d+1)*K][y + (e+1)*K]++;
                }
            }
        }

        //cout << make_pair(x, y) << endl;
    }
    for (int i = 0; i < K*5; ++i)
        for (int j = 0; j <= K*5; ++j)
            dp[i+1][j] += dp[i][j];
    for (int i = 0; i <= K*5; ++i)
        for (int j = 0; j < K*5; ++j)
            dp[i][j+1] += dp[i][j];
    int res = 0;
    for (int i = 0; i <= K*5; ++i) 
        for (int j = 0; j <= K*5; ++j)
            chmax(res, dp[i][j]);
    cout << res << endl;
    }
}