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>
#define FOR(i,a,n) for(ll i=(ll)a;i<(ll)n;i++)
#define rep(i,n) FOR(i,0,n)
using namespace std;
typedef long long ll;

template<class T>bool chmax(T &a,const T &b){
    if(a>b)return false;
    a=b;
    return true;
}
template<class T>bool chmin(T &a,const T &b){
    if(a<b)return false;
    a=b;
    return true;
}

const ll mod=1e9+7;
const ll inf=1ll<<60;

/*---------------------*/

ll n,k,x,y,num[2001][2001],a;
char c;

int main(){
    cin>>n>>k;
    ll k2=k*2;
    rep(i,n){
        cin>>x>>y>>c;
        if(c=='W')x+=k;
        num[x%k2+1][y%k2+1]++;
        num[(x+k)%k2+1][(y+k)%k2+1]++;
    }
    rep(i,k2)rep(j,k2)num[i+1][j+1]+=num[i+1][j]+num[i][j+1]-num[i][j];
    ll ans=0;
    rep(i,k)rep(j,k){
        chmax(ans,num[i+k][j+k]-num[i][j+k]-num[i+k][j]+num[i][j]);
    }
    cout<<ans<<endl;
}