Problem: 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:

cba927b2484fad94fb5ff7473e9aadef.png

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.

Examples

Input

4 3
0 1 W
1 2 W
5 3 B
5 4 B


Output

4


Input

2 1000
0 0 B
0 1 W


Output

2


Input

6 2
1 2 B
2 1 W
2 2 B
1 0 B
0 6 W
4 5 W


Output

4

Solution (in CPP):

Solution:
#include "bits/stdc++.h"
#define rep(i,n) for(int i = 0; i < (n); ++i)
using namespace std;
typedef long long int ll;
typedef pair<int, int> P;
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; }

int main(){
	cin.tie(0);
	ios::sync_with_stdio(false);
	int n, k;
	cin >> n >> k;
	int k2 = 2*k;
	vector<vector<int>> cnt(2*k, vector<int>(k2, 0));
	vector<vector<int>> twoDimSum(4*k, vector<int>(4*k, 0));
	rep(i,n){
		int x, y;
		char c;
		cin >> x >> y >> c;
		if(c == 'W') x += k;
		x %= k2;
		y %= k2;
		++cnt[y][x];
	}
	rep(i,4*k)rep(j,4*k){
		twoDimSum[i][j] = cnt[i%k2][j%k2];
	}
	rep(i,4*k)rep(j,4*k-1){
		twoDimSum[i][j+1] += twoDimSum[i][j];
	}
	rep(i,4*k-1)rep(j,4*k){
		twoDimSum[i+1][j] += twoDimSum[i][j];
	}
	int ans = 0;
	rep(i,k2)rep(j,k2){
		int score = twoDimSum[i+k][j+k] - twoDimSum[i+k][j] - twoDimSum[i][j+k] + twoDimSum[i][j];
		score += twoDimSum[i+k2][j+k2] - twoDimSum[i+k2][j+k] - twoDimSum[i+k][j+k2] + twoDimSum[i+k][j+k];
		chmax(ans, score);
	}
	cout << ans << endl;
	return 0;
}