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>
using namespace std;

int main(void) {
    long n, k;
    cin >> n >> k;
    vector<vector<long>> b(4*k+1, vector<long>(4*k+1));
    vector<vector<long>> w(4*k+1, vector<long>(4*k+1));

    for(long i=0; i<n; i++) {
        long x, y;
        string c;
        cin >> x >> y >> c;
        x %= 2*k, y %= 2*k;
        x++, y++;
        (c[0] == 'B' ? b : w)[y][x]++;
        (c[0] == 'B' ? b : w)[y][x+2*k]++;
        (c[0] == 'B' ? b : w)[y+2*k][x]++;
        (c[0] == 'B' ? b : w)[y+2*k][x+2*k]++;
    }

    for(long i=1; i<4*k; i++)
        for(long j=1; j<4*k; j++)
            b[i][j] += b[i-1][j] + b[i][j-1] - b[i-1][j-1];

    for(long i=1; i<4*k; i++)
        for(long j=1; j<4*k; j++)
            w[i][j] += w[i-1][j] + w[i][j-1] - w[i-1][j-1];

    long r = 0;
    for(long i=0; i<2*k; i++)
    for(long j=0; j<2*k; j++) {
        long t = 0;
        t += b[i+k][j+k] - b[i+k][j] - b[i][j+k] + b[i][j];
        i+=k, j+=k;
        t += b[i+k][j+k] - b[i+k][j] - b[i][j+k] + b[i][j];

        i-=k;
        t += w[i+k][j+k] - w[i+k][j] - w[i][j+k] + w[i][j];
        i+=k, j-=k;
        t += w[i+k][j+k] - w[i+k][j] - w[i][j+k] + w[i][j];
        i-=k;

        r = max(r, t);
    }
    cout << r << endl;
}