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 JavaScript (node.js v5.12) (judge verdict: Runtime Error)

// reader
if (!process.env.LOCAL_DEBUG) {
    require('fs').readFile('/dev/stdin', 'utf8', (err, data) => {
        if (err)
            console.error(err);
        main(data.trim().split('\n'));
    });
}
// main
function main(lines) {
    console.log(solve(lines));
}
// solver
function solve(lines) {
    const { K, requests } = parseLines(lines);
    const grants = [];
    for (let i = 0; i < requests.length; i++) {
        let cnt = 1;
        const [x, y] = requests[i];
        for (let j = 0; j < requests.length; j++) {
            if (i !== j) {
                const [_x, _y] = requests[j];
                const __x = Math.abs(x - _x) % (2 * K);
                const __y = Math.abs(y - _y) % (2 * K);
                if (__x === __y || Math.abs(__x + __y) % K !== 0) {
                    cnt++;
                }
            }
        }
        grants.push(cnt);
    }
    debug({ grants });
    return Math.max(...grants).toString();
}
// helpers
function parseLines(lines) {
    const [N, K] = lines[0].split(' ').map(s => +s);
    const requests = lines.slice(1, 1 + N).map(line => {
        const [x, y, c] = line.split(' ');
        return [+x, c === 'B' ? +y : +y + K];
    });
    const obj = { N, K, requests };
    debug(obj);
    return obj;
}
// general helpers
function debug(message, ...optionalParams) {
    if (!!process.env.LOCAL_DEBUG)
        console.log(message, ...optionalParams);
}