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 PYTHON3):

Solution:
import sys

#縦k、横kのマスに移動させて考える
n, k = map(int, sys.stdin.readline().strip().split())
x = []
y = []
mx = []
my = []
for _ in range(n):
    xx, yy, c = sys.stdin.readline().strip().split()
    xx = int(xx)
    yy = int(yy)
    if c == 'W':
        xx += k
    xx %= 2 * k
    yy %= 2 * k
    if xx >= k:
        if yy >= k:
            x.append(xx - k)
            y.append(yy - k)
        else:
            mx.append(xx - k)
            my.append(yy)
    else:
        if yy >= k:
            mx.append(xx)
            my.append(yy - k)
        else:
            x.append(xx)
            y.append(yy)

graph = [[0 for _ in range(k)] for __ in range(k)]

#累積和
#lx + lmx = n
lx = len(x)
graph[0][0] += lx
for i in range(lx):
    graph[x[i]][0] -= 1
    graph[0][y[i]] -= 1
    graph[x[i]][y[i]] += 2

lmx = len(mx)
graph[0][0] -= lmx
for i in range(lmx):
    graph[mx[i]][0] += 1
    graph[0][my[i]] += 1
    graph[mx[i]][my[i]] -= 2

for i in graph:
    for j in range(k-1):
        i[j+1] += i[j]

for i in range(k):
    for j in range(k-1):
        graph[j+1][i] += graph[j][i]

#最大値、最小値を取得
big = max([max(i) for i in graph]) + lmx
small = min([min(i) for i in graph]) - lx

if big + small >= 0:
    print(big)
else:
    print(-small)