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
input = sys.stdin.readline

def query(x1, y1, x2, y2, acc):
    return acc[x2+1][y2+1]-acc[x2+1][y1]-acc[x1][y2+1]+acc[x1][y1]

N, K = map(int, input().split())
W = [[0]*K for _ in range(K)]
B = [[0]*K for _ in range(K)]

for _ in range(N):
    xi, yi, ci = input().split()
    xi = int(xi)
    yi = int(yi)
    t = (xi-xi%K)//K+(yi-yi%K)//K
    
    if t%2==1:
        ci = 'B' if ci=='W' else 'W'
    
    if ci=='W':
        W[xi%K][yi%K] += 1
    else:
        B[xi%K][yi%K] += 1


W_acc = [[0]*(K+1) for _ in range(K+1)]
B_acc = [[0]*(K+1) for _ in range(K+1)]

for i in range(K):
    for j in range(K):
        W_acc[i+1][j+1] = W_acc[i+1][j]+W_acc[i][j+1]-W_acc[i][j]+W[i][j]
        B_acc[i+1][j+1] = B_acc[i+1][j]+B_acc[i][j+1]-B_acc[i][j]+B[i][j]
        
ans = 0

for i in range(K):
    for j in range(K):
        clear_w = query(0, 0, i, j, W_acc)+query(i+1, j+1, K-1, K-1, W_acc)
        clear_b = query(i+1, 0, K-1, j, B_acc)+query(0, j+1, i, K-1, B_acc)
        ans = max(ans, clear_w+clear_b)
        
        clear_w = query(0, 0, i, j, B_acc)+query(i+1, j+1, K-1, K-1, B_acc)
        clear_b = query(i+1, 0, K-1, j, W_acc)+query(0, j+1, i, K-1, W_acc)
        ans = max(ans, clear_w+clear_b)
        
print(ans)