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
import array
input = sys.stdin.readline
N,K = map(int,input().split())
xyc = []
for i in range(N):
    x,y,c = input().split()
    x = int(x)
    y = int(y)
    xyc.append([x % (2*K), y % (2*K), c])

wmap = [array.array('I',[0]*3*K) for i in [0]*3*K]
hmap = [array.array('I',[0]*3*K) for i in [0]*3*K]
for x,y,c in xyc:
    if c == 'W':
        wmap[y][x] += 1
        if y < K:
            wmap[y+2*K][x] += 1
        if x < K:
            wmap[y][x+2*K] += 1
        if x < K and y < K:
            wmap[y+2*K][x+2*K] += 1
    else:
        hmap[y][x] += 1
        if x < K:
            hmap[y][x+2*K] += 1
        if y < K:
            hmap[y+2*K][x] += 1
        if x < K and y < K:
            hmap[y+2*K][x+2*K] += 1

def accum(L):
    res = [0]*(len(L)+1)
    res[1] = L[0]
    for i in range(2,len(L)+1):
        res[i] = res[i-1] + L[i-1]
    return res
wcumsum = [array.array('I',[0]*(3*K+1))] + [array.array('I',accum(row)) for row in wmap]
hcumsum = [array.array('I',[0]*(3*K+1))] + [array.array('I',accum(row)) for row in hmap]

for y in range(1,3*K+1):
    for x in range(3*K+1):
        wcumsum[y][x] += wcumsum[y-1][x]
        hcumsum[y][x] += hcumsum[y-1][x]

def cs2(m, ltx, lty, rbx, rby):
    S = m[rby-1][rbx-1]
    S -= m[rby-1][ltx-1]
    S -= m[lty-1][rbx-1]
    S += m[lty-1][ltx-1]
    return S

ans = 0
for y in range(1,K+1):
    for x in range(1,K+1):
        ltw = cs2(wcumsum,x,y,x+K, y+K)
        rbw = cs2(wcumsum,x+K,y+K,x+2*K, y+2*K)
        lbh = cs2(hcumsum,x,y+K,x+K, y+2*K)
        rth = cs2(hcumsum,x+K,y,x+2*K, y+K)
        temp = ltw + rbw + lbh + rth
        ans = max(ans,temp)

        ltw = cs2(hcumsum,x,y,x+K, y+K)
        rbw = cs2(hcumsum,x+K,y+K,x+2*K, y+2*K)
        lbh = cs2(wcumsum,x,y+K,x+K, y+2*K)
        rth = cs2(wcumsum,x+K,y,x+2*K, y+K)
        temp = ltw + rbw + lbh + rth
        ans = max(ans,temp)

print(ans)