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;
typedef long long ll;
ll prfx[3005][3005],cnt[2][1005][1005];
int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    ll n,k;cin>>n>>k;
    for(ll i=0;i<n;i++){
        ll x,y;cin>>x>>y;
        char ch;cin>>ch;
        if(ch=='B')y+=k;
        x%=2*k;
        y%=2*k;
        prfx[x][y]++;
        prfx[x+k][y+k]++;
        prfx[x][y+k]--;
        prfx[x+k][y]--;
    }
    for(ll i=0;i<3*k;i++){
        for(ll j=0;j<3*k;j++)prfx[i][j+1]+=prfx[i][j];
    }
    for(ll i=0;i<3*k;i++){
        for(ll j=0;j<3*k;j++)prfx[i+1][j]+=prfx[i][j];
    }
    ll ans = 0;
    for(ll i=0;i<3*k;i++){
        for(ll j=0;j<3*k;j++){
            ll type = (i/k + j/k)%2;
            cnt[type][i%k][j%k]+=prfx[i][j];
        }
    }
    for(ll i=0;i<k;i++)for(ll j=0;j<k;j++)ans=max(ans , max(cnt[0][i][j],cnt[1][i][j]));
    cout<<ans;
}