Gangsters

$N$ gangsters are going to a restaurant. The $i$-th gangster arrives at time $T_i$ and has prosperity $P_i$. The restaurant door has $K+1$ states of openness, represented by the integers in the range $[0, K]$. The state of openness can change by at most $1$ per unit of time; that is, it either opens by one, closes by one, or stays the same. At the initial moment the door is closed (state $0$).

The $i$-th gangster enters the restaurant only if the door is opened specially for him, i.e. when the state of openness equals his stoutness $S_i$ exactly. If, at the moment the gangster arrives, the state of openness is not equal to his $S_i$, the gangster leaves and never returns.

The restaurant operates during the time interval $[0, T]$.

The goal is to open and close the door appropriately so that the total prosperity of the gangsters gathered in the restaurant is maximized.

The first line contains three integers $N$, $K$, and $T$, separated by spaces. ($1 \le N \le 100$, $1 \le K \le 100$, $0 \le T \le 30{,}000$)

The second line contains the arrival times $T_1, T_2, \dots, T_N$, separated by spaces. ($0 \le T_i \le T$ for $i = 1, 2, \dots, N$)

The third line contains the prosperities $P_1, P_2, \dots, P_N$, separated by spaces. ($0 \le P_i \le 300$ for $i = 1, 2, \dots, N$)

The fourth line contains the stoutnesses $S_1, S_2, \dots, S_N$, separated by spaces. ($1 \le S_i \le K$ for $i = 1, 2, \dots, N$)

All values in the input are integers.

Print a single integer — the maximal total prosperity of the gangsters gathered in the restaurant. If no gangster can enter the restaurant, print $0$.