Gangsters

Time Limit: 1 Second    Memory Limit: 32768 KB

N gangsters are going to a restaurant. The i-th gangster comes at the time Ti and has the prosperity Pi. The door of the restaurant has K+1 states of openness expressed by the integers in the range [0, K]. The state of openness can change by one in one unit of time; i.e. it either opens by one, closes by one or remains the same. At the initial moment of time 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 coincides with his stoutness Si. If at the moment of time when the gangster comes to the restaurant the state of openness is not equal to his stoutness, then the gangster goes away and never returns.

The restaurant works in the interval of time [0, T].

The goal is to gather the gangsters with the maximal total prosperity in the restaurant by opening and closing the door appropriately.

Input

  • The first line of the input contains the values N, K, and T, separated by spaces. (1 <= N <= 100, 1 <= K <= 100, 0 <= T <= 30000)
  • The second line of the input contains the moments of time when gangsters come to the restaurant T1, T2, ..., TN, separated by spaces. (0 <= Ti <= T for i = 1, 2, ..., N)
  • The third line of the input contains the values of the prosperity of gangsters P1, P2, ..., PN, separated by spaces. (0 <= Pi <= 300 for i = 1, 2, ..., N)
  • The forth line of the input contains the values of the stoutness of gangsters S1, S2, ..., SN, separated by spaces. (1 <= Si <= K for i = 1, 2, ..., N)

All values in the input file are integers.


This problem contains multiple test cases!

The first line of a multiple input is an integer N, then a blank line followed by N input blocks. Each input block is in the format indicated in the problem description. There is a blank line between input blocks.

Output

Print to the output the single integer - the maximal sum of prosperity of gangsters in the restaurant. In case when no gangster can enter the restaurant the output should be 0.

The output format consists of N output blocks. There is a blank line between output blocks.

Sample Input

2
 
4 10 20
10 16 8 16
10 11 15 1
10 7 1 8

2 17 100
5 0
50 33
6 1

Sample Output

26

0
Submit

Source: Northeastern Europe 1998