Description

The Eastowner city is perpetually haunted with water supply shortages, so in order to remedy this problem a new water-pipe has been built. Builders started the pipe from both ends simultaneously, and after some hard work both halves were connected. Well, almost. First half of pipe ended at a point (x1, y1), and the second half -- at (x2, y2). Unfortunately only few pipe segments of different length were left. Moreover, due to the peculiarities of local technology the pipes can only be put in either north-south or east-west direction, and be connected to form a straight line or 90 degree turn. You program must, given L1, L2, ... Lk -- lengths of pipe segments available and C1, C2, ... Ck -- number of segments of each length, construct a water pipe connecting given points, or declare that it is impossible. Program must output the minimum required number of segments.

Constraints

1 <= k <= 4, 1 <= xi, yi, Li <= 1000, 1 <= Ci <= 10

Input

Input contains integers x1 y1 x2 y2 k followed by 2k integers L1 L2 ... Lk C1 C2 ... Ck

Output

Output must contain a single integer -- the number of required segments, or −1 if the connection is impossible.

20 10 60 50 2 70 30 2 2

4

Source

Northeastern Europe 2003, Far-Eastern Subregion