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.
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.
The output format consists of N output blocks. There is a blank line between output blocks.
Sample Input
2
20 10 60 50 2
70 30 2 2
5 5 5 6 1
2 10
Sample Output
4
-1
