Dual Brain Exam Revision Scheduling

In the final exam, kkksc03 needs to revise 4 subjects. Each subject has its own problem set. Specifically, the four subjects have s₁, s₂, s₃, s₄ problems respectively. For the first subject, the problems take A_1, A_2, \ldots, A_{s_1} time units; for the second subject, they take B_1, B_2, \ldots, B_{s_2} time units; for the third subject, C_1, C_2, \ldots, C_{s_3}; and for the fourth subject, D_1, D_2, \ldots, D_{s_4}.

kkksc03 has a unique ability: his two brains can compute 2 different problems simultaneously, but only if the problems belong to the same subject. Moreover, he must revise one subject at a time.

For each subject, the problems can be processed in parallel on 2 'processors' (the two brains). The minimal time to finish one subject is the minimum possible maximum sum when dividing the problem times into two groups. Formally, for a subject with tasks having times \(t_1, t_2, \ldots, t_n\), if we partition the tasks into two sets \(S_1\) and \(S_2\), then the time taken is

[ T = \max\Bigl(\sum_{i \in S_1} t_i,; \sum_{i \in S_2} t_i\Bigr)]

The overall minimal time to complete the revision is the sum of the minimal times of all 4 subjects.

Your task is to compute and output the minimum total time required for kkksc03 to finish his revision.

inputFormat

The first line contains 4 integers s₁ s₂ s₃ s₄ --- indicating the number of problems in each subject.

The next 4 lines describe the problem times for each subject in order:

• The second line contains s₁ integers, representing A₁, A₂, \ldots, A_s₁.
• The third line contains s₂ integers, representing B₁, B₂, \ldots, B_s₂.
• The fourth line contains s₃ integers, representing C₁, C₂, \ldots, C_s₃.
• The fifth line contains s₄ integers, representing D₁, D₂, \ldots, D_s₄.

You can assume that all numbers are positive integers.

outputFormat

Output a single integer --- the minimum total time required to complete the revision across all subjects.

sample

2 1 1 1
3 1
4
2
5

14