Problem C
Kayaking Trip

Solution to Sample Input 1, with kayaks replaced by canoes (cc by-sa NCPC 2017)

The kayaks are of different types and have different amounts of packing, so some are more easily paddled than others. This is captured by a speed factor $c$ that you have already figured out for each kayak. The final speed $v$ of a kayak, however, is also determined by the strengths $s_1$ and $s_2$ of the two people in the kayak, by the relation $v=c(s_1+s_2)$. In your group you have some beginners with a kayaking strength of $s_b$, a number of normal participants with strength $s_n$ and some quite experienced strong kayakers with strength $s_e$.

Input

The first line of input contains three non-negative integers $b$, $n$, and $e$, denoting the number of beginners, normal participants, and experienced kayakers, respectively. The total number of participants, $b+n+e$, will be even, at least $2$, and no more than $100000$. This is followed by a line with three integers $s_b$, $s_n$, and $s_e$, giving the strengths of the corresponding participants ($1\le s_b<s_n<s_e\le 1000$). The third and final line contains $m=\frac{b+n+e}{2}$ integers $c_1,\dots ,c_m$ ($1\le c_i\le 100000$ for each $i$), each giving the speed factor of one kayak.

Output

Output a single integer, the maximum speed that the slowest kayak can get by distributing the participants two in each kayak.

3 1 0
40 60 90
18 20

1600

7 0 7
5 10 500
1 1 1 1 1 1 1

505