Problem Statement

You are given positive integers $N_A,N_B,N_C$ and integer sequences $(A_1,A_2,\dots,A_{N_A}),(B_1,B_2,\dots,B_{N_B}),(C_1,C_2,\dots,C_{N_C})$.

For a triple $(S_A,S_B,S_C)$ consisting of a subset $S_A$ of $\{1,2,\dots,N_A\}$, a subset $S_B$ of $\{1,2,\dots,N_B\}$, and a subset $S_C$ of $\{1,2,\dots,N_C\}$, its score is defined as follows. \[\left(\sum_{i\in S_A}A_i\right)|S_B|+\left(\sum_{j\in S_B}B_j\right)|S_C|+\left(\sum_{k\in S_C}C_k\right)|S_A|\]

Here, $|S|$ denotes the number of elements of a set $S$. Also, $\sum_{x\in S}f(x)$ denotes the sum of $f(x)$ over all elements $x$ of a set $S$; in particular, if $S$ is empty, then $\sum_{x\in S}f(x)=0$.

Find the maximum possible value of the score.

Note that the answer may not fit in a 32-bit integer type.

Input

$N_A\ N_B\ N_C$
$A_1\ A_2\ \dots\ A_{N_A}$
$B_1\ B_2\ \dots\ B_{N_B}$
$C_1\ C_2\ \dots\ C_{N_C}$

• $1\leq N_A,N_B,N_C\leq 10^5$
• $|A_i|,|B_j|,|C_k|\leq 3\times 10^3$
• All input values are integers.

Output

Output the maximum possible value of the score. Print a newline at the end.

Sample

2 3 3
-5 -2
2 -4 2
-3 -1 3

12

4 4 4
-33 -333 -3 -33
-22 222 22 222
11 -11 111 11

2023

10 10 10
1211 -789 -318 1533 -2837 -1408 117 -30 2777 786
1770 -73 -846 282 2173 2234 2241 -303 -1617 168
498 1150 1730 -230 -1050 730 693 -700 794 349

161276