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Statement
Goal
You have a list of natural numbers of size N and you must distribute the values in two lists A and B of size N/2, so that the squared sum of the A elements is the nearest possible to the product of the B elements.Example:
Consider the list 7 11 1 9 10 3 5 13 9 12.
The optimized distribution is:
List A: 5 9 9 12 13
List B: 1 3 7 10 11
which leads to the difference abs( (5+9+9+12+13)^2 - (1*3*7*10*11) ) = 6
Your program should therefore output 6, which is the minimum difference that can be achieved.
Input
Line 1: The list size N
Line 2: N space separated natural numbers
Line 2: N space separated natural numbers
Output
Line 1: The minimum difference between the squared sum of elements in list A and the product of elements in list B.
Constraints
1 <= N <= 40
0 < value of an element < 21
N is always even, so size(A) = size(B).
There are at most 12 different natural numbers.
0 < value of an element < 21
N is always even, so size(A) = size(B).
There are at most 12 different natural numbers.
Example
Input
10 7 11 1 9 10 3 5 13 9 12
Output
6
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