- 83

## 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

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

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 <=

0 < value of an element < 21

There are at most 12 different natural numbers.

`N`<= 400 < 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

A higher resolution is required to access the IDE