## 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 A** elements is **the nearest possible** to the **multiplication 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

Output

**Line 1:** The minimal difference between the squarred sum of elements in list A and the multiplication of elements in list B.

Constraints

1 <= `N` <= 40

0 < value of a list element < 21

`N` is always even, so size(A) = size(B).

There is at most 12 different natural numbers.

Example

Input

10
7 11 1 9 10 3 5 13 9 12