## 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

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.

Example

Input

10
7 11 1 9 10 3 5 13 9 12