Knuth Division

• Time limit: 1.00 s
• Memory limit: 512 MB

Given an array of $n$ numbers, your task is to divide it into $n$ subarrays, each of which has a single element.

On each move, you may choose any subarray and split it into two subarrays. The cost of such a move is the sum of values in the chosen subarray.

What is the minimum total cost if you act optimally?

Input

The first input line has an integer $n$: the array size. The array elements are numbered $1,2,\dots,n$.

The second line has $n$ integers $x_1,x_2,\dots,x_n$: the contents of the array.

Output

Print one integer: the minimum total cost.

Constraints

• $1 \le n \le 5000$
  
• $1 \le x_i \le 10^9$
  

Example

Input:
5
2 7 3 2 5

Output:
43