Knuth Division

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