Description

There is an old stone game. At the beginning of the game the player picks n(1<=n<=50000) piles of stones in a line. The goal is to merge the stones in one pile observing the following rules: At each step of the game,the player can merge two adjoining piles to a new pile.The score is the number of stones in the new pile. You are to write a program to determine the minimum of the total score. 就是最简单的石子合并问题.

Input

The input contains several test cases. The first line of each test case contains an integer n(N等于100) denoting the number of piles. The following n integers describe the number of stones in each pile at the beginning of the game. The last test case is followed by one zero.

Output

For each test case output the answer on a single line. You may assume the answer will not exceed 1000000000.

Samples

1
100
3
3 4 3
4
1 1 1 1
0

0
17
8