There is an old stone game.At the beginning of the game the player picks 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.

输入描述:

The input contains several test cases. The first line of each test case contains an integer n, 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.

输出描述:

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

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

0
17
8