Problem Statement

Snuke has a blackboard and N candies.
The tastiness of the i-th candy is a_i.
He will repeat the operation below until he has no more candy.

• Choose one or two of his candies and eat them (of course, they disappear). Then, write on the blackboard the total tastiness of the candies he has just chosen.

Snuke wants to minimize X-Y, where X and Y are the largest and smallest values written on the blackboard, respectively.
Find the minimum possible value of X-Y.

Input

Input is given from Standard Input in the following format:
N
$a_{1} a_{2} \cdots a_N$

Output

Print the minimum possible value of X-Y, where X and Y are the largest and smallest values written on the blackboard, respectively.

Constraints

• All values in input are integers.
• $1 \leq N \leq 5000$
• -$10^{9} \leq a_i \leq 10^9$

Sample Input 1

3
1 2 4

Sample Output 1

1

• One optimal sequence of operations is to eat the candies with the tastinesses of 1 and 2 in the first operation, and then eat the candies with the tastiness of 4 in the second operation.

Sample Input 2

2
-100 -50

Sample Output 2

0

• It is optimal to eat both candies with the tastiness of -100 and -50 in the first operation.

Sample Input 3

20
-18 31 -16 12 -44 -5 24 17 -37 -31 46 -24 -2 11 32 16 0 -39 35 38

Sample Output 3

13

见题面 Input 部分

见题面 Output 部分