Problem Statement

You are given N integers A_1, A_2, ..., A_N.
Consider the sums of all non-empty subsequences of A. There are 2^N - 1 such sums, an odd number.
Let the list of these sums in non-decreasing order be S_1, S_2, ..., S_{2^N - 1}.
Find the median of this list, S_{2^{N-1}}.

Input

Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N

Output

Print the median of the sorted list of the sums of all non-empty subsequences of A.

Constraints

• $1 \leq N \leq 2000$
• $1 \leq A_i \leq 2000$
• All input values are integers.

Sample Input 1

3
1 2 1

Sample Output 1

2

In this case, S = (1, 1, 2, 2, 3, 3, 4). Its median is S_4 = 2.

Sample Input 2

1
58

Sample Output 2

58

In this case, S = (58).

见题面 Input 部分

见题面 Output 部分