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, $S_{2^N−1}$.

Constraints

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

Input

Input is given from Standard Input in the following format:

N
A1 A2 ... AN

Output

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

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, $S=(58)$.