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

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

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 $A$.