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Contest: Task: Related: TaskB TaskD

Score : $700$ points

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 $A$.

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, $S = (58)$.