### 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 $S_1$, $S2$, …, $S{2^N}−1$.

Find the median of this list, $2^N−1$.

### 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.

3
1 2 1

### Sample Output 1

2
In this case, S=(1,1,2,2,3,3,4). Its median is S4=2.

1
58

### Sample Output 2

58
In this case, S=(58).