Median Sum

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.

Examples

Input

3 1 2 1

Output

2

Input

1 58

Output

58

inputFormat

input values are integers.

Input

Input is given from Standard Input in the following format:

N A_1 A_2 ... A_N

outputFormat

Output

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

Examples

Input

3 1 2 1

Output

2

Input

1 58

Output

58

样例

3
1 2 1

2