Problem: 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

Solution (in PYTHON3):

Solution:
import sys
input = sys.stdin.readline

n = int(input())
A = tuple(map(int, input().split()))
M = sum(A)
l = -(-M//2)
dp = 1
mask = (1<<(2*M))-1
for a in A:
  dp |= (dp<<a)&mask
dp >>= l
ans = (dp&(-dp)).bit_length() - 1 + l
print(ans)