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:
from math import ceil

N = int(input())
As = list(map(int, input().split()))

# dpの右から(j+1)ビット目: 和がjである部分列が存在するならば1
dp = 1
for A in As:
    dp |= dp << A

# 和がjである部分列が存在する、(ΣA/2)以上で最小のjが答え
ans = ceil(sum(As) / 2)
dp >>= ans
while not (dp & 1):
    dp >>= 1
    ans += 1

print(ans)