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:
#解説参照
n = int(input())
a = list(map(int, input().split( )))

dp = 1
for i in range(n):
    dp |= dp<<a[i]
ans = (sum(a)+1)//2
tmp = 1<<ans
for i in range(ans):
    if dp&tmp:
        print(ans)
        exit()
    ans+=1
    tmp <<=1
print(ans)