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:
n = int(input())
a = list(map(int,input().split()))
s = sum(a)
a.sort()
b = 1
for i in a:
  b |= b<<i
  
b &= 2**(s+1)-2**((s-1)//2)
while True:
  t = b&(-b)
  #print(i,t,b)
  if (s+1)//2 <= t.bit_length()-1 <= s:
    print(t.bit_length()-1)
    break
  b ^= t