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 = [int(i) for i in input().split()]
dp = 1
for i in range(0, len(a)):
	dp = (dp | (dp << a[i]))

asum = 0
for i in range(0, len(a)):
	asum += a[i]

for i in range(int((asum + 1) / 2), asum + 1):
	if (dp >> i) & 1:
		print(i)
		break