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 CPP):

Solution:
#include <cstdio>
#include <bitset>
#include <cstring>
#define rep(a,b,c) for(int a=b;a<=c;a++)
using std::bitset;
bitset<4000001> s;
int n,a[2001],S,sum,ans;
int main() {
	scanf("%d",&n);
	rep(i,1,n) scanf("%d",&a[i]),sum+=a[i]; S=sum; sum/=2;
	s[0]=1;
	rep(i,1,n) s|=(s<<a[i]);
	rep(i,0,sum) if(s.test(i)) ans=i;
	printf("%d",S-ans);
}