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 <bits/stdc++.h>
using namespace std;
#define REP(NAME, NUM) for (int NAME = 0; NAME < (NUM); ++NAME)

int main()
{
	int n; cin>>n;
	bitset<2000*2000/2+1> bs(1);
	int sum = 0;
	REP(i,n) { int c; cin>>c; bs |= bs<<c; sum += c; }
	for( int i = sum / 2; i >= 0; --i )
		if( bs[i] ) { cout << sum - i << endl; break; }

	return 0;
}