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 <stdio.h>
#include <bitset>

std::bitset<4000400> b;

int main(){
	int N, a[2020], s, i; 
	for (scanf("%d", &N), b[0] = 1, s = i = 0; i != N; i++)
		scanf("%d", a+i), s += a[i], b |= b<<a[i];
    for(i = s>>1; !b[i]; i--) ;
    printf("%d\n", s-i);
}