Problem:
Score : 700 points

Problem Statement

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.

Sample Input 1

3
1 2 1

Sample Output 1

2

In this case, S = (1, 1, 2, 2, 3, 3, 4). Its median is S_4 = 2.

Sample Input 2

1
58

Sample Output 2

58

In this case, S = (58).

Solution in C (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

int dp[2000000];
int min(int a,int b){return a<b?a:b;}
int max(int a,int b){return a>b?a:b;}
signed main()
{
	int n,sum=0,i;
	__builtin_scanf("%d",&n);
	dp[0]=1;
	for (i=0;i<n;++i)
	{
		int a,q;
		__builtin_scanf("%d",&a);
		sum+=a;
		for (q=min(2000000-a,2000*i);q>=0;--q)
		{
			dp[q+a]|=dp[q];
		}
	}
	for (i=sum/2;i>=0;--i)
	{
		if (dp[i])
		{
			__builtin_printf("%d",max(i,sum-i));
			return 0;
		}
	}
}