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: Runtime Error)

#include<stdio.h>
#include<string.h>
#include<stdbool.h>

long main(){
	long long N;
	scanf("%lld",&N);
	
	long long A[N];
	
	long long sum=0;
	for(long long i=0;i<N;i++){
		scanf("%lld",&A[i]);
		sum+=A[i];
	}
	
	bool dp[N+1][sum+1];
	
	memset(dp,0,sizeof(dp));
	
	dp[0][0]=1;
	
	for(long long i=0;i<N;i++){
		for(long long j=0;j<=sum;j++){
			dp[i+1][j] |= dp[i][j];
			if(j>=A[i])dp[i+1][j] |= dp[i][j-A[i]];
		}
	}
	
	for(long long i=(sum+1)/2;;i++){
		if(dp[N][i]==1){
			printf("%lld\n",i);
			break;
		}
	}
	
	return 0;
}