Score : 700 points
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}}.
Input is given from Standard Input in the following format:
N A_1 A_2 ... A_N
Print the median of the sorted list of the sums of all non-empty subsequences of A.
3 1 2 1
2
In this case, S = (1, 1, 2, 2, 3, 3, 4). Its median is S_4 = 2.
1 58
58
In this case, S = (58).