Smallest Missing Positive Sum

You are given an array of n positive integers. Your task is to determine the smallest positive integer S that cannot be represented as the sum of some subset of the given array.

More formally, let the array be A = [a₁, a₂, ..., a_n]. Define the set of all possible subset sums as:

$$G = \left\{ \sum_{i\in I} a_i : I \subseteq \{1,2,\ldots,n\} \right\}. $$

Your goal is to find the smallest positive integer which is not in G.

Example:

• For A = [1, 2, 2, 5, 7], the answer is 18.
• For A = [1, 1, 1], the answer is 4.

Hint: A greedy approach is effective. Sort the array, then iteratively determine the smallest unreachable sum.

inputFormat

The first line of input contains a single integer n (1 ≤ n ≤ 10⁵), representing the number of elements in the array.

The second line contains n space-separated positive integers.

outputFormat

Output a single integer — the smallest positive integer that cannot be represented as the sum of a subset of the given array.

## sample

5
1 2 2 5 7

18

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