Smallest missing ticket number

Problem

Tickets are numbered 1, 2, 3, and so on, but some numbers in a list are missing. Find the smallest positive integer that does not appear in the list. The list may contain zero, negative numbers and repeats.

Input, output and limits

Input: Line 1: the integer n. Line 2: n integers.
Output: One integer: the smallest positive integer not in the list.
Constraints: 1 ≤ n ≤ 2 * 10^5
-10^9 ≤ value ≤ 10^9

Examples

Example

Input

5
3 1 4 1 7

Output

1 is present, 2 is not.

Hints

Try the problem first. Open one hint at a time.

Hint 1

Put the values in a set so a lookup is quick.

Hint 2

Try 1, 2, 3, ... until one is not in the set. The answer is never larger than n + 1.

Write your Python code, run it on the examples and submit it to hidden tests.

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