LogiQuest

431. First Missing Positive

HardArrayCyclic Sort

Print the smallest positive integer that does not appear in the array. Aim for O(n) time and O(1) extra space.

Input format

Line 1: n Line 2: n integers

Output format

The smallest missing positive.

Example 1

Input

3
1 2 0

Output

3

Example 2

Input

4
3 4 -1 1

Output

2

Constraints

1 ≤ n ≤ 10⁵

Read input from standard input and print the answer to standard output. Your code is judged against 6 test cases, most of them hidden.

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