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First Missing Positive

1. Given an unsorted integer array 'arr'. 2. Find the smallest missing positive integer. Note : You must implement an algorithm that runs in O(n) time and uses constant extra space.

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First Missing Positive

hard

1. Given an unsorted integer array 'arr'. 2. Find the smallest missing positive integer. Note : You must implement an algorithm that runs in O(n) time and uses constant extra space.

Constraints

1. 1 <= nums.length <= 10^5 2. -2^31 <= nums[i] <= 2^31 - 1

Format

Input

Input is managed for you.

Output

Output is managed for you.

Example

Sample Input

4 3 4 -1 1

Sample Output

2

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