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KILO 2018 4/5

Start:2018-09-27 16:30:00
End:2018-09-27 18:30:00
 

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CSES - KILO 2018 4/5 - ConjectureCSES - Conjecture

Conjecture

Time limit:1.00 s
Memory limit:128 MB

Uolevi proposed the following conjecture:

Every positive integer that can be written as a sum of three distinct positive integers can be written as a sum of three equal positive integers.

To prove Uolevi wrong, Maija asked you to write a program to produce counterexamples for the conjecture.

In particular, given integer $n$, your program has to output the smallest positive integer that is larger than $n$ and can be written as a sum of three distinct positive integers but can't be written as a sum of three equal positive integers.

Input

The only input line contains a single integer $n$.

Output

Output the smallest counterexample larger than $n$.

Constraints
Example

Input:
8

Output:
10

Explanation: Number $10$ can be written as $2+3+5=10$, but there is no positive integer $x$ such that $x+x+x=10$.