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Time Limit: 1 s Memory Limit: 128 MB Total points: 10

#6065. Square

The problem was used in the following contests:

Potyczki Algorytmiczne 2013, Runda próbna

AI Translation — This statement was translated using AI and may contain inaccuracies. Please refer to the original statement if in doubt.

Given a natural number $n$, find the smallest multiple of $n$ that is a perfect square of a natural number.

Input

The first and only line of input contains a single natural number $n$ ($1 \le n \le 500\,000\,000$).

Output

The first and only line of output should contain the smallest natural number $m$ that is a multiple of $n$ and is also a perfect square of a natural number.

Examples

Input 1

Output 1

Input 2

Output 2

970599336100

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