Degree

To assess her students' counting abilities, Maria Ivanovna gives them the same challenge each year: for a given natural number A, determine the smallest natural number N such that N raised to the power of N (N multiplied by itself N times) is divisible by A. The only variation from year to year and student to student is the number A.

You've decided to assist future students by writing a program to solve this problem.

Input

The input consists of a single number A (1 ≤ A ≤ 1000000000). This range is provided just in case Maria Ivanovna decides to challenge someone with a particularly large number.

Output

Output a single number N.

Examples