Calculation of the multiplicative Euler's totient function for large numbers

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Task «Calculation of the multiplicative Euler's totient function for large numbers»

Given a natural number n (1 ≤ n ≤ 10^12). It is necessary to compute the value of Euler's totient function φ(n) — the number of integers from 1 to n that are coprime to n. Use prime factorization by trial division up to sqrt(n) and the Sieve of Eratosthenes algorithm for precomputing prime numbers up to 10^6. Output the result.

Input Format

One integer n.

Output Format

One integer — the value of φ(n).

Examples

Example 1

INPUT

1

OUTPUT

1

Example 2

INPUT

2024-12-31

OUTPUT

Вторник

Example 3

INPUT

10

OUTPUT

4

Example 4

INPUT

2000-01-01

OUTPUT

Суббота

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