Problem:
Euler's Phi Function

For given integer n, count the totatives of n, that is, the positive integers less than or equal to n that are relatively prime to n.

Input

n

An integer n (1 ≤ n ≤ 1000000000).

Output

The number of totatives in a line.

Sample Input 1

6

Sample Output 1

2

Sample Input 2

1000000

Sample Output 2

400000

Solution in Python3 (judge verdict: Accepted)

import math

def prime_factorize(N): #素因数分解
    exponent = 0
    while N%2 == 0:
        exponent += 1
        N //= 2
    if exponent: factorization = [[2,exponent]]
    else: factorization = []
    i=1
    while i*i <=N:
        i += 2
        if N%i: continue
        exponent = 0
        while N%i == 0:
            exponent += 1
            N //= i
        factorization.append([i,exponent])
    if N!= 1: factorization.append([N,1])
    assert N != 0, "zero"
    return factorization

N = int(input())

f = prime_factorize(N)
ans = N
for p,_ in f:
    ans *= (p-1)/p

print(int(ans))