Primes up to n

Problem

A licence server hands out prime numbers as keys. Write is_prime(n) and use it to count how many primes there are from 1 to n, including n.

Example

Input

Output

The primes are 2, 3, 5 and 7.

Try the problem first. Open one hint at a time.

Hint 1

Write the prime test as its own function, then call it for each number in a loop.

Hint 2

Keep a counter and add 1 each time the function returns True.

Write your Python code, run it on the examples and submit it to hidden tests.