Generate Prime Numbers using the Sieve of Eratosthenes

You are given a single integer n. Your task is to generate and output all prime numbers less than or equal to n using the Sieve of Eratosthenes algorithm. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

If n < 2, output nothing.

Note: The expected output should be the prime numbers separated by a single space on one line. Ensure that your solution reads input from stdin and writes the answer to stdout.

Mathematical Formulation:

For a given integer \( n \), let \( S = \{2, 3, \dots, n\} \). We remove all multiples of each prime number \( p \) starting from \( p^2 \) until \( n \). The remaining numbers in \( S \) are the primes up to \( n \).

inputFormat

The input consists of a single line containing one integer n (\( -10^5 \leq n \leq 10^5 \)).

outputFormat

Output a single line containing all prime numbers less than or equal to n, separated by a single space. If there are no primes, output an empty line.

## sample

10

2 3 5 7

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