Sieve of Eratosthenes: Generate Prime Numbers

This problem requires you to generate all prime numbers less than a given integer n using the Sieve of Eratosthenes algorithm. The Sieve of Eratosthenes is an efficient algorithm to identify primes by iteratively marking the multiples of primes.

You are given a single integer n. Your task is to output all prime numbers less than n in ascending order. Use the following formula to define the sieve procedure: $$\text{sieve}[0\ldots n-1] = \text{True}$$ with \(\text{sieve}[0]\) and \(\text{sieve}[1]\) set to \(\text{False}\) since 0 and 1 are not prime numbers.

If there are no prime numbers below n, print an empty line.

inputFormat

The input consists of a single line containing one integer n (0 ≤ n ≤ 10⁶).

outputFormat

Output a single line containing all prime numbers less than 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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