In this problem you must implement Sieve of Sundaram, other solutions (algorithms) not acceptable.

Given one integer n, write prime numbers not greater than n in ascending order.

Input

One integer number2≤n≤100000.

Output

Print space separated prime numbers not greater than n in one line.

Example

Input:
7

Output:
2 3 5 7

23/06/2019 - Time limit increased.