Prime Factors of Factorial

By Kay Akashi

Problem Statement

You are given a positive integer $n$. Your task is to find prime factors of $n!$. For example, if $n = 3$, you are asked to find the prime factors of $3! = 6$ hence they are $2$ and $3$.

Note that, prime factors of $n$ are the numbers that can divide $n$ without no remainder and are prime numbers.

Also note that, $n!$ is equal to the product of all numbers smaller than or equal to $n$. For example, $5! = 1 × 2 × 3 × 4 × 5 = 120$.

Constraints

$1 \leq n \leq 10^{5}$.

Subtask 1 (20%)

$1 \leq n \lt 100$.

Subtask 2 (80%)

$100 \leq n \leq 10^{5}$.

Input

The input consists of one number, $n$.

Output

Output the prime factors of $n!$ in a single line. Note that the prime factors should be arranged in an increasing order.

Examples

3

2 3

1