Problem Statement

Nagase is a top student in high school. One day, she's analyzing some properties of special sets of positive integers.
She thinks that a set S = {a_{1}, a_{2}, ..., a_{N}} of distinct positive integers is called special if for all $1 \leq i \leq N$, the gcd (greatest common divisor) of a_{i} and the sum of the remaining elements of S is not 1.
Nagase wants to find a special set of size N. However, this task is too easy, so she decided to ramp up the difficulty. Nagase challenges you to find a special set of size N such that the gcd of all elements are 1 and the elements of the set does not exceed 30000.

Input

Input is given from Standard Input in the following format:
N

Output

Output N space-separated integers, denoting the elements of the set S. S must satisfy the following conditions :

• The elements must be distinct positive integers not exceeding 30000.
• The gcd of all elements of S is 1, i.e. there does not exist an integer d > 1 that divides all elements of S.
• S is a special set.

If there are multiple solutions, you may output any of them. The elements of S may be printed in any order. It is guaranteed that at least one solution exist under the given contraints.

Constraints

• $3 \leq N \leq 20000$

Sample Input 1

3

Sample Output 1

2 5 63

{2, 5, 63} is special because gcd(2, 5 + 63) = 2, gcd(5, 2 + 63) = 5, gcd(63, 2 + 5) = 7. Also, gcd(2, 5, 63) = 1. Thus, this set satisfies all the criteria.
Note that {2, 4, 6} is not a valid solution because gcd(2, 4, 6) = 2 > 1.

Sample Input 2

4

Sample Output 2

2 5 20 63

{2, 5, 20, 63} is special because gcd(2, 5 + 20 + 63) = 2, gcd(5, 2 + 20 + 63) = 5, gcd(20, 2 + 5 + 63) = 10, gcd(63, 2 + 5 + 20) = 9. Also, gcd(2, 5, 20, 63) = 1. Thus, this set satisfies all the criteria.

见题面 Input 部分

见题面 Output 部分