GCD Sequence

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.

Constraints

• 3 \leq N \leq 20000

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.

Examples

Input

3

Output

2 5 63

Input

4

Output

2 5 20 63

inputFormat

Input

Input is given from Standard Input in the following format:

N

outputFormat

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.

Examples

Input

3

Output

2 5 63

Input

4

Output

2 5 20 63

样例

3

2 5 63