Reconstruction of Byteland

Memory limit: 32 MB

Everyone get to work! Byteland needs to be reconstructed after a devastating war!

You are responsible for assigning postal codes to bytean cities. Each city should receive one postal code - a positive integer not greater than . Different cities should be assigned different postal codes.

The Bytean Postal Service is organized in a quite strange way; a letter can be sent from city to city only if the postal codes of these two cities have a common divisor greater than . Obviously, one of your objectives is that there should be a possibility of sending letters directly from every city to every other city after the postal codes are assigned.

Additionally, the new anti-corruption law requires that for each set of cities, containing more than a half of bytean cities, postal codes assigned to cities from this set must not have any common divisor greater than one.

Task

Write a program that:

• reads the number of cities of Byteland from the standard input,
• assigns a postal code to each bytean city,
• writes the assignment to the standard output.

Input

The first and only line of input contains one integer () denoting the number of cities of Byteland.

Output

The output should consist of exactly lines. The -th line should contain one positive integer not greater than - the postal code of the -th bytean city. You can assume that for each possible input there exists a valid assignment of postal codes to the cities. If there are multiple correct solutions, your program should output any one of them.

Example

For the input data:

5

the correct result is:

714
2090
4485
29029
215441

Task author: Marcin Pilipczuk.