8365번 - Reconstruction of Byteland 다국어

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 10⁹. 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 A to city B only if the postal codes of these two cities have a common divisor greater than 1. 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.

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.

The first and only line of input contains one integer n (4 ≤ n ≤ 100) denoting the number of cities of Byteland.

The output should consist of exactly n lines. The i-th line should contain one positive integer not greater than 10⁹ - the postal code of the i-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.