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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.
Write a program that:
The first and only line of input contains one integer () denoting the number of cities of Byteland.
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.
For the input data:
the correct result is:
714 2090 4485 29029 215441
Task author: Marcin Pilipczuk.