Given an integer , find the lexicographically smallest permutation
of
such that
is prime for all
, or report that no such permutation exists.
Constraints
Subtask 1 [5%]
Subtask 2 [25%]
Subtask 3 [15%]
Subtask 4 [30%]
Subtask 5 [25%]
No additional constraints.
Input Specification
The first and only line of input contains a single integer .
Output Specification
If no such permutation exists, output on a line by itself. Otherwise, output
space-separated integers
, the lexicographically smallest permutation such that
is prime for all
.
Sample Input
3
Sample Output
1 3 2
Explanation
Note that ,
, and
are all prime.
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