A sequence of positive integers is $$$1$$$-stable if any two adjacent elements in it differ by at most $$$1$$$.

For two sequences of the same length, one sequence is lexicographically less than another if the first $$$k$$$ numbers in them coincide, and the $$$(k + 1)$$$-th number in the first sequence is less than the respective number in the second one.

A list of sequences is lexicographically ordered if each sequence is lexicographically less than the next one in the list.

It is clear that we can uniquely construct a lexicographically ordered list of all $$$n$$$-element $$$1$$$-stable sequences. For example, for $$$n = 3$$$, such list starts as follows: $$$$$$(1, 1, 1),\; (1, 1, 2),\; (1, 2, 1),\; (1, 2, 2),\; (1, 2, 3),\; (2, 1, 1),\; (2, 1, 2),\; \ldots$$$$$$

The lexicographical number of an $$$n$$$-element $$$1$$$-stable sequence is its number in the lexicographically ordered list of all $$$n$$$-element $$$1$$$-stable sequences. The sequences are numbered starting from $$$0$$$. For any $$$n$$$, the lexicographically ordered list of such sequences is obviously infinite. So, for any number, there exists a $$$1$$$-stable sequence with this lexicographical number.

You need to write a program that will find an $$$n$$$-element $$$1$$$-stable sequence by its lexicographical number $$$x$$$.