Maximum number in base three

Here, we consider the base three representation of the natural numbers. For example, 59 is represented as 2012, because $2 \cdot 3^3 + 0 \cdot 3^2 + 1 \cdot 3^1 + 2 \cdot 3^0 = 59$ . Note that all digits are between 0 and 2, and that we have no zeros on the left.

Write a program to print the result of rearranging the base three digits of each given number, so that the result is the maximum possible, with an additional condition: we cannot have two equal consecutive digits.

Input

Input consists of several $n$ , all between 1 and $10^{18}$ .

Output

For every given $n$ , print its base three digit rearrangement without equal adjacent digits that produces the maximum possible result. If no reordering is possible, tell so.

Problem information

Author: Salvador Roura

Generation: 2026-01-25T11:05:45.896Z