Knight jumps P98620

Given a board with three columns and $n$ rows, find a way for a chess knight to visit exactly $3n - 2$ cells, starting at any cell, and never repeating any cell nor going outside the board.

Input

Input consists of several cases, each with an $n$ between 3 and $10^5$.

Output

Print one line for each case, with any solution. Columns are labelled with ‘a’, ‘b’ and ‘c’ in this order, while rows are numbered from 1 to $n$. Follow strictly the format of the sample output.