In the game of Sudoku, you are given a large \textbf{9}×\textbf{9} grid divided into smaller \textbf{3}×\textbf{3} subgrids. For example, \includegraphics{https://static.e-olymp.com/content/b3/b331223804dfbb4a04a0e2c738137219f3ba060b.jpg} Given some of the numbers in the grid, your goal is to determine the remaining numbers such that the numbers \textbf{1} through \textbf{9} appear exactly once in \begin{itemize} \item (\textbf{1}) each of nine \textbf{3}×\textbf{3} subgrids, \item (\textbf{2}) each of the nine rows, and \item (\textbf{3}) each of the nine columns. \end{itemize} \InputFile The input test file will contain multiple cases. Each test case consists of a single line containing \textbf{81} characters, which represent the \textbf{81} squares of the Sudoku grid, given one row at a time. Each character is either a digit (from \textbf{1} to \textbf{9}) or a period (used to indicate an unfilled square). You may assume that each puzzle in the input will have exactly one solution. The end-of-file is denoted by a single line containing the word "\textbf{end}". \OutputFile For each test case, print a line representing the completed Sudoku puzzle.