Sudoku
In the game of Sudoku, you are given a large 9×9 grid divided into smaller 3×3 subgrids. For example,
Given some of the numbers in the grid, your goal is to determine the remaining numbers such that the numbers 1 through 9 appear exactly once in
(1) each of nine 3×3 subgrids,
(2) each of the nine rows, and
(3) each of the nine columns.
Input
The input test file will contain multiple cases. Each test case consists of a single line containing 81 characters, which represent the 81 squares of the Sudoku grid, given one row at a time. Each character is either a digit (from 1 to 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 "end".
Output
For each test case, print a line representing the completed Sudoku puzzle.