Sudoku is a logic$-$based, combinatorial number placement puzzle. The objective

is to fill a $9$x$9$ grid with digits so that each column, each row, and each of

the nine $3$x$3$ sub$-$grids that compose the grid $($also called $$boxes$,$blocks$,$

$$regions$,$ or $$sub$-$squares$)$ contains all of the digits from $1$ to $9.$ The puzzle

setter provides a partially completed grid, which for a well$-$posed puzzle has a

unique solution$\mathrm{.}1$

$2$ Requirements

Write a C program that reads a bunch of sudoku puzzles from standard in$-$

put and solves them. Each puzzle is given as a line of $81$ characters, with $.$

characters representing unknown digits.

$$ If a solution exists that uses the given digits in the given order, find it and

print it$.$ Specifically, echo the input on one line and print the solution on

a new line.

$$ If not, echo the input and print $$No Solution$$ on a new line.

$$ If the input does not follow the specified format, print $$Error$$ on a new

line.

$$ After each test case, output a blank line to standard output. So$,$ each line

of input will produce $3$ lines of output: echo of input, output line, and

blank line.

$$ Whether or not the test was a valid sudoku puzzle, your program must

be prepared to handle the next test. Make sure that you do not leave

your program in an invalid state as the result of an error test case. This

is a particularly common issue when dealing with lines that were not of

the expected length. Make sure you reset all relevant bookkeeping before

beginning the next line of input.

$1$Thank you, Wikipedia.

$1$

$2\mathrm{.}1$ Input Format

$$ A record is a sequence of characters followed by the newline character:

$$

$.$

$$ The input will consist of some number of records $($lines$).$

$$ Each valid record will consist of $81$ characters, representing the $9$ rows of

a sudoku puzzle, each consisting of $9$ characters.

$$ The only valid characters in a record are the nine possible digits $(1-9)$ and

$..$

$$ A valid record does not have the same number appear twice in the same

row, column, or box