$3\mathrm{.}15$ Sudoku is a logic puzzle that has recently become very popular worldwide. In it$,$ you are given a $99$ grid with some numbers from $1$ to $9$ in various squares. To solve the puzzle, you must fill in the remaining squares so that, in each row, column, and $33$ block, each number from $1$ to $9$ appears exactly once. Below is a sample puzzle.

Formulate an integer program that will solve the given puzzle. write the model manually