Latin square P91748

A latin square of order $n$ is a matrix $n \times n$ such that in each row and column appears all the numbers between 1 and $n$. For instance, $$\left( \begin{array}{ccc} 2 & 3 & 1 \\ 1 & 2 & 3 \\ 3 & 1 & 2 \\ \end{array} \right) \qquad \mbox{and} \qquad \left( \begin{array}{cccc} 1 & 2 & 3 & 4 \\ 2 & 1 & 4 & 3 \\ 3 & 4 & 1 & 2 \\ 4 & 3 & 2 & 1 \\ \end{array} \right)$$ are respectively latin squares of order 3 and 4.

Using the declarations

    typedef vector<int> Row;
    typedef vector<Row> Square;

write a function

    bool is_latin(const Square& q);

that prints if |q| is a latin square or not.

Precondition

|q| is not empty and really squared. All its numbers are natural.

Observation

You only need to submit the required procedure; your main program will be ignored.