F003A. Pentadiagonal matrices P55168

A square matrix is called pentadiagonal if all the elements out of the main diagonal and of the two diagonals over and under the main diagonal are 0.

For instance, the matrix on the left is pentadiagonal, but, the matrix on the right is not (it would be pentadiagonal if the 9 on the second and the sixth row were 0).

Using the definition

    typedef vector<vector<int> > Matrix;

Implement the function

    bool is_pentadiagonal(const Matrix& mat);

that prints whether |mat| is pentadiagonal or it is not.

Also, using the definition

    struct Info {
        int sum;
        int max;
    };

Implement the procedure

    void calculate(const Matrix& mat, Info& inf);

that stores in the fields |sum| and |max| of the output parameter |inf| the sum and the maximum of all the |mat| elements, under the precondition that |mat| is pentadiagonal.

The main program is already done; do not modify it. It reads square matrices of integers, and for each one, if the matrix is pentadiagonal, writes the sum and the maximum of its elements; Otherwise, it prints that the matrix is not pentadiagonal.

Precondition

The matrices |mat| are $n\times n$ with $n\ge6$.