An *n*×*n* *harmonic* magic square is a square array
of *n*^{2} __distinct__ numbers such that each number is
the reciprocal of a positive integer and the entries in each row, each
column, and the two main diagonals sum to the same number, which is also
the reciprocal of a positive integer.

- Find a 3×3 harmonic magic square.
- Find a 4×4 harmonic magic square.