The natural numbers from 1 to $n^{2}$ are randomly distributed over the fields of an $n \times n$ square ($n \geq 2$). For each pair of numbers within a row or a column, we divide the larger number by the smaller one. The smallest of these $n^{2}(n-1)$ quotients is denoted as the characteristic C of the random arrangement.
What is the largest possible value for C? (The answer must be justified.)

## 2. Selection Test