Description

The spectrum $\operatorname{Spec}(\alpha)$ of a real number $\alpha$ is an infinite sequence of integers defined as $\lceil \alpha \rceil - 1, \lceil 2\alpha \rceil - 1, \lceil 3\alpha \rceil - 1, \cdots$. For example, the beginning of the spectrum of $\frac{3}{5}$ is $0, 1, 1, 2, 2, 3, 4, \cdots$.

Given $n$ integers $x_1, x_2, \ldots, x_n$, find the largest real number $\alpha$ such that every $x_i$ appears in $\operatorname{Spec}(\alpha)$.

Input Format

The first line contains a positive integer $n$.

The second line contains $n$ positive integers $x_1, x_2, \ldots, x_n$.

Output Format

Output the largest $\alpha$. Your answer will be considered correct if its absolute error is less than $10^{-5}$.

3
1 2 3

1.3333333

3
2 4 7

2.5000000

Hint

This problem uses subtask scoring.

Data Constraints:

• Subtask 0 (10 points): $n, x_i \le 100$.
• Subtask 1 (15 points): Valid answers form a continuous interval.
• Subtask 2 (25 points): Every $x_i$ is a non-negative integer power of 2.
• Subtask 3 (50 points): No additional constraints.

For all test cases, $1 \le n, x_i \le 1000$.

Translation by DeepSeek R1