Problem Statement

There is a sequence $A=(A_1,A_2,\dots,A_N)\ (A_1 < A_2 < \cdots < A_N)$ of length $N$.

For a positive integer $X$, define $$f(X) := (X+1) \times \left| \left\{ \left \lfloor \frac{A_1}{X} \right \rfloor , \left \lfloor \frac{A_2}{X} \right \rfloor, \dots, \left \lfloor \frac{A_N}{X} \right \rfloor \right\} \right|$$ . In other words, $f(X)$ is the product of $X+1$ and the number of distinct values among $\displaystyle \left \lfloor \frac{A_1}{X} \right \rfloor , \left \lfloor \frac{A_2}{X} \right \rfloor, \dots, \left \lfloor \frac{A_N}{X} \right \rfloor$.

Find the minimum value of $f(X)$ and the smallest $X$ that achieves this minimum value.

Input

$N$
$A_1$ $A_2$ $\dots$ $A_N$

• All inputs are integers.
• $1 \leq N \leq 10^5$
• $0 \leq A_1 < A_2 < \cdots < A_N \leq 10^9$

Output

Let $X_{\min}$ be the smallest $X$ that minimizes $f(X)$. Output in the following format.

$X_{\min}$
$f(X_{\min})$

Sample

4
0 1 2 3

4
5

6
3 4 5 6 7 8

3
8

8
0 1 2 6 7 9 10 11

3
12