H. Hidden divisor
time limit per test
1 second
memory limit per test
1024 megabytes
input
standard input
output
standard output

A mysterious positive integer $$$X$$$ has exactly $$$N+1$$$ positive divisors. $$$N$$$ of them are known and given to you in a list.

Your task is to find the mysterious number $$$X$$$ and the missing divisor, or indicate that the provided information is not enough to exactly determine those two values.

Input

The first line consists of an integer $$$N$$$ ($$$1 \leq N \leq 2\cdot 10^5$$$) which indicates the number of divisors in the list.

The second line consists of $$$N$$$ positive integers $$$A_1,A_2,\dots,A_N$$$ ($$$1\leq A_i\leq 10^{18}$$$). These are all but one of the divisors of the mysterious number $$$X$$$ ($$$1\leq X \leq 10^{18}$$$).

Output

A single line containing two integers: the mysterious number and the missing divisor. If it is not possible to determine them, print the character $$$\textbf{*}$$$ (asterisk).

Examples
Input
5
3 18 1 9 2
Output
18 6
Input
1
1
Output
*
Input
3
5 1 2
Output
10 10
Note

In the first example, the mysterious number is $$$18$$$, whose divisors are $$$1$$$, $$$2$$$, $$$3$$$, $$$6$$$, $$$9$$$, and $$$18$$$. The missing divisor is $$$6$$$.

In the second example, more than one number could be the mysterious number.