sqr
Consider a positive integer n and a₁, a₂, ..., a_n a sequence made up of n non-zero positive integers.

Task
Determine the smallest number which multiplied with the product a₁*a₂*...*a_n is a non-zero perfect square.

Input data
Input file sqr.in contains on the first line the positive integer n. On the second line there are n non-zero positive integers a₁ a₂ ... a_n, separated by blanks.

Output data
Output file sqr.out will contain a single line with a non-zero positive integer, representing the smallest number which multiplied with the product a₁*a₂*...*a_n is a non-zero perfect square.

Constraints

0 < n <= 1000
0 < a_i <= 100000
The result has at most 1000 digits.

Example

Time limit: 0.1 seconds

prof. Marinel Serban
Liceul de Informatica "Grigore Moisil" Iasi
Contact:marinel_serban@yahoo.com