Given an array ~ A ~ consisting of ~ N ~ positive integers, the task is to find the smallest positive integer ~ D ~ such that ~ D > 1 ~ and all elements in the array are divisible by ~ D ~.

Input

• The first line contains a positive integer ~ N ~ (~ N \leq 10^5 ~).
• The second line contains ~ N ~ positive integers ~ A_1, A_2, \ldots, A_N ~ (~ A_i \leq 10^{10} ~).

Output

• A single integer which is the smallest common divisor greater than ~1~ of the array. If no such divisor exists, print ~-1~.

Sample Input

3
2 4 6

Sample Output

2