Avoiding Supermarket Delays

Little Z is running along a highway that has n supermarkets, with the i-th supermarket located at position a_i. He starts at position 0 and runs to the right with a constant speed v (a positive integer) and covers v units per unit time. When Little Z passes a supermarket, if the time of passing is an odd number, he will be tempted to enter the supermarket, which leads to an undesirable outcome.

Your task is to determine the maximum possible value of v such that for every supermarket, the time at which Little Z arrives is an even integer. Formally, for each supermarket at position a_i, let the time taken be t_i = a_i / v. We require that:

[ \frac{a_i}{v} = 2k \quad \text{for some integer } k \geq 1, ]

This condition is equivalent to requiring that v divides a_i and that a_i / v is even for all i. It can be observed that since each a_i must be divisible by v and yield an even quotient, the maximum valid v is given by the greatest common divisor (gcd) of all the numbers a_i/2.

inputFormat

The first line contains a single integer n (the number of supermarkets). The second line contains n space-separated integers a₁, a₂, ..., a_n representing the positions of the supermarkets. It is guaranteed that each a_i is even and that v exists.

outputFormat

Output a single integer — the maximum valid speed v such that Little Z arrives at every supermarket at an even time.

sample

3
4 8 12

2