In the ancient temple of Thoth, the priests have prepared ~n~ altars with offerings of valuables, each with a certain weight. However, everyone knows that Thoth likes order and symmetry, so the priest has ensured that all the offerings weigh the same, modulo some hidden constant ~d~. As an outlooker, you want to learn the ways of this temple by deciphering the largest such ~d~ given the weight of each offering.

Input

The first line contains a single integer ~n~ (~2 \leq n \leq 10^5~), the number of offerings presented on the altars.

The next line contains ~n~ space-separated integers ~x_1\ \dots\ x_n~ (~1 \leq x_i \leq 10^6~). Each ~x_i~ represents the weight of the ~i~th offering. The priest assures you that we cannot have all ~x_i~ be the same, as that would cause ~d~ to be possibly infinite, displeasing Thoth.

Output

Output the largest integer ~d~ such that all ~x_i~ are equal modulo ~d~.

I.e. the largest ~d~ such that, for some fixed integer ~r~, ~x_i \equiv r\mod d~ for all ~i\in \{1,2,\dots,n\}~.

Example

Input 1

4
6 10 18 14

Output 1

4

These offerings all weigh ~2~ modulo ~4~.

Input 2

3
10067 67 167

Output 2

100

Input 3

5
4 5 10 2 9

Output 3

1