###### Category

###### Similar Problems

## 0753. Greatest Greatest Common Divisor

###### Time limit : 2000 ms

Memory limit : 64 mb

# Andrew
has just made a breakthrough in sociology: he realized how to predict whether
two persons will be good friends or not. It turns out that each person has an
inner *friendship number* (a positive integer). And the *quality of friendship* between two persons is equal to the greatest common divisor of their
friendship number. That means there are *prime* people (with a prime friendship number) who just
can't find a good friend, andWait,
this is irrelevant to this problem. You are given a list of friendship numbers
for several people. Find the highest possible quality of friendship among all
pairs of given people.

Input

The first line of the input file contains an integer *n* (2≤*n*≤10^{6}) — the
number of people to process. The next *n* lines contain one
integer each, between 1 and 10^{6} (inclusive), the friendship
numbers of the given people. All given friendship numbers are distinct.

Output

Output one integer — the highest possible quality of friendship. In other words, output the greatest greatest common divisor among all pairs of given friendship numbers.

Samples

№ |
Input |
Output |

1 |
4 9 15 25 16 |
5 |

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