Problem:
Score : 300 points

Problem Statement

There are N integers, A_1, A_2, ..., A_N, written on the blackboard.

You will choose one of them and replace it with an integer of your choice between 1 and 10^9 (inclusive), possibly the same as the integer originally written.

Find the maximum possible greatest common divisor of the N integers on the blackboard after your move.

Constraints

All values in input are integers.

2 \leq N \leq 10^5

1 \leq A_i \leq 10^9

Output

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the maximum possible greatest common divisor of the N integers on the blackboard after your move.

Sample Input 1

3
7 6 8

Sample Output 1

2

If we replace 7 with 4, the greatest common divisor of the three integers on the blackboard will be 2, which is the maximum possible value.

Sample Input 2

3
12 15 18

Sample Output 2

6

Sample Input 3

2
1000000000 1000000000

Sample Output 3

1000000000

We can replace an integer with itself.

Solution in Pascal (FPC 2.6.2) (judge verdict: Accepted)

var
	n,i,ans,now:Longint;
	L,R:Array[0..100000]of Longint;
	A:Array[1..100000]of Longint;
function gcd(a,b:Longint):Longint;
begin
	if b=0 then gcd:=a else gcd:=gcd(b,a mod b);
end;
begin
	read(n);
	for i:=1 to n do read(A[i]);
	for i:=1 to n do L[i]:=gcd(L[i-1],A[i]);
	for i:=n downto 1 do R[i-1]:=gcd(R[i],A[i]);
	for i:=1 to n do begin
		now:=gcd(L[i-1],R[i]);
		if ans<now then ans:=now;
	end;
	writeln(ans);
end.