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 Scala (2.11.7) (judge verdict: Accepted)

import scala.annotation.tailrec

object Main{
	@tailrec
	def gcd(a:Int,b:Int):Int ={
		if(b==0) a else gcd(b,a % b)
	}
	def main(args:Array[String]){
		val s = new java.util.Scanner(System.in)
		val n = s.nextInt
		val a = Array.fill(n)(s.nextInt)
		val l,r = Array.fill(n + 2)(0)
		for(i <- 1 to n)
			l(i) = gcd(l(i - 1),a(i - 1))
		for(i <- n to 1 by -1)
			r(i) = gcd(r(i + 1),a(i - 1))
		println((1 to n).map(i => gcd(l(i - 1),r(i + 1))).max)
	}
}