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 Kotlin (1.0.0) (judge verdict: Accepted)

import java.util.*
import java.math.*
fun main(args: Array<String>) {

    val N = readLine()!!.toInt()
    //val N = readLine()!!.split("").map{it.toInt()}
    val A = readLine()!!.split(" ").map{it.toLong()}
    //val S = readLine()!!

    if (N == 2) {
        println(Math.max(A[0],A[1]))
        return
    }

    fun gcd(a:Long,b:Long) :Long{
        if(b == 0L)
            return a
        return gcd(b, a%b)
    }

    var ans = longArrayOf(0,0)
    ans[0] = gcd(gcd(A[0],A[1]),A[2])
    ans[1] = longArrayOf(gcd(A[0],A[1]),gcd(A[0],A[2]),gcd(A[1],A[2])).max()!!
    for (i in 3 until N) {
        ans[1] = Math.max(gcd(ans[1],A[i]),ans[0])
        ans[0] = gcd(ans[0],A[i])
    }


    println(ans.max());
}