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: Wrong Answer)

fun main(args: Array<String>) {
    val n = readLine()!!.toLong()
    val aList = readLine()!!.split(" ").map { it.toLong() }

    var maxGcd = gcd(aList[0], aList[1])
    aList.forEach { it ->
        val aListExeptIt = aList.toMutableList()
        aListExeptIt.remove(it)

        var gcd = if (aListExeptIt.size > 1) gcd(aListExeptIt[0], aListExeptIt[1]) else aListExeptIt[0]
        aListExeptIt.forEach { gcd = gcd(gcd, it) }
        if (gcd > maxGcd) maxGcd = gcd
    }
    println(maxGcd)
}

fun gcd(a: Long, b: Long): Long {
    var temp: Long
    var aTemp = a
    var bTemp = b
    while (aTemp % bTemp != 0.toLong()) {
        temp = bTemp % aTemp
        bTemp = aTemp
        aTemp = temp
    }
    return bTemp
}