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

    A.sort()
    var replaced = false
    var former = A[0]

    val ans = A.reduce { acc, a ->
        var result = gcd(acc, a)
        if (result == 1L && !replaced) {
            result = listOf(gcd(acc, former), gcd(acc, a)).max()!!
            replaced = true
        }
        former = a

        result
    }

    if (replaced) {
        println(ans)
    } else {
        A [1] = A[0]
        val another = A.reduce { acc, a -> gcd(acc, a)}
        println(another)
    }
}

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