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 gcd(n: Collection<Int>): Int {
    var w = n
    while (w.size != 1) {
        val min = w.min()!!
        w = w.map { if (it == min) it else it % min }
            .filter { it != 0 }
            .distinct()
    }
    return w.first()
}

fun gcd(a: Int, b: Int): Int {
    var x = a
    var y = b
    while (true) {
        if (y < x) {
            val z = x
            x = y
            y = z
        }
        if (x == 0) break
        y %= x
    }
    return y
}

fun main(args: Array<String>) {
    readLine()
    var a = readLine()!!.split(' ').map(String::toInt)
    while (true) {
        if (a.size == 2) {
            println(a.max())
            break
        } else if (a.size == 3) {
            val s = gcd(a[0], a[1])
            val t = gcd(a[1], a[2])
            val u = gcd(a[2], a[0])
            println(Math.max(Math.max(s, t), u))
            break
        }
        val p = a.size shr 1
        val x = a.subList(0, p)
        val y = a.subList(p, a.size)
        val xx = gcd(x)
        val yy = gcd(y)
        a = if (xx < yy) x.plusElement(yy) else y.plusElement(xx)
    }
}