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)

fun main(args: Array<String>) {
    val n = readLine()!!.toInt()
    val xs = readLine()!!.split(' ').map { it.toInt() }

    val l = IntArray(n)
    val r = IntArray(n)

    for (i in (0 until n)) {
        l[i] = if (i == 0) {
            gcd(xs[0], 0)
        } else {
            gcd(xs[i], l[i - 1])
        }
    }

    for (i in (n - 1 downTo 0)) {
        r[i] = if (i == n - 1) {
            gcd(xs[i], 0)
        } else {
            gcd(xs[i], r[i + 1])
        }
    }

    var ans = 0

    for (i in (0 until n)) {
        val d = when (i) {
            0 -> r[i + 1]
            n - 1 -> l[i - 1]
            else -> gcd(l[i - 1], r[i + 1])
        }
        ans = Math.max(ans, d)
    }

    println(ans)
}

private fun gcd(a: Int, b: Int): Int {
    if (b == 0) return a
    return gcd(b, a % b)
}