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: Time Limit Exceeded)

fun main(args: Array<String>) {
    val n = readLine()!!.toInt()
    val a = readLine()!!.split(" ").map { it.toInt() }
    val x = mutableListOf<Int>()
    val y = mutableListOf<Int>()
    for (i in 0 until n step 2) {
        if (i != n - 1) y.add(gcd(a[i], a[i + 1]))
        else y.add(a[i])
    }
    var nn = y.size
    val set = mutableSetOf<Int>()
    for (i in 0 until n) {
        x.addAll(y)
        x.add(a[i])
        x.removeAt(i / 2)
        set.add(order(x, nn))
        x.clear()
    }
    println(set.max())
}

fun order(x: List<Int>, n: Int): Int {
    if (n == 1) return x[0]
    val y = mutableListOf<Int>()
    for (i in 0 until n step 2) {
        if (i != n - 1) y.add(gcd(x[i], x[i + 1]))
        else y.add(x[i])
    }
    return order(y, y.size)
}

fun gcd(x: Int, y: Int): Int {
    if (x < y) return gcd(y, x)
    if (y == 0) return x
    return gcd(y, x % y)
}