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>) = println(run {
    tailrec fun gcd(a: Int, b: Int): Int = if (b == 0) a else gcd(b, a % b)
    val n = readLine()!!.toInt()
    val a = readLine()!!.split(" ").map { it.toInt() }

    val l = IntArray(n)
    val r = IntArray(n)
    l[0] = a.first()
    r[n-1] = a.last()
    for (i in 1..l.lastIndex) {
        val j = r.lastIndex-i
        l[i] = gcd(l[i-1], a[i])
        r[j] = gcd(r[j+1], a[j])
    }
    
    ((1..n-2).map { i ->
        gcd(l[i-1], r[i+1])
    }+l[n-2]+r[1]).max()!!

})