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>) {
    abc125c()
}

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

fun abc125c() {
    val n = readLine()!!.toInt()
    val aList = readLine()!!.split(' ').map { it.toLong() }

    val cumulativeGcdFromLeft = LongArray(n + 1)
    for (i in 0 until n) cumulativeGcdFromLeft[i + 1] = gcd(cumulativeGcdFromLeft[i], aList[i])

    val cumulativeGcdFromRight = LongArray(n + 1)
    for (i in n - 1 downTo 0) cumulativeGcdFromRight[i] = gcd(cumulativeGcdFromRight[i + 1], aList[i])

    val answer = (0 until n).map { gcd(cumulativeGcdFromLeft[it], cumulativeGcdFromRight[it + 1]) }.max()!!

    println(answer)
}