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 f = { i: Int -> xs.filter { it % i == 0 }.count() >= n - 1 }

    val ans = xs.take(2).map { a ->
        generateSequence(1) { it + 1 }
                .takeWhile { it * it <= a }
                .filter { a % it == 0 }
                .map {
                    var r = 0
                    if (f(it)) r = Math.max(r, it)
                    if (f(a / it)) r = Math.max(r, a / it)
                    r
                }.max()?: 0
    }.max()

    println(ans)
}