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>) {
    var (count) = readLine()!!.split(" ").map { it.toInt() }
    val values = readLine()!!.split(" ").map { it.toInt() }

    var mx = 0

    for (musi in 0 until count) {
        if (values[musi] < mx) continue

        val tmp = values
            .filterIndexed { index, i -> index != musi }
            .reduceRight { i, acc -> gcd(i, acc) }

        if (tmp > mx) mx = tmp
    }

    print(mx)
}

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

    return gcd(b, a % b)
}