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)

import java.util.*

class Scanner(`in`: java.io.InputStream) {
    private val reader = java.io.BufferedReader(java.io.InputStreamReader(`in`))
    private var tokenizer: StringTokenizer? = null

    fun next(): String {
        if (tokenizer?.hasMoreTokens() != true) {
            tokenizer = StringTokenizer(reader.readLine())
        }
        return tokenizer!!.nextToken()
    }

    fun nextLine(): String {
        return if (tokenizer?.hasMoreTokens() != true) {
            reader.readLine()
        } else tokenizer!!.nextToken("\n")
    }
}

fun main(args: Array<String>) {
    val pw = java.io.PrintWriter(System.out)
    Problem.solve(Scanner(System.`in`), pw)
    pw.flush()
}

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object Problem {
    fun gcd(a: Int, b: Int): Int = if (b == 0) a else gcd(b, a % b)
    fun gcd(numbers: Iterable<Int>): Int = numbers.reduce { acc, n -> gcd(acc, n) }
    fun gcd(a: Long, b: Long): Long = if (b == 0L) a else gcd(b, a % b)
    fun gcd(numbers: Iterable<Long>): Long = numbers.reduce { acc, n -> gcd(acc, n) }

    fun solve(sc: Scanner, pw: java.io.PrintWriter) {
        val N = sc.next().toInt()
        val A = LongArray(N) { sc.next().toLong() }
        val L = LongArray(N)
        val R = LongArray(N)
        L[0] = A[0]
        R[N - 1] = A[N - 1]
        for (i in 1 until N) {
            L[i] = gcd(L[i - 1], A[i])
            R[N - 1 - i] = gcd(R[N - 1 - i + 1], A[N - 1 - i])
        }
//        println("L=" + L.joinToString(" "))
//        println("R=" + R.joinToString(" "))

        val can = mutableListOf(L[N - 2], R[1])
        for (i in 0..N - 3) {
            val a = gcd(L[i], R[i + 2])
            can += a
        }
        pw.println(can.max()!!)
    }
}