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 Go (1.6) (judge verdict: Wrong Answer)

package main

import "fmt"

func gcd(x, y int) int {
    for y > 0 {
        x, y = y, x % y
    }
    return x
}

func max(x, y int) int {
    if x > y {
        return x
    }
    return y
}

func main() {
    var n int
    fmt.Scan(&n)
    a := make([]int, n)
    for i := 0; i < n; i++ {
        fmt.Scan(&a[i])
    }
    if n == 2 {
        fmt.Println(max(a[0], a[1]))
    } else {
        g := gcd(a[0], a[n - 1])
        forward, backword := make([]int, n), make([]int, n)
        forward[0], backword[n - 1] = g, g
        for i := 1; i < n; i++ {
            g := gcd(g, a[i])
            forward[i] = g
        }
        g = a[n - 1]
        for i := n - 2; i >= 0; i-- {
            g := gcd(g, a[i])
            backword[i] = g
        }
        first, second := 1000000007, 1000000007
        for i := 0; i < n; i++ {
            v := max(forward[i], backword[i])
            if v < first {
                second = first
                first = v
            } else if v < second {
                second = v
            }
        }
        fmt.Println(second)
    }
}