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: Accepted)

package main

import (
	"fmt"
)

func main() {
	var n int
	fmt.Scan(&n)
	a := make([]int, n)
	for i := 0; i < n; i++ {
		fmt.Scan(&a[i])
	}

	m := make([]int, n)
	l := make([]int, n-1)
	r := make([]int, n-1)
	l[0] = a[0]
	r[0] = a[n-1]

	for i := 1; i < n-1; i++ {
		l[i] = gcd(l[i-1], a[i])
		r[i] = gcd(r[i-1], a[n-1-i])
	}

	for i := 0; i < n; i++ {
		if i == 0 {
			m[i] = r[n-i-2]
		} else if i == n-1 {
			m[i] = l[n-2]
		} else {
			m[i] = gcd(l[i-1], r[n-i-2])
		}
	}

	ret := m[0]
	for i := 1; i < n; i++ {
		if m[i] > ret {
			ret = m[i]
		}
	}

	fmt.Println(ret)
}

func gcd(a int, b int) int {
	for {
		if b > a {
			a, b = b, a
		}
		c := a % b
		if c == 0 {
			return b
		}
		a, b = b, c
	}
}