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 (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

func gcd(a, b int) int {
	if b > a {
		a, b = b, a
	}
	// 書き換え可能なパターンの計算簡略化のため
	if b == 0 {
		return a
	}
	var r int
	for {
		r = a % b
		if r == 0 {
			return b
		}
		a = b
		b = r
	}
}

func main() {
	var n int
	fmt.Scan(&n)
	a := make([]int, n)
	sc := bufio.NewScanner(os.Stdin)
	sc.Split(bufio.ScanWords)
	for i := 0; i < n; i++ {
		sc.Scan()
		a[i], _ = strconv.Atoi(sc.Text())
	}

	l := make([]int, n+1)
	l[0] = 0
	for i := 0; i < n; i++ {
		l[i+1] = gcd(l[i], a[i])
	}
	r := make([]int, n+1)
	r[n] = 0
	for i := n - 1; i >= 0; i-- {
		r[i] = gcd(r[i+1], a[i])
	}

	max := 0
	for i := 0; i < n; i++ {
		if v := gcd(l[i], r[i+1]); v > max {
			max = v
		}
	}

	fmt.Println(max)
}