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"
	"math"
	"os"
	"sort"
)

func scanNums(len int) (nums []int) {
	var num int
	for i := 0; i < len; i++ {
		fmt.Scan(&num)
		nums = append(nums, num)
	}
	return nums
}

func gcd(a, b int) int {
	for b != 0 {
		rem := math.Mod(float64(a), float64(b))
		a = b
		b = int(rem)
	}

	return a
}

func main() {
	var N int
	fmt.Scan(&N)

	A := scanNums(N)

	sort.Sort(sort.Reverse(sort.IntSlice(A)))

	if N <= 2 {
		if A[0] > A[1] {
			fmt.Println(A[0])
			os.Exit(0)
		}
		fmt.Println(A[1])
		os.Exit(0)
	}

	a := gcd(A[0], A[1])
	b := gcd(A[1], A[2])
	c := gcd(A[2], A[0])

	var m int

	countA := 0
	countB := 0
	countC := 0

	for i := 0; i < N; i++ {
		if countA > 1 {
			a = 1
			break
		}
		if A[i]%a != 0 {
			countA += 1
		}
	}
	m = a

	for i := 0; i < N; i++ {
		if countB > 1 {
			b = 1
			break
		}
		if A[i]%b != 0 {
			countB += 1
		}
	}
	if b > m {
		m = b
	}

	for i := 0; i < N; i++ {
		if countC > 1 {
			c = 1
			break
		}
		if A[i]%c != 0 {
			countC += 1
		}
	}
	if c > m {
		m = c
	}

	fmt.Println(m)
}