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

var sc = bufio.NewScanner(os.Stdin)

func stringLineScan() string {
	sc.Scan()
	return sc.Text()
}

func main() {
	buf := make([]byte, 0)
	sc.Buffer(buf, 1000000009)
	sc.Split(bufio.ScanWords)
	n, _ := strconv.Atoi(stringLineScan())
	d := make(map[int]int)
	ans := 1
	for i := 0; i < n; i++ {
		a, _ := strconv.Atoi(stringLineScan())
		x := PrimeFactors(a)
		for _, y := range x {
			d[y]++
		}
	}
	z := 1
	for k, v := range d {
		if v%n == n-1 && k > z {
			z = k
		}
		ans *= int(math.Pow(float64(k), float64(v/n)))
	}
	fmt.Println(ans * z)
}
func PrimeFactors(n int) (pfs []int) {
	for n%2 == 0 {
		pfs = append(pfs, 2)
		n = n / 2
	}
	for i := 3; i*i <= n; i = i + 2 {
		for n%i == 0 {
			pfs = append(pfs, i)
			n = n / i
		}
	}
	if n > 2 {
		pfs = append(pfs, n)
	}
	return
}