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 main() {
	var N int
	fmt.Scan(&N)
	A := make([]int64, N)
	var Amax int64
	for i := 0; i < N; i++ {
		fmt.Scan(&A[i])
		if A[i] > Amax {
			Amax = A[i]
		}
	}

	if N == 2 {
		if A[0] > A[1] {
			fmt.Println(A[0])
		} else {
			fmt.Println(A[1])
		}
	} else {
		fmt.Println(solve(N, A, Amax))
	}
}

func solve(N int, A []int64, Amax int64) int64 {
	var a int
	var b int64
	for i := 0; i < N; i++ {
		if A[i] == Amax {
			a++
		} else {
			b = A[i]
		}
	}
	if a == 1 {
		return b
	}
	if a == N-1 {
		return Amax
	}

	for i := Amax; i >= 1; i-- {
		miss := 0
		for j := 0; j < N; j++ {
			if A[j]%i != 0 {
				miss++
			}
			if miss >= 2 {
				break
			}
		}
		if miss <= 1 {
			return i
		}
	}
	return 1
}