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 Python (3.4.3) (judge verdict: Accepted)

from fractions import gcd
N = int(input())
array = list(map(int,input().split()))
all_gcd = [0]*N
#calc from start to end
gcd_L = [array[0]]
for i in range(N-1):
  gcd_L.append(gcd(gcd_L[-1],array[i+1]))
  
#calc from end to start
gcd_R = [array[-1]]
for j in range(N-1,0,-1):
  gcd_R.append(gcd(gcd_R[-1],array[j-1]))
  
gcd_arr = []
  
for idx in range(N):
  if idx==0:
    gcd_arr.append(gcd_R[-2])
  elif idx==N-1:
    gcd_arr.append(gcd_L[-2])
  else:
    gcd_arr.append(gcd(gcd_L[idx-1],gcd_R[N-1-idx-1]))
print(max(gcd_arr))