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 PyPy3 (2.4.0) (judge verdict: Accepted)

from fractions import gcd

N=int(input())
A=list(map(int,input().split()))
X=[A[0]]
Y=[A[-1]]
for i in range(N):
    X.append(gcd(X[-1],A[i]))
    Y.append(gcd(Y[-1],A[N-1-i]))
X=X[1:]
Y=Y[1:]
Y=Y[::-1]
ans=1
for i in range(N):
    if i==0:
        ans_=Y[i+1]
    elif i==N-1:
        ans_=X[i-1]
    else:
        ans_=gcd(X[i-1],Y[i+1])
    ans=max(ans,ans_)
print(ans)