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)

import sys
import math 
ni = lambda: int(ns())
na = lambda: list(map(int, input().split()))
ns = lambda: input()

N = ni()
A = na()

def gcd(x,y):
    r = x%y
    while(r!=0):
        x,y = y,r
        r = x%y
    return y
L = []
R = []
l = A[0]
r = A[-1]
for i in range(N-1):
    l = gcd(l,A[i])
    L.append(l)
for i in range(N-1,0,-1):
    r = gcd(r,A[i])
    R.append(r)
M = 0
M = max(R[-1],L[-1])
for i in range(N-2):
    M = max(M,gcd(L[i],R[-(i+2)]))
print(M)