Buggy python submission (verdict: Time Limit Exceeded):
import sys, re
from collections import deque, defaultdict, Counter
from math import ceil, sqrt, hypot, factorial, pi, sin, cos, radians
from itertools import accumulate, permutations, combinations, product
from operator import itemgetter, mul
from copy import deepcopy
from string import ascii_lowercase, ascii_uppercase, digits
from bisect import bisect, bisect_left
from fractions import gcd
from heapq import heappush, heappop
from functools import reduce
def input(): return sys.stdin.readline().strip()
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(): return list(map(int, input().split()))
def ZIP(n): return zip(*(MAP() for _ in range(n)))
sys.setrecursionlimit(10 ** 9)
INF = float('inf')
mod = 10 ** 9 + 7

class SegmentTree:
    """
    引数：
        N: 処理する区間の長さ
        operator: モノイド演算 (max, min, __add__,ラムダ式,関数定義など)
        UNIT: 単位元
        a: 長さNの配列 a で初期化（a を与えない場合、単位元で初期化）
    注意: 内部的には 1-indexed
    """
    def __init__(self, N, operator, unit, a=None):
        self.op = operator
        self.UNIT = unit
        self.N0 = 2**(N-1).bit_length()
        self.tree = [self.UNIT]*(2*self.N0)
        if a != None:
            self.tree[self.N0:self.N0+N] = a[:]
            for k in range(self.N0-1, 0, -1):
                self.tree[k] = self.op(self.tree[2*k], self.tree[2*k+1])
    # k番目 の値を x に更新
    def update(self, k, x):
        k += self.N0
        self.tree[k] = x
        k //= 2
        while k:
            self.tree[k] = self.op(self.tree[2*k], self.tree[2*k+1])
            k //= 2
    # 区間[l,r]をopでまとめる
    def query(self, l, r):
        L = l + self.N0
        R = r + self.N0 + 1
        s = self.UNIT
        while L < R:
            if R & 1:
                R -= 1
                s = self.op(self.tree[R], s)
            if L & 1:
                s = self.op(s, self.tree[L])
                L += 1
            L >>= 1
            R >>= 1
        return s
    def get(self, k):  # k番目の値を取得。query[k,k]と同じ
        return self.tree[k+self.N0]

N = INT()
A = LIST()
lcm_base = lambda x, y: (x * y) // gcd(x, y)
many_lcm = lambda numbers: reduce(lcm_base, numbers)
unit = many_lcm(A)
seg = SegmentTree(N+1, gcd, unit)

for i, x in enumerate(A):
	seg.update(i+1, x)

ans = 0
for i, x in enumerate(A):
	seg.update(i+1, unit)
	ans = max(ans, seg.query(1, N))
	seg.update(i+1, A[i])
print(ans)


Fixed submission:
import sys, re
from collections import deque, defaultdict, Counter
from math import ceil, sqrt, hypot, factorial, pi, sin, cos, radians
from itertools import permutations, combinations, product
from operator import itemgetter, mul
from copy import deepcopy
from string import ascii_lowercase, ascii_uppercase, digits

def input(): return sys.stdin.readline().strip()
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(): return list(map(int, input().split()))
sys.setrecursionlimit(10 ** 9)
INF = float('inf')
MOD = 10 ** 9 + 7

N = INT()
A = LIST()

def gcd(a, b):
	# if a == 0:
	# 	return b
	# elif b == 0:
	# 	return a
    if a < b:
        a, b = b, a
    if b == 0:
        return a
    c = a % b
    return gcd(b, c)

Li = [0]*(N+2)
Ri = [0]*(N+2)
A.append(0)
A.insert(0, 0)

for i in range(N+1):
	Li[i+1] = gcd(Li[i], A[i])

for i in range(N, -1, -1):
	Ri[i] = gcd(Ri[i+1], A[i])

# print(Li)
# print(Ri)

M = []
for i in range(1, N+1):
	M.append(gcd(Li[i],Ri[i+1]))
# print(M)
print(max(M))