Buggy python submission (verdict: Runtime Error):
from itertools import*;from fractions import*;u=accumulate;g=gcd;n,a=open(0);*a,=map(int,a.split());a=[0]+a+[0];print(max(starmap(g,zip(u(a,g),list(u(a[:1:-1],g))[::-1]))))

Fixed submission:
from collections import*
from functools import*
from fractions import*
def dv(n):
    divisors = []
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            divisors.append(i)
            if i != n // i:
                divisors.append(n//i)
 
    # divisors.sort()
    return Counter(divisors)

n,*a=map(int,open(0).read().split())
if n<1000:
    ans=Counter()
    for i in range(n):
        ans+=dv(a[i])
    l=[]
    for k,v in ans.items():
        if v==n-1 or v==n:
            l.append(k)
    print(max(l))
else:
    print(max(reduce(gcd,a[n//4:]),reduce(gcd,a[:n//4]+a[n//2:]),reduce(gcd,a[:n//2]+a[3*n//4:]),reduce(gcd,a[:3*n//4])))

Buggy python submission (verdict: Time Limit Exceeded):
from collections import*
def dv(n):
    divisors = []
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            divisors.append(i)
            if i != n // i:
                divisors.append(n//i)
 
    # divisors.sort()
    return Counter(divisors)
 
n,*a=map(int,open(0).read().split())
ans=Counter()
for i in range(n):
    ans+=dv(a[i])
l=[]
for k,v in ans.items():
    if v==n-1 or v==n:
        l.append(k)
print(max(l))

Fixed submission:
from collections import*
from functools import*
from fractions import*
def dv(n):
    divisors = []
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            divisors.append(i)
            if i != n // i:
                divisors.append(n//i)
 
    # divisors.sort()
    return Counter(divisors)

n,*a=map(int,open(0).read().split())
if n<1000:
    ans=Counter()
    for i in range(n):
        ans+=dv(a[i])
    l=[]
    for k,v in ans.items():
        if v==n-1 or v==n:
            l.append(k)
    print(max(l))
else:
    print(max(reduce(gcd,a[n//4:]),reduce(gcd,a[:n//4]+a[n//2:]),reduce(gcd,a[:n//2]+a[3*n//4:]),reduce(gcd,a[:3*n//4])))

Buggy python submission (verdict: Time Limit Exceeded):
from collections import*
def dv(n):
    divisors = []
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            divisors.append(i)
            if i != n // i:
                divisors.append(n//i)

    # divisors.sort()
    return Counter(divisors)

n,*a=map(int,open(0).read().split())
ans=Counter()
for i in range(n):
    ans+=dv(a[i])
l=[]
for k,v in ans.items():
    if v==n-1 or v==n:
        l.append(k)
print(max(l))

Fixed submission:
from collections import*
from functools import*
from fractions import*
def dv(n):
    divisors = []
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            divisors.append(i)
            if i != n // i:
                divisors.append(n//i)
 
    # divisors.sort()
    return Counter(divisors)

n,*a=map(int,open(0).read().split())
if n<1000:
    ans=Counter()
    for i in range(n):
        ans+=dv(a[i])
    l=[]
    for k,v in ans.items():
        if v==n-1 or v==n:
            l.append(k)
    print(max(l))
else:
    print(max(reduce(gcd,a[n//4:]),reduce(gcd,a[:n//4]+a[n//2:]),reduce(gcd,a[:n//2]+a[3*n//4:]),reduce(gcd,a[:3*n//4])))