Buggy python submission (verdict: Time Limit Exceeded):
from fractions import gcd
def init(init_val,n):
    #set_val
    for i in range(n):
        seg[i+num-1]=init_val[i]
    #built
    for i in range(num-2,-1,-1) :
        seg[i]=segfunc(seg[2*i+1],seg[2*i+2])

def segfunc(x,y):
    if x*y == 0:
        return max([x,y])
    return gcd(x,y)

def update(k,x):
    k += num-1
    seg[k] = x
    while k:
        k = (k-1)//2
        seg[k] = segfunc(seg[k*2+1],seg[k*2+2])

def query(p,q):
    if q<=p:
        return ide_ele
    p += num-1
    q += num-2
    res=ide_ele
    while q-p>1:
        if p&1 == 0:
            res = segfunc(res,seg[p])
        if q&1 == 1:
            res = segfunc(res,seg[q])
            q -= 1
        p = p//2
        q = (q-1)//2
    if p == q:
        res = segfunc(res,seg[p])
    else:
        res = segfunc(segfunc(res,seg[p]),seg[q])
    return res
N = int(input())
a = list(map(int,input().split()))
#####単位元######
ide_ele = 0

#num:n以上の最小の2のべき乗
num =2**(N-1).bit_length()
seg=[ide_ele]*2*num

init(a,N)
res = 0
for i in range(N):
    tmp = gcd(query(0,i),query(i+1,N))
    if tmp >= res:
        res = tmp
print(res)


Fixed submission:
from fractions import gcd
def init(init_val,n):
    #set_val
    for i in range(n):
        seg[i+num-1]=init_val[i]
    #built
    for i in range(num-2,-1,-1) :
        seg[i]=segfunc(seg[2*i+1],seg[2*i+2])

def segfunc(x,y):
    return gcd(x,y)

def update(k,x):
    k += num-1
    seg[k] = x
    while k:
        k = (k-1)//2
        seg[k] = segfunc(seg[k*2+1],seg[k*2+2])

def query(p,q):
    if q<=p:
        return ide_ele
    p += num-1
    q += num-2
    res=ide_ele
    while q-p>1:
        if p&1 == 0:
            res = segfunc(res,seg[p])
        if q&1 == 1:
            res = segfunc(res,seg[q])
            q -= 1
        p = p//2
        q = (q-1)//2
    if p == q:
        res = segfunc(res,seg[p])
    else:
        res = segfunc(segfunc(res,seg[p]),seg[q])
    return res
N = int(input())
a = list(map(int,input().split()))
#####単位元######
ide_ele = 0

#num:n以上の最小の2のべき乗
num =2**(N-1).bit_length()
seg=[ide_ele]*2*num

init(a,N)
res = 0
for i in range(N):
    tmp = gcd(query(0,i),query(i+1,N))
    if tmp >= res:
        res = tmp
print(res)

Buggy python submission (verdict: Time Limit Exceeded):
from fractions import gcd
def init(init_val,n):
    #set_val
    for i in range(n):
        seg[i+num-1]=init_val[i]
    #built
    for i in range(num-2,-1,-1) :
        seg[i]=segfunc(seg[2*i+1],seg[2*i+2])

def segfunc(x,y):
    if x*y == 0:
        return max([x,y])
    return gcd(x,y)

def update(k,x):
    k += num-1
    seg[k] = x
    while k:
        k = (k-1)//2
        seg[k] = segfunc(seg[k*2+1],seg[k*2+2])

def query(p,q):
    if q<=p:
        return ide_ele
    p += num-1
    q += num-2
    res=ide_ele
    while q-p>1:
        if p&1 == 0:
            res = segfunc(res,seg[p])
        if q&1 == 1:
            res = segfunc(res,seg[q])
            q -= 1
        p = p//2
        q = (q-1)//2
    if p == q:
        res = segfunc(res,seg[p])
    else:
        res = segfunc(segfunc(res,seg[p]),seg[q])
    return res
N = int(input())
a = list(map(int,input().split()))
#####単位元######
ide_ele = 0

#num:n以上の最小の2のべき乗
num =2**(N-1).bit_length()
seg=[ide_ele]*2*num

init(a,N)
res = 0
for i,elem in enumerate(a):
    update(i,0)
    tmp = query(0,N)
    if tmp >= res:
        res = tmp
    update(i,a[i])
print(res)


Fixed submission:
from fractions import gcd
def init(init_val,n):
    #set_val
    for i in range(n):
        seg[i+num-1]=init_val[i]
    #built
    for i in range(num-2,-1,-1) :
        seg[i]=segfunc(seg[2*i+1],seg[2*i+2])

def segfunc(x,y):
    return gcd(x,y)

def update(k,x):
    k += num-1
    seg[k] = x
    while k:
        k = (k-1)//2
        seg[k] = segfunc(seg[k*2+1],seg[k*2+2])

def query(p,q):
    if q<=p:
        return ide_ele
    p += num-1
    q += num-2
    res=ide_ele
    while q-p>1:
        if p&1 == 0:
            res = segfunc(res,seg[p])
        if q&1 == 1:
            res = segfunc(res,seg[q])
            q -= 1
        p = p//2
        q = (q-1)//2
    if p == q:
        res = segfunc(res,seg[p])
    else:
        res = segfunc(segfunc(res,seg[p]),seg[q])
    return res
N = int(input())
a = list(map(int,input().split()))
#####単位元######
ide_ele = 0

#num:n以上の最小の2のべき乗
num =2**(N-1).bit_length()
seg=[ide_ele]*2*num

init(a,N)
res = 0
for i in range(N):
    tmp = gcd(query(0,i),query(i+1,N))
    if tmp >= res:
        res = tmp
print(res)