Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())
A = list(map(int, input().split()))

L = len(A)
from functools import reduce
from fractions import gcd

def lcm(a,b):
  return (a*b)//gcd(a,b)

g = reduce(gcd, A)
l = reduce(lcm, A)

def _gcd(a,b):
  if a is None and b is None:
    return None
  if a is None:
    return b
  if b is None:
    return a
  else:
    return gcd(a,b)

class SegTree():
  import math
  def __init__(self, func, A, identity=1):
    self._func = func
    self._N = 1
    while self._N < len(A):
      self._N *= 2
       # 長さ 7 なら N=3 (2^3=8)
    self._identity = identity # maxなら-1e9, sumなら0, productなら1

    self._tree = [self._identity] * (2*self._N -1) 
    self._tree[self._N-1:self._N-1+ len(A)] = A #最下段に元の配列を
    for i in range(self._N-2, -1, -1):
      self._update_single_node(i)
    ########
    # N=3: #
    # 0000 #
    # 1122 #
    # 3456 #
    ########
    self._node_range = [(i-self._N+1,i-self._N+2) for i in range(2*self._N-1)] #right_exclusive
    for i in range(self._N-2, -1, -1):
      self._node_range[i] = (self._node_range[2*i+1][0], self._node_range[2*i+2][1])

  def _update_single_node(self,i):
    self._tree[i] = self._func(self._tree[2*i+1], self._tree[2*i+2])

  def point_update(self,i,x):
    # A[i] = x (addではないので注意)
    j = self._N-1+i
    self._tree[j] = x
    while j>0:
      j = (j-1)//2
      self._update_single_node(j)

  def range_query(self, l, r, on=0):
    # reduce(func, A[l:r])
    # onはノード[on]上と重なる部分の，ということ
    onl, onr = self._node_range[on]
    
    # ノード[on]上はすべて覆う
    if l<=onl and onr<=r:
      return self._tree[on]
    
    # 重なりなし
    elif onr<=l or r<=onl:
      return self._identity
    
    else:
      return self._func(self.range_query(l, r, on=2*on+1),
                        self.range_query(l, r, on=2*on+2))

st = SegTree(_gcd, A, identity=None)

answer = 0
for i in range(len(A)):
  st.point_update(i, A[i-1])
  answer = max(answer, st._tree[0])
  st.point_update(i, A[i])

print(answer)

Fixed submission:
N = int(input())
A = list(map(int, input().split()))

L = len(A)
from functools import reduce
from fractions import gcd

def lcm(a,b):
  return (a*b)//gcd(a,b)

g = reduce(gcd, A)
l = reduce(lcm, A)

def _gcd(a,b):
  if a is None and b is None:
    return None
  if a is None:
    return b
  if b is None:
    return a
  else:
    return gcd(a,b)

class SegTree():
  import math
  def __init__(self, func, A, identity=1):
    self._func = func
    self._N = 1
    while self._N < len(A):
      self._N *= 2
       # 長さ 7 なら N=3 (2^3=8)
    self._identity = identity # maxなら-1e9, sumなら0, productなら1

    self._tree = [self._identity] * (2*self._N -1) 
    self._tree[self._N-1:self._N-1+ len(A)] = A #最下段に元の配列を
    for i in range(self._N-2, -1, -1):
      self._update_single_node(i)
    ########
    # N=3: #
    # 0000 #
    # 1122 #
    # 3456 #
    ########
    self._node_range = [(i-self._N+1,i-self._N+2) for i in range(2*self._N-1)] #right_exclusive
    for i in range(self._N-2, -1, -1):
      self._node_range[i] = (self._node_range[2*i+1][0], self._node_range[2*i+2][1])

  def _update_single_node(self,i):
    self._tree[i] = self._func(self._tree[2*i+1], self._tree[2*i+2])

  def point_update(self,i,x):
    # A[i] = x (addではないので注意)
    j = self._N-1+i
    self._tree[j] = x
    while j>0:
      j = (j-1)//2
      self._update_single_node(j)

  def range_query(self, l, r, on=0):
    # reduce(func, A[l:r])
    # onはノード[on]上と重なる部分の，ということ
    onl, onr = self._node_range[on]
    
    # ノード[on]上はすべて覆う
    if l<=onl and onr<=r:
      return self._tree[on]
    
    # 重なりなし
    elif onr<=l or r<=onl:
      return self._identity
    
    else:
      return self._func(self.range_query(l, r, on=2*on+1),
                        self.range_query(l, r, on=2*on+2))

st = SegTree(_gcd, A, identity=None)

answer = 0
for i in range(len(A)):
  st.point_update(i, A[i-1])
  answer = max(answer, st._tree[0])
  st.point_update(i, A[i])

print(answer)

Buggy python submission (verdict: Runtime Error):
N = int(input())
A = list(map(int, input().split()))

L = len(A)
from functools import reduce
from fractions import gcd

g = reduce(gcd, A)

class SegTree():
  import math
  def __init__(self, func, A, identity=1):
    self._func = func
    self._N = 1
    while self._N < len(A):
      self._N *= 2
       # 長さ 7 なら N=3 (2^3=8)
    self._identity = identity # maxなら-1e9, sumなら0, productなら1

    self._tree = [self._identity] * (2*self._N -1) 
    self._tree[self._N-1:self._N-1+ len(A)] = A #最下段に元の配列を
    for i in range(self._N-2, -1, -1):
      self._update_single_node(i)
    ########
    # N=3: #
    # 0000 #
    # 1122 #
    # 3456 #
    ########
    self._node_range = [(i-self._N+1,i-self._N+2) for i in range(2*self._N-1)] #right_exclusive
    for i in range(self._N-2, -1, -1):
      self._node_range[i] = (self._node_range[2*i+1][0], self._node_range[2*i+2][1])

  def _update_single_node(self,i):
    self._tree[i] = self._func(self._tree[2*i+1], self._tree[2*i+2])

  def point_update(self,i,x):
    # A[i] = x (addではないので注意)
    j = self._N-1+i
    self._tree[j] = x
    while j>0:
      j = (j-1)//2
      self._update_single_node(j)

  def range_query(self, l, r, on=0):
    # reduce(func, A[l:r])
    # onはノード[on]上と重なる部分の，ということ
    onl, onr = self._node_range[on]
    
    # ノード[on]上はすべて覆う
    if l<=onl and onr<=r:
      return self._tree[on]
    
    # 重なりなし
    elif onr<=l or r<=onl:
      return self._identity
    
    else:
      return self._func(self.range_query(l, r, on=2*on+1),
                        self.range_query(l, r, on=2*on+2))

st = SegTree(gcd, A, identity=l)

answer = 0
for i in range(len(A)):
  st
  st.point_update(i, A[i-1])
  answer = max(answer, st._tree[0])
  st.point_update(i, A[i])

print(answer)


Fixed submission:
N = int(input())
A = list(map(int, input().split()))

L = len(A)
from functools import reduce
from fractions import gcd

def lcm(a,b):
  return (a*b)//gcd(a,b)

g = reduce(gcd, A)
l = reduce(lcm, A)

def _gcd(a,b):
  if a is None and b is None:
    return None
  if a is None:
    return b
  if b is None:
    return a
  else:
    return gcd(a,b)

class SegTree():
  import math
  def __init__(self, func, A, identity=1):
    self._func = func
    self._N = 1
    while self._N < len(A):
      self._N *= 2
       # 長さ 7 なら N=3 (2^3=8)
    self._identity = identity # maxなら-1e9, sumなら0, productなら1

    self._tree = [self._identity] * (2*self._N -1) 
    self._tree[self._N-1:self._N-1+ len(A)] = A #最下段に元の配列を
    for i in range(self._N-2, -1, -1):
      self._update_single_node(i)
    ########
    # N=3: #
    # 0000 #
    # 1122 #
    # 3456 #
    ########
    self._node_range = [(i-self._N+1,i-self._N+2) for i in range(2*self._N-1)] #right_exclusive
    for i in range(self._N-2, -1, -1):
      self._node_range[i] = (self._node_range[2*i+1][0], self._node_range[2*i+2][1])

  def _update_single_node(self,i):
    self._tree[i] = self._func(self._tree[2*i+1], self._tree[2*i+2])

  def point_update(self,i,x):
    # A[i] = x (addではないので注意)
    j = self._N-1+i
    self._tree[j] = x
    while j>0:
      j = (j-1)//2
      self._update_single_node(j)

  def range_query(self, l, r, on=0):
    # reduce(func, A[l:r])
    # onはノード[on]上と重なる部分の，ということ
    onl, onr = self._node_range[on]
    
    # ノード[on]上はすべて覆う
    if l<=onl and onr<=r:
      return self._tree[on]
    
    # 重なりなし
    elif onr<=l or r<=onl:
      return self._identity
    
    else:
      return self._func(self.range_query(l, r, on=2*on+1),
                        self.range_query(l, r, on=2*on+2))

st = SegTree(_gcd, A, identity=None)

answer = 0
for i in range(len(A)):
  st.point_update(i, A[i-1])
  answer = max(answer, st._tree[0])
  st.point_update(i, A[i])

print(answer)

Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())
A = list(map(int, input().split()))

n=100

from fractions import gcd
from functools import reduce
gs = [reduce(gcd, A[100*i:100*(i+1)]) for i in range((N-1)//100 + 1)]

answer = 0

for i in range(N):
  k = i%100
  i = (i//100)
  
  g = reduce(gcd, A[i*100:k] + A[k+1:(i+1)*100] + gs[0:i] + gs[i+1:])

  answer = max(answer, g)

print(answer)


Fixed submission:
N = int(input())
A = list(map(int, input().split()))

L = len(A)
from functools import reduce
from fractions import gcd

def lcm(a,b):
  return (a*b)//gcd(a,b)

g = reduce(gcd, A)
l = reduce(lcm, A)

def _gcd(a,b):
  if a is None and b is None:
    return None
  if a is None:
    return b
  if b is None:
    return a
  else:
    return gcd(a,b)

class SegTree():
  import math
  def __init__(self, func, A, identity=1):
    self._func = func
    self._N = 1
    while self._N < len(A):
      self._N *= 2
       # 長さ 7 なら N=3 (2^3=8)
    self._identity = identity # maxなら-1e9, sumなら0, productなら1

    self._tree = [self._identity] * (2*self._N -1) 
    self._tree[self._N-1:self._N-1+ len(A)] = A #最下段に元の配列を
    for i in range(self._N-2, -1, -1):
      self._update_single_node(i)
    ########
    # N=3: #
    # 0000 #
    # 1122 #
    # 3456 #
    ########
    self._node_range = [(i-self._N+1,i-self._N+2) for i in range(2*self._N-1)] #right_exclusive
    for i in range(self._N-2, -1, -1):
      self._node_range[i] = (self._node_range[2*i+1][0], self._node_range[2*i+2][1])

  def _update_single_node(self,i):
    self._tree[i] = self._func(self._tree[2*i+1], self._tree[2*i+2])

  def point_update(self,i,x):
    # A[i] = x (addではないので注意)
    j = self._N-1+i
    self._tree[j] = x
    while j>0:
      j = (j-1)//2
      self._update_single_node(j)

  def range_query(self, l, r, on=0):
    # reduce(func, A[l:r])
    # onはノード[on]上と重なる部分の，ということ
    onl, onr = self._node_range[on]
    
    # ノード[on]上はすべて覆う
    if l<=onl and onr<=r:
      return self._tree[on]
    
    # 重なりなし
    elif onr<=l or r<=onl:
      return self._identity
    
    else:
      return self._func(self.range_query(l, r, on=2*on+1),
                        self.range_query(l, r, on=2*on+2))

st = SegTree(_gcd, A, identity=None)

answer = 0
for i in range(len(A)):
  st.point_update(i, A[i-1])
  answer = max(answer, st._tree[0])
  st.point_update(i, A[i])

print(answer)

Buggy python submission (verdict: Runtime Error):
N = int(input())
A = list(map(int, input().split()))

L = len(A)
from functools import reduce
from fractions import gcd

g = reduce(gcd, A)

class SegTree():
  import math
  def __init__(self, func, A, identity=1):
    self._func = func
    self._N = 1
    while self._N < len(A):
      self._N *= 2
       # 長さ 7 なら N=3 (2^3=8)
    self._identity = identity # maxなら-1e9, sumなら0, productなら1

    self._tree = [self._identity] * (2*self._N -1) 
    self._tree[self._N-1:self._N-1+ len(A)] = A #最下段に元の配列を
    for i in range(self._N-1+len(A), -1, -1):
      self._update_single_node(i)
    ########
    # N=3: #
    # 0000 #
    # 1122 #
    # 3456 #
    ########
    self._node_range = [(i-self._N+1,i-self._N+2) for i in range(2*self._N-1)] #right_exclusive
    for i in range(self._N-2, -1, -1):
      self._node_range[i] = (self._node_range[2*i+1][0], self._node_range[2*i+2][1])

  def _update_single_node(self,i):
    self._tree[i] = self._func(self._tree[2*i+1], self._tree[2*i+2])

  def point_update(self,i,x):
    # A[i] = x (addではないので注意)
    j = self._N-1+i
    self._tree[j] = x
    while j>0:
      j = (j-1)//2
      self._update_single_node(j)

  def range_query(self, l, r, on=0):
    # reduce(func, A[l:r])
    # onはノード[on]上と重なる部分の，ということ
    onl, onr = self._node_range[on]
    
    # ノード[on]上はすべて覆う
    if l<=onl and onr<=r:
      return self._tree[on]
    
    # 重なりなし
    elif onr<=l or r<=onl:
      return self._identity
    
    else:
      return self._func(self.range_query(l, r, on=2*on+1),
                        self.range_query(l, r, on=2*on+2))

st = SegTree(gcd, A, identity=l)

answer = 0
for i in range(len(A)):
  st.point_update(i, A[i-1])
  answer = max(answer, st._tree[0])
  st.point_update(i, A[i])

print(answer)


Fixed submission:
N = int(input())
A = list(map(int, input().split()))

L = len(A)
from functools import reduce
from fractions import gcd

def lcm(a,b):
  return (a*b)//gcd(a,b)

g = reduce(gcd, A)
l = reduce(lcm, A)

def _gcd(a,b):
  if a is None and b is None:
    return None
  if a is None:
    return b
  if b is None:
    return a
  else:
    return gcd(a,b)

class SegTree():
  import math
  def __init__(self, func, A, identity=1):
    self._func = func
    self._N = 1
    while self._N < len(A):
      self._N *= 2
       # 長さ 7 なら N=3 (2^3=8)
    self._identity = identity # maxなら-1e9, sumなら0, productなら1

    self._tree = [self._identity] * (2*self._N -1) 
    self._tree[self._N-1:self._N-1+ len(A)] = A #最下段に元の配列を
    for i in range(self._N-2, -1, -1):
      self._update_single_node(i)
    ########
    # N=3: #
    # 0000 #
    # 1122 #
    # 3456 #
    ########
    self._node_range = [(i-self._N+1,i-self._N+2) for i in range(2*self._N-1)] #right_exclusive
    for i in range(self._N-2, -1, -1):
      self._node_range[i] = (self._node_range[2*i+1][0], self._node_range[2*i+2][1])

  def _update_single_node(self,i):
    self._tree[i] = self._func(self._tree[2*i+1], self._tree[2*i+2])

  def point_update(self,i,x):
    # A[i] = x (addではないので注意)
    j = self._N-1+i
    self._tree[j] = x
    while j>0:
      j = (j-1)//2
      self._update_single_node(j)

  def range_query(self, l, r, on=0):
    # reduce(func, A[l:r])
    # onはノード[on]上と重なる部分の，ということ
    onl, onr = self._node_range[on]
    
    # ノード[on]上はすべて覆う
    if l<=onl and onr<=r:
      return self._tree[on]
    
    # 重なりなし
    elif onr<=l or r<=onl:
      return self._identity
    
    else:
      return self._func(self.range_query(l, r, on=2*on+1),
                        self.range_query(l, r, on=2*on+2))

st = SegTree(_gcd, A, identity=None)

answer = 0
for i in range(len(A)):
  st.point_update(i, A[i-1])
  answer = max(answer, st._tree[0])
  st.point_update(i, A[i])

print(answer)

Buggy python submission (verdict: Runtime Error):
N = int(input())
A = list(map(int, input().split()))

L = len(A)
from functools import reduce
from fractions import gcd

g = reduce(gcd, A)

class SegTree():
  import math
  def __init__(self, func, A, identity=0):
    self._func = func
    self._N = 1
    while self._N < len(A):
      self._N *= 2
       # 長さ 7 なら N=3 (2^3=8)
    self._identity = identity # maxなら-1e9, sumなら0, productなら1

    self._tree = [self._identity] * (2*self._N -1) 
    self._tree[self._N-1:self._N-1+ len(A)] = A #最下段に元の配列を
    for i in range(self._N-1+len(A), -1, -1):
      self._update_single_node(i)
    ########
    # N=3: #
    # 0000 #
    # 1122 #
    # 3456 #
    ########
    self._node_range = [(i-self._N+1,i-self._N+2) for i in range(2*self._N-1)] #right_exclusive
    for i in range(self._N-2, -1, -1):
      self._node_range[i] = (self._node_range[2*i+1][0], self._node_range[2*i+2][1])

  def _update_single_node(self,i):
    self._tree[i] = self._func(self._tree[2*i+1], self._tree[2*i+2])

  def point_update(self,i,x):
    # A[i] = x (addではないので注意)
    j = self._N-1+i
    self._tree[j] = x
    while j>0:
      j = (j-1)//2
      self._update_single_node(j)

  def range_query(self, l, r, on=0):
    # reduce(func, A[l:r])
    # onはノード[on]上と重なる部分の，ということ
    onl, onr = self._node_range[on]
    
    # ノード[on]上はすべて覆う
    if l<=onl and onr<=r:
      return self._tree[on]
    
    # 重なりなし
    elif onr<=l or r<=onl:
      return self._identity
    
    else:
      return self._func(self.range_query(l, r, on=2*on+1),
                        self.range_query(l, r, on=2*on+2))

st = SegTree(gcd, A, identity=l)

answer = 0
for i in range(len(A)):
  st.point_update(i, A[i-1])
  answer = max(answer, st._tree[0])
  st.point_update(i, A[i])

print(answer)


Fixed submission:
N = int(input())
A = list(map(int, input().split()))

L = len(A)
from functools import reduce
from fractions import gcd

def lcm(a,b):
  return (a*b)//gcd(a,b)

g = reduce(gcd, A)
l = reduce(lcm, A)

def _gcd(a,b):
  if a is None and b is None:
    return None
  if a is None:
    return b
  if b is None:
    return a
  else:
    return gcd(a,b)

class SegTree():
  import math
  def __init__(self, func, A, identity=1):
    self._func = func
    self._N = 1
    while self._N < len(A):
      self._N *= 2
       # 長さ 7 なら N=3 (2^3=8)
    self._identity = identity # maxなら-1e9, sumなら0, productなら1

    self._tree = [self._identity] * (2*self._N -1) 
    self._tree[self._N-1:self._N-1+ len(A)] = A #最下段に元の配列を
    for i in range(self._N-2, -1, -1):
      self._update_single_node(i)
    ########
    # N=3: #
    # 0000 #
    # 1122 #
    # 3456 #
    ########
    self._node_range = [(i-self._N+1,i-self._N+2) for i in range(2*self._N-1)] #right_exclusive
    for i in range(self._N-2, -1, -1):
      self._node_range[i] = (self._node_range[2*i+1][0], self._node_range[2*i+2][1])

  def _update_single_node(self,i):
    self._tree[i] = self._func(self._tree[2*i+1], self._tree[2*i+2])

  def point_update(self,i,x):
    # A[i] = x (addではないので注意)
    j = self._N-1+i
    self._tree[j] = x
    while j>0:
      j = (j-1)//2
      self._update_single_node(j)

  def range_query(self, l, r, on=0):
    # reduce(func, A[l:r])
    # onはノード[on]上と重なる部分の，ということ
    onl, onr = self._node_range[on]
    
    # ノード[on]上はすべて覆う
    if l<=onl and onr<=r:
      return self._tree[on]
    
    # 重なりなし
    elif onr<=l or r<=onl:
      return self._identity
    
    else:
      return self._func(self.range_query(l, r, on=2*on+1),
                        self.range_query(l, r, on=2*on+2))

st = SegTree(_gcd, A, identity=None)

answer = 0
for i in range(len(A)):
  st.point_update(i, A[i-1])
  answer = max(answer, st._tree[0])
  st.point_update(i, A[i])

print(answer)

Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())
A = list(map(int, input().split()))

n=100

from fractions import gcd
from functools import reduce
gs = [reduce(gcd, A[100*i:100*(i+1)]) for i in range((N-1)//100 + 1)]

answer = 0

for i in range(N):
  k = i%100
  i = (i//100)
  
  g = reduce(gcd, A[i*100:k] + A[k+1:(i+1)*100] + gs[0:i] + gs[i+1:])

  answer = max(answer, g)

print(answer)

Fixed submission:
N = int(input())
A = list(map(int, input().split()))

L = len(A)
from functools import reduce
from fractions import gcd

def lcm(a,b):
  return (a*b)//gcd(a,b)

g = reduce(gcd, A)
l = reduce(lcm, A)

def _gcd(a,b):
  if a is None and b is None:
    return None
  if a is None:
    return b
  if b is None:
    return a
  else:
    return gcd(a,b)

class SegTree():
  import math
  def __init__(self, func, A, identity=1):
    self._func = func
    self._N = 1
    while self._N < len(A):
      self._N *= 2
       # 長さ 7 なら N=3 (2^3=8)
    self._identity = identity # maxなら-1e9, sumなら0, productなら1

    self._tree = [self._identity] * (2*self._N -1) 
    self._tree[self._N-1:self._N-1+ len(A)] = A #最下段に元の配列を
    for i in range(self._N-2, -1, -1):
      self._update_single_node(i)
    ########
    # N=3: #
    # 0000 #
    # 1122 #
    # 3456 #
    ########
    self._node_range = [(i-self._N+1,i-self._N+2) for i in range(2*self._N-1)] #right_exclusive
    for i in range(self._N-2, -1, -1):
      self._node_range[i] = (self._node_range[2*i+1][0], self._node_range[2*i+2][1])

  def _update_single_node(self,i):
    self._tree[i] = self._func(self._tree[2*i+1], self._tree[2*i+2])

  def point_update(self,i,x):
    # A[i] = x (addではないので注意)
    j = self._N-1+i
    self._tree[j] = x
    while j>0:
      j = (j-1)//2
      self._update_single_node(j)

  def range_query(self, l, r, on=0):
    # reduce(func, A[l:r])
    # onはノード[on]上と重なる部分の，ということ
    onl, onr = self._node_range[on]
    
    # ノード[on]上はすべて覆う
    if l<=onl and onr<=r:
      return self._tree[on]
    
    # 重なりなし
    elif onr<=l or r<=onl:
      return self._identity
    
    else:
      return self._func(self.range_query(l, r, on=2*on+1),
                        self.range_query(l, r, on=2*on+2))

st = SegTree(_gcd, A, identity=None)

answer = 0
for i in range(len(A)):
  st.point_update(i, A[i-1])
  answer = max(answer, st._tree[0])
  st.point_update(i, A[i])

print(answer)

Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())
A = list(map(int, input().split()))

from fractions import gcd
from functools import reduce
gs = [reduce(gcd, A[300*i:300*(i+1)]) for i in range((N-1)//300 + 1)]

answer = 0

for i in range(N):
  k = i%300
  i = (i//300)
  
  g = reduce(gcd, A[i*300:k] + A[k+1:(i+1)*300] + gs[0:i] + gs[i+1:])

  answer = max(answer, g)

print(answer)

Fixed submission:
N = int(input())
A = list(map(int, input().split()))

L = len(A)
from functools import reduce
from fractions import gcd

def lcm(a,b):
  return (a*b)//gcd(a,b)

g = reduce(gcd, A)
l = reduce(lcm, A)

def _gcd(a,b):
  if a is None and b is None:
    return None
  if a is None:
    return b
  if b is None:
    return a
  else:
    return gcd(a,b)

class SegTree():
  import math
  def __init__(self, func, A, identity=1):
    self._func = func
    self._N = 1
    while self._N < len(A):
      self._N *= 2
       # 長さ 7 なら N=3 (2^3=8)
    self._identity = identity # maxなら-1e9, sumなら0, productなら1

    self._tree = [self._identity] * (2*self._N -1) 
    self._tree[self._N-1:self._N-1+ len(A)] = A #最下段に元の配列を
    for i in range(self._N-2, -1, -1):
      self._update_single_node(i)
    ########
    # N=3: #
    # 0000 #
    # 1122 #
    # 3456 #
    ########
    self._node_range = [(i-self._N+1,i-self._N+2) for i in range(2*self._N-1)] #right_exclusive
    for i in range(self._N-2, -1, -1):
      self._node_range[i] = (self._node_range[2*i+1][0], self._node_range[2*i+2][1])

  def _update_single_node(self,i):
    self._tree[i] = self._func(self._tree[2*i+1], self._tree[2*i+2])

  def point_update(self,i,x):
    # A[i] = x (addではないので注意)
    j = self._N-1+i
    self._tree[j] = x
    while j>0:
      j = (j-1)//2
      self._update_single_node(j)

  def range_query(self, l, r, on=0):
    # reduce(func, A[l:r])
    # onはノード[on]上と重なる部分の，ということ
    onl, onr = self._node_range[on]
    
    # ノード[on]上はすべて覆う
    if l<=onl and onr<=r:
      return self._tree[on]
    
    # 重なりなし
    elif onr<=l or r<=onl:
      return self._identity
    
    else:
      return self._func(self.range_query(l, r, on=2*on+1),
                        self.range_query(l, r, on=2*on+2))

st = SegTree(_gcd, A, identity=None)

answer = 0
for i in range(len(A)):
  st.point_update(i, A[i-1])
  answer = max(answer, st._tree[0])
  st.point_update(i, A[i])

print(answer)

Buggy python submission (verdict: Time Limit Exceeded):
N = int(input())
A = list(map(int, input().split()))

L = len(A)
from functools import reduce
from fractions import gcd
def lcm(a,b):
  return a*b//gcd(a,b)

g = reduce(gcd, A)
l = reduce(lcm, A)

class SegTree():
  import math
  def __init__(self, func, A, identity=1e9):
    self._func = func
    self._N = 1
    while self._N < len(A):
      self._N *= 2
       # 長さ 7 なら N=3 (2^3=8)
    self._identity = identity # maxなら-1e9, sumなら0, productなら1

    self._tree = [self._identity] * (2*self._N -1) 
    self._tree[self._N-1:self._N-1+ len(A)] = A #最下段に元の配列を
    for i in range(self._N-2, -1, -1):
      self._update_single_node(i)
    ########
    # N=3: #
    # 0000 #
    # 1122 #
    # 3456 #
    ########
    self._node_range = [(i-self._N+1,i-self._N+2) for i in range(2*self._N-1)] #right_exclusive
    for i in range(self._N-2, -1, -1):
      self._node_range[i] = (self._node_range[2*i+1][0], self._node_range[2*i+2][1])

  def _update_single_node(self,i):
    self._tree[i] = self._func(self._tree[2*i+1], self._tree[2*i+2])

  def point_update(self,i,x):
    # A[i] = x (addではないので注意)
    j = self._N-1+i
    self._tree[j] = x
    while j>0:
      j = (j-1)//2
      self._update_single_node(j)

  def range_query(self, l, r, on=0):
    # reduce(func, A[l:r])
    # onはノード[on]上と重なる部分の，ということ
    onl, onr = self._node_range[on]
    
    # ノード[on]上はすべて覆う
    if l<=onl and onr<=r:
      return self._tree[on]
    
    # 重なりなし
    elif onr<=l or r<=onl:
      return self._identity
    
    else:
      return self._func(self.range_query(l, r, on=2*on+1),
                        self.range_query(l, r, on=2*on+2))

st = SegTree(gcd, A, identity=l)

answer = 0
for i in range(len(A)):
  st
  st.point_update(i, A[i-1])
  answer = max(answer, st._tree[0])
  st.point_update(i, A[i])

print(answer)

Fixed submission:
N = int(input())
A = list(map(int, input().split()))

L = len(A)
from functools import reduce
from fractions import gcd

def lcm(a,b):
  return (a*b)//gcd(a,b)

g = reduce(gcd, A)
l = reduce(lcm, A)

def _gcd(a,b):
  if a is None and b is None:
    return None
  if a is None:
    return b
  if b is None:
    return a
  else:
    return gcd(a,b)

class SegTree():
  import math
  def __init__(self, func, A, identity=1):
    self._func = func
    self._N = 1
    while self._N < len(A):
      self._N *= 2
       # 長さ 7 なら N=3 (2^3=8)
    self._identity = identity # maxなら-1e9, sumなら0, productなら1

    self._tree = [self._identity] * (2*self._N -1) 
    self._tree[self._N-1:self._N-1+ len(A)] = A #最下段に元の配列を
    for i in range(self._N-2, -1, -1):
      self._update_single_node(i)
    ########
    # N=3: #
    # 0000 #
    # 1122 #
    # 3456 #
    ########
    self._node_range = [(i-self._N+1,i-self._N+2) for i in range(2*self._N-1)] #right_exclusive
    for i in range(self._N-2, -1, -1):
      self._node_range[i] = (self._node_range[2*i+1][0], self._node_range[2*i+2][1])

  def _update_single_node(self,i):
    self._tree[i] = self._func(self._tree[2*i+1], self._tree[2*i+2])

  def point_update(self,i,x):
    # A[i] = x (addではないので注意)
    j = self._N-1+i
    self._tree[j] = x
    while j>0:
      j = (j-1)//2
      self._update_single_node(j)

  def range_query(self, l, r, on=0):
    # reduce(func, A[l:r])
    # onはノード[on]上と重なる部分の，ということ
    onl, onr = self._node_range[on]
    
    # ノード[on]上はすべて覆う
    if l<=onl and onr<=r:
      return self._tree[on]
    
    # 重なりなし
    elif onr<=l or r<=onl:
      return self._identity
    
    else:
      return self._func(self.range_query(l, r, on=2*on+1),
                        self.range_query(l, r, on=2*on+2))

st = SegTree(_gcd, A, identity=None)

answer = 0
for i in range(len(A)):
  st.point_update(i, A[i-1])
  answer = max(answer, st._tree[0])
  st.point_update(i, A[i])

print(answer)