Buggy python submission (verdict: Runtime Error):
# 区間[i,j]における最小値を返す
# 値の更新をする
import fractions
input = sys.stdin.readline
class segment_tree:
    '''
    init_val(int): 初期化値
    Input(array):  入力
    '''
    def __init__(self, init_val, Input):
        #self.num:n以上の最小の2のべき乗(一番下のNodeの数)
        n=len(Input)
        self.init_val = init_val
        self.num = 2 ** (n - 1).bit_length()
        self.seg = [init_val] * 2 * self.num
        for i in range(n):
            self.seg[i + self.num - 1] = Input[i]
        for i in range(self.num - 2, -1, -1):
            self.seg[i]=self._segfunc(self.seg[2*i+1],self.seg[2*i+2])
    def _segfunc(self, left, right):
        '''
        ここに求めたい関数を入れる
        ex)最小値問題→min, 
        left:左の子
        right:右の子
        '''
        res=fractions.gcd(left,right)
        return res
    def update(self, k, x):
        '''
        k番目の値をxに書き換える
        '''
        k += self.num - 1
        self.seg[k] = x
        while k > 0:
            k = (k - 1) // 2
            self.seg[k] = self._segfunc(self.seg[k * 2 + 1], self.seg[k * 2 + 2])
    def query(self, p, q):
        '''
        区間[p,q)の目的の値を取り出す
        '''
        if q <= p:
            return self.init_val
        p += self.num - 1
        q += self.num - 2
        res = self.init_val
        while q - p > 1:
            if p % 2 == 0: #始点が偶数or終点が奇数だと端っこが余る
                res = self._segfunc(res, self.seg[p])
            if q % 2 == 1:
                res = self._segfunc(res, self.seg[q])
                q -= 1
            p = p // 2
            q = (q - 1) // 2
        res = self._segfunc(res, self.seg[p])
        res = self._segfunc(res, self.seg[q])
        return res
INF = 10 ** 10
n=int(input())
a=list(map(int,input().split()))

# a = [randint(0,N*2) for _ in range(N)]
dp = segment_tree(0, a)
ans=-1
for i in range(n):
  ans=max(ans,fractions.gcd(dp.query(0,i),dp.query(i+1,n)))
print(ans)

Fixed submission:
def gcd(x, y):
  if y == 0:
    return x
  else:
    return gcd(y, x % y) #再帰定義
n=int(input())
a=list(map(int,input().split()))
l=[0]*n
r=[0]*n
for i in range(1,n):
  if i==1:
    l[1]=a[0]
    r[-2]=a[-1]
  else:
    l[i]=gcd(l[i-1],a[i-1])
    r[-i-1]=gcd(r[-i],a[-i])
g=[0]*n
for i in range(n):
  if l[i]==0 or r[i]==0:
    g[i]=l[i]+r[i]
  else:
    g[i]=gcd(l[i],r[i])
print(max(g))

Buggy python submission (verdict: Time Limit Exceeded):
# 区間[i,j]における最小値を返す
# 値の更新をする
import fractions
class segment_tree:
    '''
    init_val(int): 初期化値
    Input(array):  入力
    '''
    def __init__(self, init_val, Input):
        #self.num:n以上の最小の2のべき乗(一番下のNodeの数)
        n=len(Input)
        self.init_val = init_val
        self.num = 2 ** (n - 1).bit_length()
        self.seg = [init_val] * 2 * self.num
        for i in range(n):
            self.seg[i + self.num - 1] = Input[i]
        for i in range(self.num - 2, -1, -1):
            self.seg[i]=self._segfunc(self.seg[2*i+1],self.seg[2*i+2])
    def _segfunc(self, left, right):
        '''
        ここに求めたい関数を入れる
        ex)最小値問題→min, 
        left:左の子
        right:右の子
        '''
        res=fractions.gcd(left,right)
        return res
    def update(self, k, x):
        '''
        k番目の値をxに書き換える
        '''
        k += self.num - 1
        self.seg[k] = x
        while k > 0:
            k = (k - 1) // 2
            self.seg[k] = self._segfunc(self.seg[k * 2 + 1], self.seg[k * 2 + 2])
    def query(self, p, q):
        '''
        区間[p,q)の目的の値を取り出す
        '''
        if q <= p:
            return self.init_val
        p += self.num - 1
        q += self.num - 2
        res = self.init_val
        while q - p > 1:
            if p % 2 == 0: #始点が偶数or終点が奇数だと端っこが余る
                res = self._segfunc(res, self.seg[p])
            if q % 2 == 1:
                res = self._segfunc(res, self.seg[q])
                q -= 1
            p = p // 2
            q = (q - 1) // 2
        res = self._segfunc(res, self.seg[p])
        res = self._segfunc(res, self.seg[q])
        return res
INF = 10 ** 10
n=int(input())
a=list(map(int,input().split()))

# a = [randint(0,N*2) for _ in range(N)]
dp = segment_tree(0, a)
ans=-1
for i in range(n):
  ans=max(ans,fractions.gcd(dp.query(0,i),dp.query(i+1,n)))
print(ans)

Fixed submission:
def gcd(x, y):
  if y == 0:
    return x
  else:
    return gcd(y, x % y) #再帰定義
n=int(input())
a=list(map(int,input().split()))
l=[0]*n
r=[0]*n
for i in range(1,n):
  if i==1:
    l[1]=a[0]
    r[-2]=a[-1]
  else:
    l[i]=gcd(l[i-1],a[i-1])
    r[-i-1]=gcd(r[-i],a[-i])
g=[0]*n
for i in range(n):
  if l[i]==0 or r[i]==0:
    g[i]=l[i]+r[i]
  else:
    g[i]=gcd(l[i],r[i])
print(max(g))

Buggy python submission (verdict: Time Limit Exceeded):
from functools import reduce
import copy
def gcd(x, y):
  if y == 0:
    return x
  else:
    return gcd(y, x % y) #再帰定義
  
def gcd_list(numbers):
    return reduce(gcd, numbers)
  
n=int(input())
a_o=list(map(int,input().split()))
g=[1]*n
for i in range(n):
  a=copy.copy(a_o)
  a.pop(i)
  g[i]=gcd_list(a)
print(max(g))

Fixed submission:
def gcd(x, y):
  if y == 0:
    return x
  else:
    return gcd(y, x % y) #再帰定義
n=int(input())
a=list(map(int,input().split()))
l=[0]*n
r=[0]*n
for i in range(1,n):
  if i==1:
    l[1]=a[0]
    r[-2]=a[-1]
  else:
    l[i]=gcd(l[i-1],a[i-1])
    r[-i-1]=gcd(r[-i],a[-i])
g=[0]*n
for i in range(n):
  if l[i]==0 or r[i]==0:
    g[i]=l[i]+r[i]
  else:
    g[i]=gcd(l[i],r[i])
print(max(g))

Buggy python submission (verdict: Time Limit Exceeded):
import fractions
from functools import reduce
import copy
def gcd_list(numbers):
    return reduce(fractions.gcd, numbers)
n=int(input())
a_o=list(map(int,input().split()))
g=[1]*n
for i in range(n):
  a=copy.copy(a_o)
  a.pop(i)
  g[i]=gcd_list(a)
print(max(g))

Fixed submission:
def gcd(x, y):
  if y == 0:
    return x
  else:
    return gcd(y, x % y) #再帰定義
n=int(input())
a=list(map(int,input().split()))
l=[0]*n
r=[0]*n
for i in range(1,n):
  if i==1:
    l[1]=a[0]
    r[-2]=a[-1]
  else:
    l[i]=gcd(l[i-1],a[i-1])
    r[-i-1]=gcd(r[-i],a[-i])
g=[0]*n
for i in range(n):
  if l[i]==0 or r[i]==0:
    g[i]=l[i]+r[i]
  else:
    g[i]=gcd(l[i],r[i])
print(max(g))