Buggy python submission (verdict: Time Limit Exceeded):
import math
import copy
import fractions
import numpy as np
from functools import reduce

# ===FUNCTION===

def getInputNum():
    inputNum = int(input())
    return inputNum

def getInputListInt():
    outputoData = []
    inputData = input().split()
    outputData = [int(n) for n in inputData]

    return outputData

def getSomeInputInt(n):
    outputDataList = []
    for i in range(n):
        inputData = int(input())
        outputDataList.append(inputData)

    return outputDataList

def getSomeInputListInt(n):
    inputDataList = []
    outputDataList = []
    for i in range(n):
        inputData = input().split()
        inputDataList = [int(n) for n in inputData]
        outputDataList.append(inputDataList)

    return outputDataList

# ===CODE===

n, = map(int, input().split())
data = getInputListInt()

ans = 0

for i in range(n):
    tmp = []
    tmp = copy.deepcopy(data)
    tmp.pop(i)

    gcdans = reduce(fractions.gcd, tmp)

    ans = max(ans, gcdans)

print(ans)


Fixed submission:
import math
import copy
import fractions
import numpy as np
from functools import reduce

# ===FUNCTION===

def getInputNum():
    inputNum = int(input())
    return inputNum

def getInputListInt():
    outputoData = []
    inputData = input().split()
    outputData = [int(n) for n in inputData]

    return outputData

def getSomeInputInt(n):
    outputDataList = []
    for i in range(n):
        inputData = int(input())
        outputDataList.append(inputData)

    return outputDataList

def getSomeInputListInt(n):
    inputDataList = []
    outputDataList = []
    for i in range(n):
        inputData = input().split()
        inputDataList = [int(n) for n in inputData]
        outputDataList.append(inputDataList)

    return outputDataList

# ===CODE===

n, = map(int, input().split())
data = getInputListInt()

gcdNormal = np.zeros(n)
gcdReverse = np.zeros(n)

ans = 0

for i in range(1, n):
    if i==1:
        ans = fractions.gcd(data[i-1], data[i])
        gcdNormal[i] = ans
        gcdNormal[0] = data[0]
    else:
        gcdans = fractions.gcd(ans, data[i])
        ans = min(ans, gcdans)
        gcdNormal[i] = ans

ans = 0

for i in range(n-2, -1, -1):
    if i==n-2:
        ans = fractions.gcd(data[i], data[i+1])
        gcdReverse[i] = ans
        gcdReverse[i+1] = data[i+1]
    else:
        gcdans = fractions.gcd(ans, data[i])
        ans = min(ans, gcdans)
        gcdReverse[i] = ans

ans= 0
for i in range(n):
    if i ==0:
        ans = max(ans, gcdReverse[1])
    elif i == n-1:
        ans = max(ans, gcdNormal[n-2])
    else:
        ans = max(ans, fractions.gcd(gcdNormal[i-1], gcdReverse[i+1]))

print(int(ans))

Buggy python submission (verdict: Time Limit Exceeded):
import math
import copy
import fractions
import numpy as np
from functools import reduce

# ===FUNCTION===

def getInputNum():
    inputNum = int(input())
    return inputNum

def getInputListInt():
    outputoData = []
    inputData = input().split()
    outputData = [int(n) for n in inputData]

    return outputData

def getSomeInputInt(n):
    outputDataList = []
    for i in range(n):
        inputData = int(input())
        outputDataList.append(inputData)

    return outputDataList

def getSomeInputListInt(n):
    inputDataList = []
    outputDataList = []
    for i in range(n):
        inputData = input().split()
        inputDataList = [int(n) for n in inputData]
        outputDataList.append(inputDataList)

    return outputDataList

# ===CODE===

n, = map(int, input().split())
data = getInputListInt()

data.sort()

ans = 0

for i in range(n):
    tmp = []
    tmp = copy.deepcopy(data)
    tmp.pop(i)

    gcdans = reduce(fractions.gcd, tmp)

    ans = max(ans, gcdans)

print(ans)


Fixed submission:
import math
import copy
import fractions
import numpy as np
from functools import reduce

# ===FUNCTION===

def getInputNum():
    inputNum = int(input())
    return inputNum

def getInputListInt():
    outputoData = []
    inputData = input().split()
    outputData = [int(n) for n in inputData]

    return outputData

def getSomeInputInt(n):
    outputDataList = []
    for i in range(n):
        inputData = int(input())
        outputDataList.append(inputData)

    return outputDataList

def getSomeInputListInt(n):
    inputDataList = []
    outputDataList = []
    for i in range(n):
        inputData = input().split()
        inputDataList = [int(n) for n in inputData]
        outputDataList.append(inputDataList)

    return outputDataList

# ===CODE===

n, = map(int, input().split())
data = getInputListInt()

gcdNormal = np.zeros(n)
gcdReverse = np.zeros(n)

ans = 0

for i in range(1, n):
    if i==1:
        ans = fractions.gcd(data[i-1], data[i])
        gcdNormal[i] = ans
        gcdNormal[0] = data[0]
    else:
        gcdans = fractions.gcd(ans, data[i])
        ans = min(ans, gcdans)
        gcdNormal[i] = ans

ans = 0

for i in range(n-2, -1, -1):
    if i==n-2:
        ans = fractions.gcd(data[i], data[i+1])
        gcdReverse[i] = ans
        gcdReverse[i+1] = data[i+1]
    else:
        gcdans = fractions.gcd(ans, data[i])
        ans = min(ans, gcdans)
        gcdReverse[i] = ans

ans= 0
for i in range(n):
    if i ==0:
        ans = max(ans, gcdReverse[1])
    elif i == n-1:
        ans = max(ans, gcdNormal[n-2])
    else:
        ans = max(ans, fractions.gcd(gcdNormal[i-1], gcdReverse[i+1]))

print(int(ans))