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

gcd_max = 1

if N == 2:
    print(max(A_array[0], A_array[1]))
    exit()
for i in range(N):
    gcd = 0
    for j, A in enumerate(A_array):
        if i == j:
            continue
        if gcd == 0:
            gcd = A
            continue
        # print(A,gcd)
        gcd = min(gcd, fractions.gcd(A, gcd))
        if gcd <= gcd_max:
            break
    gcd_max = max(gcd_max, gcd)
print(gcd_max)

Fixed submission:
import fractions
N = int(input())
A_array = list(map(int, input().split()))

if N == 2:
    print(max(A_array[0], A_array[1]))
    exit()

remove_index = []
for i, A in enumerate(A_array):
    if i == 0:
        gcd_max = A
        remove_index.append(i)
        continue
    gcd = fractions.gcd(gcd_max, A)
    # print(i, gcd_max, gcd)
    if gcd_max > gcd:
        gcd_max = gcd
        remove_index.append(i)
# print(remove_index)
# print(gcd_max, remove_index)

gcd_ans = gcd_max
for index in remove_index:
    gcd = 0
    for i, A in enumerate(A_array):
        if i == index:
            continue
        if gcd == 0:
            gcd = A
            continue
        # print(gcd,A)
        gcd = fractions.gcd(gcd, A)
        if gcd_ans >= gcd:
            break
    # print(gcd_ans,gcd)
    gcd_ans = max(gcd_ans, gcd)
print(gcd_ans)

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

gcd_max = 1

if N == 2:
    print(max(A_array[0], A_array[1]))
    exit()
for i in range(N):
    gcd = 0
    for j, A in enumerate(A_array):
        if i == j:
            continue
        if gcd == 0:
            gcd = A
            continue
        # print(A,gcd)
        gcd = min(gcd, fractions.gcd(A, gcd))
        if gcd < gcd_max:
            continue
    gcd_max = max(gcd_max, gcd)
print(gcd_max)

Fixed submission:
import fractions
N = int(input())
A_array = list(map(int, input().split()))

if N == 2:
    print(max(A_array[0], A_array[1]))
    exit()

remove_index = []
for i, A in enumerate(A_array):
    if i == 0:
        gcd_max = A
        remove_index.append(i)
        continue
    gcd = fractions.gcd(gcd_max, A)
    # print(i, gcd_max, gcd)
    if gcd_max > gcd:
        gcd_max = gcd
        remove_index.append(i)
# print(remove_index)
# print(gcd_max, remove_index)

gcd_ans = gcd_max
for index in remove_index:
    gcd = 0
    for i, A in enumerate(A_array):
        if i == index:
            continue
        if gcd == 0:
            gcd = A
            continue
        # print(gcd,A)
        gcd = fractions.gcd(gcd, A)
        if gcd_ans >= gcd:
            break
    # print(gcd_ans,gcd)
    gcd_ans = max(gcd_ans, gcd)
print(gcd_ans)

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

gcd_max = 1

if N == 2:
    print(max(A_array[0],A_array[1]))
    exit()
for i in range(N):
    gcd = 0
    for j, A in enumerate(A_array):
        if i == j:
            continue
        if gcd == 0:
            gcd = A
            continue
        # print(A,gcd)
        gcd = min(gcd, fractions.gcd(A, gcd))
    gcd_max = max(gcd_max, gcd)
print(gcd_max)

Fixed submission:
import fractions
N = int(input())
A_array = list(map(int, input().split()))

if N == 2:
    print(max(A_array[0], A_array[1]))
    exit()

remove_index = []
for i, A in enumerate(A_array):
    if i == 0:
        gcd_max = A
        remove_index.append(i)
        continue
    gcd = fractions.gcd(gcd_max, A)
    # print(i, gcd_max, gcd)
    if gcd_max > gcd:
        gcd_max = gcd
        remove_index.append(i)
# print(remove_index)
# print(gcd_max, remove_index)

gcd_ans = gcd_max
for index in remove_index:
    gcd = 0
    for i, A in enumerate(A_array):
        if i == index:
            continue
        if gcd == 0:
            gcd = A
            continue
        # print(gcd,A)
        gcd = fractions.gcd(gcd, A)
        if gcd_ans >= gcd:
            break
    # print(gcd_ans,gcd)
    gcd_ans = max(gcd_ans, gcd)
print(gcd_ans)