Buggy python submission (verdict: Time Limit Exceeded):
import numpy as np
N=int(input())
A=list(map(int,input().split()))
# cnt=[0]*(10**6+1)
cnt=np.zeros(10**6+1, dtype='int')
for a in A:cnt[a]+=1
 
if np.gcd.reduce(A)!=1:
  print("not coprime")
elif np.all([sum(cnt[i::i])<=1 for i in range(2,10**6+1)]):
  print("pairwise coprime")
else:
  print("setwise coprime")

Fixed submission:
from math import gcd, sqrt, ceil
from functools import reduce

def sieve(n):
    A = list(range(n+1))
    for i in range(2, n+1 ,2):
        A[i] = 2
    for j in range(3, ceil(sqrt(n+1))+1, 2)[::-1]:
        for i in range(j, n+1, j):
            A[i] = j
    return A

def factorize(n, A):
    factors = set()
    while n != 1:
        f = A[n]
        factors.add(f)
        n //= f
    return factors

_, *aa = map(int, open(0).read().split())

def main(aa):
    pair_co = True
    A = sieve(10**6)
    all_factors = [0] * (10**6+1)
    for a in aa:
        factors = factorize(a, A)
        for factor in factors:
            if all_factors[factor]:
                pair_co = False
                break
            else:
                all_factors[factor] = 1
        if not pair_co:
            break
    if pair_co:
        return 'pairwise coprime'
    elif reduce(gcd, aa) == 1:
        return 'setwise coprime'
    else:
        return 'not coprime'

print(main(aa))

Buggy python submission (verdict: Time Limit Exceeded):
import numpy as np
n = int(input())
aa = np.array(input().split(), dtype='int')
ma = np.max(aa)
cnt = np.zeros(max(aa)+1, dtype='int')

for a in aa:
    cnt[a] += 1

if np.gcd.reduce(aa) != 1:
    print('not coprime')

elif np.all([cnt[i::i].sum() <= 1 for i in range(2, ma)]):
    print('pairwise coprime')
else:
    print('setwise coprime')

Fixed submission:
from math import gcd, sqrt, ceil
from functools import reduce

def sieve(n):
    A = list(range(n+1))
    for i in range(2, n+1 ,2):
        A[i] = 2
    for j in range(3, ceil(sqrt(n+1))+1, 2)[::-1]:
        for i in range(j, n+1, j):
            A[i] = j
    return A

def factorize(n, A):
    factors = set()
    while n != 1:
        f = A[n]
        factors.add(f)
        n //= f
    return factors

_, *aa = map(int, open(0).read().split())

def main(aa):
    pair_co = True
    A = sieve(10**6)
    all_factors = [0] * (10**6+1)
    for a in aa:
        factors = factorize(a, A)
        for factor in factors:
            if all_factors[factor]:
                pair_co = False
                break
            else:
                all_factors[factor] = 1
        if not pair_co:
            break
    if pair_co:
        return 'pairwise coprime'
    elif reduce(gcd, aa) == 1:
        return 'setwise coprime'
    else:
        return 'not coprime'

print(main(aa))

Buggy python submission (verdict: Time Limit Exceeded):
from math import gcd, sqrt, ceil
from functools import reduce

def sieve(n):
    A = list(range(n+1))
    for i in range(2, n+1 ,2):
        A[i] = 2
    for j in range(3, ceil(sqrt(n+1))+1, 2)[::-1]:
        for i in range(j, n+1, j):
            A[i] = j
    return A

def factorize(n, A):
    factors = set()
    while n != 1:
        f = A[n]
        factors.add(f)
        n //= f
    return factors

_, *aa = map(int, open(0).read().split())

def main(aa):
    pair_co = True
    max_factors = set()
    A = sieve(10**6)
    for a in aa:
        factors = factorize(a, A)
        new_max_factors = max_factors | factors
        if len(new_max_factors) < len(max_factors) + len(factors):
            pair_co = False
            break
        max_factors = new_max_factors
    if pair_co:
        return 'pairwise coprime'
    elif reduce(gcd, aa) == 1:
        return 'setwise coprime'
    else:
        return 'not coprime'

print(main(aa))

Fixed submission:
from math import gcd, sqrt, ceil
from functools import reduce

def sieve(n):
    A = list(range(n+1))
    for i in range(2, n+1 ,2):
        A[i] = 2
    for j in range(3, ceil(sqrt(n+1))+1, 2)[::-1]:
        for i in range(j, n+1, j):
            A[i] = j
    return A

def factorize(n, A):
    factors = set()
    while n != 1:
        f = A[n]
        factors.add(f)
        n //= f
    return factors

_, *aa = map(int, open(0).read().split())

def main(aa):
    pair_co = True
    A = sieve(10**6)
    all_factors = [0] * (10**6+1)
    for a in aa:
        factors = factorize(a, A)
        for factor in factors:
            if all_factors[factor]:
                pair_co = False
                break
            else:
                all_factors[factor] = 1
        if not pair_co:
            break
    if pair_co:
        return 'pairwise coprime'
    elif reduce(gcd, aa) == 1:
        return 'setwise coprime'
    else:
        return 'not coprime'

print(main(aa))

Buggy python submission (verdict: Time Limit Exceeded):
from math import gcd, sqrt, ceil
from functools import reduce
_, *aa = map(int, open(0).read().split())

def factorize(n):
    factors = set()
    if n % 2 == 0:
        factors.add(2)
        n //= 2
    while n % 2 == 0:
        n //= 2
    for i in range(3, ceil(sqrt(n + 1)) + 1):
        if n % i == 0:
            factors.add(i)
            n //= i
        while n % i == 0:
            n //= i
    if n > 2:
        factors.add(n)
    return factors

def main(aa):
    
    pair_co = True
    max_factors = set()
    for a in aa:
        factors = factorize(a)
        new_max_factors = max_factors | factors
        if len(new_max_factors) < len(max_factors) + len(factors):
            pair_co = False
            break
        max_factors = new_max_factors
#     if min_factors:
#         return 'not coprime'
#     elif pair_co
    if pair_co:
        return 'pairwise coprime'
    elif reduce(gcd, aa) == 1:
        return 'setwise coprime'
    else:
        return 'not coprime'
        

print(main(aa))

Fixed submission:
from math import gcd, sqrt, ceil
from functools import reduce

def sieve(n):
    A = list(range(n+1))
    for i in range(2, n+1 ,2):
        A[i] = 2
    for j in range(3, ceil(sqrt(n+1))+1, 2)[::-1]:
        for i in range(j, n+1, j):
            A[i] = j
    return A

def factorize(n, A):
    factors = set()
    while n != 1:
        f = A[n]
        factors.add(f)
        n //= f
    return factors

_, *aa = map(int, open(0).read().split())

def main(aa):
    pair_co = True
    A = sieve(10**6)
    all_factors = [0] * (10**6+1)
    for a in aa:
        factors = factorize(a, A)
        for factor in factors:
            if all_factors[factor]:
                pair_co = False
                break
            else:
                all_factors[factor] = 1
        if not pair_co:
            break
    if pair_co:
        return 'pairwise coprime'
    elif reduce(gcd, aa) == 1:
        return 'setwise coprime'
    else:
        return 'not coprime'

print(main(aa))

Buggy python submission (verdict: Time Limit Exceeded):
from math import gcd, sqrt, ceil
_, *aa = map(int, open(0).read().split())

from collections import defaultdict
def factorize(n):
    factors = set()
    if n % 2 == 0:
        factors.add(2)
    while n % 2 == 0:
        n //= 2
    for i in range(3, ceil(sqrt(n + 1)) + 1):
        if n % i == 0:
            factors.add(i)
        while n % i == 0:
            n //= i
    if n > 2:
        factors.add(n)
    return factors

def main(aa):
    pair_co = True
    min_factors = None
    max_factors = set()
    for a in aa:
        factors = factorize(a)
        new_max_factors = max_factors | factors
        if len(new_max_factors) < len(max_factors) + len(factors):
            pair_co = False
        max_factors = new_max_factors
        if min_factors is not None:
            min_factors &= factors
        else:
            min_factors = factors
#     if min_factors:
#         return 'not coprime'
#     elif pair_co
    if pair_co:
        return 'pairwise coprime'
    elif min_factors:
        return 'not coprime'
    else:
        return 'setwise coprime'
        

print(main(aa))

Fixed submission:
from math import gcd, sqrt, ceil
from functools import reduce

def sieve(n):
    A = list(range(n+1))
    for i in range(2, n+1 ,2):
        A[i] = 2
    for j in range(3, ceil(sqrt(n+1))+1, 2)[::-1]:
        for i in range(j, n+1, j):
            A[i] = j
    return A

def factorize(n, A):
    factors = set()
    while n != 1:
        f = A[n]
        factors.add(f)
        n //= f
    return factors

_, *aa = map(int, open(0).read().split())

def main(aa):
    pair_co = True
    A = sieve(10**6)
    all_factors = [0] * (10**6+1)
    for a in aa:
        factors = factorize(a, A)
        for factor in factors:
            if all_factors[factor]:
                pair_co = False
                break
            else:
                all_factors[factor] = 1
        if not pair_co:
            break
    if pair_co:
        return 'pairwise coprime'
    elif reduce(gcd, aa) == 1:
        return 'setwise coprime'
    else:
        return 'not coprime'

print(main(aa))