Buggy python submission (verdict: Runtime Error):
def gcd(x, y):
    if y == 0:
        return x
    else:
        return gcd(y, x % y)

def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append(i)

    if temp!=1:
        arr.append(temp)

    return arr

N=int(input())
A=list(map(int, input().split()))
p=1
A=sorted(A)
num1=A.count(1)
B=list(set(A))
if len(B)<len(A)-num1+1:
    p=0
S=set(factorization(B[0]))
T=set(factorization(B[0]))
flg=0
for i in range(1,len(B)):
    prime=set(factorization(B[i])
    if T&prime!=set():
        flg=1
    S=S&prime
    T=T|prime    #print(S,T)
if S!=1:
    print('not coprime')
elif flg==1 or p=0:
    print('setwise coprime')
else:
    print('pairwise coprime')


Fixed submission:
from math import gcd
from functools import reduce

def make_prime_table(n):
    sieve = list(range(n + 1))
    sieve[0] = -1
    sieve[1] = -1
    for i in range(4, n + 1, 2):
        sieve[i] = 2
    for i in range(3, int(n ** 0.5) + 1, 2):
        if sieve[i] != i:
            continue
        for j in range(i * i, n + 1, i * 2):
            if sieve[j] == j:
                sieve[j] = i
    return sieve


def prime_factorize(n):#1を除く(素因数,指数)のリスト
    result = []
    while n != 1:
        p = prime_table[n]
        e = 0
        while n % p == 0:
            n //= p
            e += 1
        result.append((p, e)) 
    return result


def f():
    s = set()
    for i in range(N):
        t = prime_factorize(A[i])
        for p, _ in t:
            if p in s:
                return False
            s.add(p)
    return True


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

prime_table = make_prime_table(10 ** 6)
if f():
    print('pairwise coprime')
elif reduce(gcd, A) == 1:
    print('setwise coprime')
else:
    print('not coprime')

Buggy python submission (verdict: Time Limit Exceeded):
def gcd(x, y):
    if y == 0:
        return x
    else:
        return gcd(y, x % y)

def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append(i)

    if temp!=1:
        arr.append(temp)

    return arr

N=int(input())
A=list(map(int, input().split()))
S=set(factorization(A[0]))
T=set(factorization(A[0]))
flg=0
for i in range(1,N):
    k=A[i]
    prime=set(factorization(k))
    if T&prime!=set():
        flg=1
    S=S&prime
    T=T|prime
    #print(S,T)
if S!=set():
    print('not coprime')
elif flg==1:
    print('setwise coprime')
else:
    print('pairwise coprime')


Fixed submission:
from math import gcd
from functools import reduce

def make_prime_table(n):
    sieve = list(range(n + 1))
    sieve[0] = -1
    sieve[1] = -1
    for i in range(4, n + 1, 2):
        sieve[i] = 2
    for i in range(3, int(n ** 0.5) + 1, 2):
        if sieve[i] != i:
            continue
        for j in range(i * i, n + 1, i * 2):
            if sieve[j] == j:
                sieve[j] = i
    return sieve


def prime_factorize(n):#1を除く(素因数,指数)のリスト
    result = []
    while n != 1:
        p = prime_table[n]
        e = 0
        while n % p == 0:
            n //= p
            e += 1
        result.append((p, e)) 
    return result


def f():
    s = set()
    for i in range(N):
        t = prime_factorize(A[i])
        for p, _ in t:
            if p in s:
                return False
            s.add(p)
    return True


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

prime_table = make_prime_table(10 ** 6)
if f():
    print('pairwise coprime')
elif reduce(gcd, A) == 1:
    print('setwise coprime')
else:
    print('not coprime')