Buggy python submission (verdict: Time Limit Exceeded):
import sys
# sys.setrecursionlimit(100000)
from collections import defaultdict
from functools import lru_cache


@lru_cache(None)
def gcd(x: int, y: int) -> int:
    if x < y:
        x, y = y, x
    while y > 0:
        r = x % y
        x, y = y, r
    return x


def merge_dict(d1, d2):
    for k, v in d2.items():
        d1[k] += v
    return d1


def input():
    return sys.stdin.readline().strip()


def gen_prime_table(last: int, first=2) -> list:
    if last < 1:
        return [False]
    elif last < 2:
        return [False, False]
    primes = []
    table = [True] * (last + 1)
    table[0] = False
    table[1] = False

    for i in range(first, last + 1):
        if table[i]:
            primes.append(i)
            for j in range(i * 2, last + 1, i):
                table[j] = False
    return primes


def prime_factorization(N: int, prime_list: list) -> dict:
    if N < 2:
        return {1: 1}
    primes = dict()
    primes[1] = 1
    i = 2
    for i in prime_list:
        while N % i == 0:
            if i in primes.keys():
                primes[i] += 1
            else:
                primes[i] = 1
            N = N // i
        if N == 1:
            break
    if N != 1:
        primes[N] = 1
    return primes


def main():
    n = int(input())
    A = [int(i) for i in input().split()]
    primes = defaultdict(int)
    is_pair_gcd = True
    set_gcd = A[0]
    prime_list = gen_prime_table(max(A))
    for i in range(n):
        set_gcd = gcd(set_gcd, A[i])
        if is_pair_gcd:
            p = prime_factorization(A[i], prime_list)  # この部分の計算不可が大きい (n*log_log_n)
            for k, v in p.items():
                if k == 1:
                    continue
                if k in primes.keys():
                    is_pair_gcd = False
                else:
                    primes[k] += v

    if is_pair_gcd:
        print("pairwise coprime")
        return

    if set_gcd == 1:
        print("setwise coprime")
    else:
        print("not coprime")

    return


if __name__ == "__main__":
    main()


Fixed submission:
import sys
# sys.setrecursionlimit(100000)
from collections import defaultdict
from functools import lru_cache


@lru_cache(None)
def gcd(x: int, y: int) -> int:
    if x < y:
        x, y = y, x
    while y > 0:
        r = x % y
        x, y = y, r
    return x


def merge_dict(d1, d2):
    for k, v in d2.items():
        d1[k] += v
    return d1


def input():
    return sys.stdin.readline().strip()


def prime_factorization(N: int) -> dict:
    primes = defaultdict(int)
    primes[1] = 1
    if N < 2:
        return primes
    i = 2
    while i * i <= N:
        while N % i == 0:
            primes[i] += 1
            N = N // i
        i += 1
    if N != 1:
        primes[N] = 1
    return primes


def main():
    n = int(input())
    A = [int(i) for i in input().split()]
    primes = defaultdict(int)
    is_pair_gcd = True
    # pre-process
    for i in range(n):
        p = prime_factorization(A[i])
        for k, v in p.items():
            if k == 1:
                continue
            if k in primes.keys():
                is_pair_gcd = False
                break
            else:
                primes[k] += v
        else:
            continue
        break

    if is_pair_gcd:
        print("pairwise coprime")
        return

    set_gcd = A[0]
    for i in range(1, n):
        set_gcd = gcd(set_gcd, A[i])

    if set_gcd == 1:
        print("setwise coprime")
    else:
        print("not coprime")

    return


if __name__ == "__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
import sys
# sys.setrecursionlimit(100000)
from collections import defaultdict
from functools import lru_cache


@lru_cache(None)
def gcd(x: int, y: int) -> int:
    if x < y:
        x, y = y, x
    while y > 0:
        r = x % y
        x, y = y, r
    return x


def merge_dict(d1, d2):
    for k, v in d2.items():
        d1[k] += v
    return d1


def input():
    return sys.stdin.readline().strip()


def prime_factorization(N: int) -> dict:
    primes = defaultdict(int)
    primes[1] = 1
    if N < 2:
        return primes
    i = 2
    while i * i <= N:
        while N % i == 0:
            primes[i] += 1
            N = N // i
        i += 1
    if N != 1:
        primes[N] = 1
    return primes


def main():
    n = int(input())
    A = [int(i) for i in input().split()]
    primes = defaultdict(int)
    is_pair_gcd = True
    set_gcd = A[0]
    for i in range(n):
        set_gcd = gcd(set_gcd, A[i])
        p = prime_factorization(A[i])
        if is_pair_gcd:
            for k, v in p.items():
                if k == 1:
                    continue
                if k in primes.keys():
                    is_pair_gcd = False
                else:
                    primes[k] += v

    if is_pair_gcd:
        print("pairwise coprime")
        return

    if set_gcd == 1:
        print("setwise coprime")
    else:
        print("not coprime")

    return


if __name__ == "__main__":
    main()


Fixed submission:
import sys
# sys.setrecursionlimit(100000)
from collections import defaultdict
from functools import lru_cache


@lru_cache(None)
def gcd(x: int, y: int) -> int:
    if x < y:
        x, y = y, x
    while y > 0:
        r = x % y
        x, y = y, r
    return x


def merge_dict(d1, d2):
    for k, v in d2.items():
        d1[k] += v
    return d1


def input():
    return sys.stdin.readline().strip()


def prime_factorization(N: int) -> dict:
    primes = defaultdict(int)
    primes[1] = 1
    if N < 2:
        return primes
    i = 2
    while i * i <= N:
        while N % i == 0:
            primes[i] += 1
            N = N // i
        i += 1
    if N != 1:
        primes[N] = 1
    return primes


def main():
    n = int(input())
    A = [int(i) for i in input().split()]
    primes = defaultdict(int)
    is_pair_gcd = True
    # pre-process
    for i in range(n):
        p = prime_factorization(A[i])
        for k, v in p.items():
            if k == 1:
                continue
            if k in primes.keys():
                is_pair_gcd = False
                break
            else:
                primes[k] += v
        else:
            continue
        break

    if is_pair_gcd:
        print("pairwise coprime")
        return

    set_gcd = A[0]
    for i in range(1, n):
        set_gcd = gcd(set_gcd, A[i])

    if set_gcd == 1:
        print("setwise coprime")
    else:
        print("not coprime")

    return


if __name__ == "__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
import sys
# sys.setrecursionlimit(100000)
from collections import defaultdict
from functools import lru_cache


@lru_cache(None)
def gcd(x: int, y: int) -> int:
    if x < y:
        x, y = y, x
    while y > 0:
        r = x % y
        x, y = y, r
    return x


def merge_dict(d1, d2):
    for k, v in d2.items():
        d1[k] += v
    return d1


def input():
    return sys.stdin.readline().strip()


def prime_factorization(N: int) -> dict:
    primes = defaultdict(int)
    primes[1] = 1
    if N < 2:
        return primes
    i = 2
    while i * i <= N:
        while N % i == 0:
            primes[i] += 1
            N = N // i
        i += 1
    if N != 1:
        primes[N] = 1
    return primes


def main():
    n = int(input())
    A = [int(i) for i in input().split()]
    primes = defaultdict(int)
    is_pair_gcd = True
    # pre-process
    for i in range(n):
        primes = merge_dict(primes, prime_factorization(A[i]))

    set_gcd = A[0]
    for i in range(1, n):
        set_gcd = gcd(set_gcd, A[i])
        if is_pair_gcd:
            p = prime_factorization(A[i])
            for k, v in p.items():
                if k == 1:
                    continue
                if primes[k] != v:
                    is_pair_gcd = False
                    break
    if is_pair_gcd:
        print("pairwise coprime")
    elif not is_pair_gcd and set_gcd == 1:
        print("setwise coprime")
    else:
        print("not coprime")

    return


if __name__ == "__main__":
    main()


Fixed submission:
import sys
# sys.setrecursionlimit(100000)
from collections import defaultdict
from functools import lru_cache


@lru_cache(None)
def gcd(x: int, y: int) -> int:
    if x < y:
        x, y = y, x
    while y > 0:
        r = x % y
        x, y = y, r
    return x


def merge_dict(d1, d2):
    for k, v in d2.items():
        d1[k] += v
    return d1


def input():
    return sys.stdin.readline().strip()


def prime_factorization(N: int) -> dict:
    primes = defaultdict(int)
    primes[1] = 1
    if N < 2:
        return primes
    i = 2
    while i * i <= N:
        while N % i == 0:
            primes[i] += 1
            N = N // i
        i += 1
    if N != 1:
        primes[N] = 1
    return primes


def main():
    n = int(input())
    A = [int(i) for i in input().split()]
    primes = defaultdict(int)
    is_pair_gcd = True
    # pre-process
    for i in range(n):
        p = prime_factorization(A[i])
        for k, v in p.items():
            if k == 1:
                continue
            if k in primes.keys():
                is_pair_gcd = False
                break
            else:
                primes[k] += v
        else:
            continue
        break

    if is_pair_gcd:
        print("pairwise coprime")
        return

    set_gcd = A[0]
    for i in range(1, n):
        set_gcd = gcd(set_gcd, A[i])

    if set_gcd == 1:
        print("setwise coprime")
    else:
        print("not coprime")

    return


if __name__ == "__main__":
    main()