Buggy python submission (verdict: Time Limit Exceeded):
import math
import sys
import random

def gcd(x, y):
    if y == 0:
        return x
    return gcd(y, x % y)

input = sys.stdin.readline
n = int(input())
a = list(map(int, input().split()))

def sieve_of_erastosthenes(num):
    input_list = [False if i % 2 == 0 or i % 3 == 0 or i % 5 == 0 else True for i in range(num)]
    input_list[0] = input_list[1] = False
    input_list[2] = input_list[3] = input_list[5] = True
    sqrt = math.sqrt(num)

    for serial in range(3, num, 2):

        if serial >= sqrt:
            return input_list

        for s in range(serial ** 2, num, serial): 
            input_list[s] = False

input_list = sieve_of_erastosthenes(int(-(-1000//1))+1)
prime_list = [i for i, b in enumerate(input_list) if b == True]

def factorization(n):
    arr = []
    temp = n
    for i in prime_list:
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append(i)
    if temp!=1:
        arr.append(temp)
    if arr==[]:
        arr.append(n)
    return arr
random.shuffle(a)
g = a[0]
arr = factorization(a[0])
used = set()
for i in arr:
    if i == 1: continue
    used.add(i)

pair = True
for i in range(n-1):
    g = gcd(g, a[i+1])
    # 一度でも互いに素でない組合せが出たらpariwise coprimeではない
    if pair:
        arr = set(factorization(a[i+1]))
        arr -= {1}
        if used&arr:
            pair = False
        else:
            used |= arr
if g > 1:
    print('not coprime')
    exit(0)
if not pair:
    print('setwise coprime')
    exit(0)
else:
    print('pairwise coprime')


Fixed submission:
import math
import sys
import random

def gcd(x, y):
    if y == 0:
        return x
    return gcd(y, x % y)

input = sys.stdin.readline
n = int(input())
a = list(map(int, input().split()))

def sieve_of_erastosthenes(num):
    input_list = [False if i % 2 == 0 or i % 3 == 0 or i % 5 == 0 else True for i in range(num)]
    input_list[0] = input_list[1] = False
    input_list[2] = input_list[3] = input_list[5] = True
    sqrt = math.sqrt(num)

    for serial in range(3, num, 2):

        if serial >= sqrt:
            return input_list

        for s in range(serial ** 2, num, serial): 
            input_list[s] = False

input_list = sieve_of_erastosthenes(10**6+1)
prime_list = [i for i, b in enumerate(input_list) if b == True]

def factorization(n):
    arr = []
    temp = n
    for i in prime_list:
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append(i)
    if temp!=1:
        arr.append(temp)
    if arr==[]:
        arr.append(n)
    return arr
random.shuffle(a)
g = a[0]
arr = factorization(a[0])
used = set()
for i in arr:
    if i == 1: continue
    used.add(i)

# not coprimeか判定
for i in range(n-1):
    g = gcd(g, a[i+1])
if g > 1:
    print('not coprime')
    exit(0)

# pairwise coprimeか判定
used = [0] * (10**6+1)
pair = True
for _a in a:
    if _a == 1:
        continue
    if used[_a]:
        print('setwise coprime')
        exit(0)
    else:
        used[_a] = True

for p in prime_list:
    v = p
    cnt = 0
    while v < 10**6+1:
        if used[v]:
            cnt+=1
        v += p
    if cnt > 1:
        print('setwise coprime')
        exit(0)
print('pairwise coprime')

Buggy python submission (verdict: Time Limit Exceeded):
import math
import sys
import random

def gcd(x, y):
    if y == 0:
        return x
    return gcd(y, x % y)

input = sys.stdin.readline
n = int(input())
a = list(map(int, input().split()))
used = [False] * (10**6+1)

def sieve_of_erastosthenes(num):
    input_list = [False if i % 2 == 0 or i % 3 == 0 or i % 5 == 0 else True for i in range(num)]
    input_list[0] = input_list[1] = False
    input_list[2] = input_list[3] = input_list[5] = True
    sqrt = math.sqrt(num)

    for serial in range(3, num, 2):

        if serial >= sqrt:
            return input_list

        for s in range(serial ** 2, num, serial): 
            input_list[s] = False

input_list = sieve_of_erastosthenes(int(-(-1000//1))+1)
prime_list = [i for i, b in enumerate(input_list) if b == True]

def factorization(n):
    arr = []
    temp = n
    for i in prime_list:
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append(i)
    if temp!=1:
        arr.append(temp)
    if arr==[]:
        arr.append(n)
    return arr
random.shuffle(a)
g = a[0]
arr = factorization(a[0])
for i in arr:
    used[i] = True

pair = True
for i in range(n-1):
    g = gcd(g, a[i+1])
    # 一度でも互いに素でない組合せが出たらpariwise coprimeではない
    if pair:
        arr = factorization(a[i+1])
        for i in arr:
            if i == 1: continue
            if used[i]: pair=False
            used[i] = True
if g > 1:
    print('not coprime')
    exit(0)
if not pair:
    print('setwise coprime')
    exit(0)
else:
    print('pairwise coprime')


Fixed submission:
import math
import sys
import random

def gcd(x, y):
    if y == 0:
        return x
    return gcd(y, x % y)

input = sys.stdin.readline
n = int(input())
a = list(map(int, input().split()))

def sieve_of_erastosthenes(num):
    input_list = [False if i % 2 == 0 or i % 3 == 0 or i % 5 == 0 else True for i in range(num)]
    input_list[0] = input_list[1] = False
    input_list[2] = input_list[3] = input_list[5] = True
    sqrt = math.sqrt(num)

    for serial in range(3, num, 2):

        if serial >= sqrt:
            return input_list

        for s in range(serial ** 2, num, serial): 
            input_list[s] = False

input_list = sieve_of_erastosthenes(10**6+1)
prime_list = [i for i, b in enumerate(input_list) if b == True]

def factorization(n):
    arr = []
    temp = n
    for i in prime_list:
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append(i)
    if temp!=1:
        arr.append(temp)
    if arr==[]:
        arr.append(n)
    return arr
random.shuffle(a)
g = a[0]
arr = factorization(a[0])
used = set()
for i in arr:
    if i == 1: continue
    used.add(i)

# not coprimeか判定
for i in range(n-1):
    g = gcd(g, a[i+1])
if g > 1:
    print('not coprime')
    exit(0)

# pairwise coprimeか判定
used = [0] * (10**6+1)
pair = True
for _a in a:
    if _a == 1:
        continue
    if used[_a]:
        print('setwise coprime')
        exit(0)
    else:
        used[_a] = True

for p in prime_list:
    v = p
    cnt = 0
    while v < 10**6+1:
        if used[v]:
            cnt+=1
        v += p
    if cnt > 1:
        print('setwise coprime')
        exit(0)
print('pairwise coprime')

Buggy python submission (verdict: Time Limit Exceeded):
import math
from math import gcd
import sys
input = sys.stdin.readline
n = int(input())
a = list(map(int, input().split()))
used = [False] * (10**6+1)

def sieve_of_erastosthenes(num):
    input_list = [False if i % 2 == 0 or i % 3 == 0 or i % 5 == 0 else True for i in range(num)]
    input_list[0] = input_list[1] = False
    input_list[2] = input_list[3] = input_list[5] = True
    sqrt = math.sqrt(num)

    for serial in range(3, num, 2):

        if serial >= sqrt:
            return input_list

        for s in range(serial ** 2, num, serial): 
            input_list[s] = False

input_list = sieve_of_erastosthenes(int(-(-10**3//1))+1)
prime_list = [i for i, b in enumerate(input_list) if b == True]

def factorization(n):
    arr = []
    temp = n
    for i in prime_list:
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append(i)
    if temp!=1:
        arr.append(temp)
    if arr==[]:
        arr.append(n)
    return arr

a.sort(reverse=True)
g = a[0]
arr = factorization(a[0])
for i in arr:
    used[i] = True

pair = True
for i in range(n-1):
    g = gcd(g, a[i+1])
    # 一度でも互いに素でない組合せが出たらpariwise coprimeではない
    if pair:
        arr = factorization(a[i+1])
        for i in arr:
            if i == 1: continue
            if used[i]: pair=False
            used[i] = True
if g > 1:
    print('not coprime')
    exit(0)
if not pair:
    print('setwise coprime')
    exit(0)
else:
    print('pairwise coprime')


Fixed submission:
import math
import sys
import random

def gcd(x, y):
    if y == 0:
        return x
    return gcd(y, x % y)

input = sys.stdin.readline
n = int(input())
a = list(map(int, input().split()))

def sieve_of_erastosthenes(num):
    input_list = [False if i % 2 == 0 or i % 3 == 0 or i % 5 == 0 else True for i in range(num)]
    input_list[0] = input_list[1] = False
    input_list[2] = input_list[3] = input_list[5] = True
    sqrt = math.sqrt(num)

    for serial in range(3, num, 2):

        if serial >= sqrt:
            return input_list

        for s in range(serial ** 2, num, serial): 
            input_list[s] = False

input_list = sieve_of_erastosthenes(10**6+1)
prime_list = [i for i, b in enumerate(input_list) if b == True]

def factorization(n):
    arr = []
    temp = n
    for i in prime_list:
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append(i)
    if temp!=1:
        arr.append(temp)
    if arr==[]:
        arr.append(n)
    return arr
random.shuffle(a)
g = a[0]
arr = factorization(a[0])
used = set()
for i in arr:
    if i == 1: continue
    used.add(i)

# not coprimeか判定
for i in range(n-1):
    g = gcd(g, a[i+1])
if g > 1:
    print('not coprime')
    exit(0)

# pairwise coprimeか判定
used = [0] * (10**6+1)
pair = True
for _a in a:
    if _a == 1:
        continue
    if used[_a]:
        print('setwise coprime')
        exit(0)
    else:
        used[_a] = True

for p in prime_list:
    v = p
    cnt = 0
    while v < 10**6+1:
        if used[v]:
            cnt+=1
        v += p
    if cnt > 1:
        print('setwise coprime')
        exit(0)
print('pairwise coprime')

Buggy python submission (verdict: Time Limit Exceeded):
import math
from math import gcd
n = int(input())
a = list(map(int, input().split()))
used = [False] * (10**6+1)

def sieve_of_erastosthenes(num):
    input_list = [False if i % 2 == 0 or i % 3 == 0 or i % 5 == 0 else True for i in range(num)]
    input_list[0] = input_list[1] = False
    input_list[2] = input_list[3] = input_list[5] = True
    sqrt = math.sqrt(num)

    for serial in range(3, num, 2):

        if serial >= sqrt:
            return input_list

        for s in range(serial ** 2, num, serial): 
            input_list[s] = False

input_list = sieve_of_erastosthenes(int(-(-10**3//1))+1)
prime_list = [i for i, b in enumerate(input_list) if b == True]

def factorization(n):
    arr = []
    temp = n
    for i in prime_list:
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append(i)
    if temp!=1:
        arr.append(temp)
    if arr==[]:
        arr.append(n)
    return arr

a.sort(reverse=True)
g = a[0]
arr = factorization(a[0])
for i in arr:
    used[i] = True

pair = True
for i in range(n-1):
    g = gcd(g, a[i+1])
    # 一度でも互いに素でない組合せが出たらpariwise coprimeではない
    if pair:
        arr = factorization(a[i+1])
        for i in arr:
            if i == 1: continue
            if used[i]: pair=False
            used[i] = True
if g > 1:
    print('not coprime')
    exit(0)
if not pair:
    print('setwise coprime')
    exit(0)
else:
    print('pairwise coprime')


Fixed submission:
import math
import sys
import random

def gcd(x, y):
    if y == 0:
        return x
    return gcd(y, x % y)

input = sys.stdin.readline
n = int(input())
a = list(map(int, input().split()))

def sieve_of_erastosthenes(num):
    input_list = [False if i % 2 == 0 or i % 3 == 0 or i % 5 == 0 else True for i in range(num)]
    input_list[0] = input_list[1] = False
    input_list[2] = input_list[3] = input_list[5] = True
    sqrt = math.sqrt(num)

    for serial in range(3, num, 2):

        if serial >= sqrt:
            return input_list

        for s in range(serial ** 2, num, serial): 
            input_list[s] = False

input_list = sieve_of_erastosthenes(10**6+1)
prime_list = [i for i, b in enumerate(input_list) if b == True]

def factorization(n):
    arr = []
    temp = n
    for i in prime_list:
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append(i)
    if temp!=1:
        arr.append(temp)
    if arr==[]:
        arr.append(n)
    return arr
random.shuffle(a)
g = a[0]
arr = factorization(a[0])
used = set()
for i in arr:
    if i == 1: continue
    used.add(i)

# not coprimeか判定
for i in range(n-1):
    g = gcd(g, a[i+1])
if g > 1:
    print('not coprime')
    exit(0)

# pairwise coprimeか判定
used = [0] * (10**6+1)
pair = True
for _a in a:
    if _a == 1:
        continue
    if used[_a]:
        print('setwise coprime')
        exit(0)
    else:
        used[_a] = True

for p in prime_list:
    v = p
    cnt = 0
    while v < 10**6+1:
        if used[v]:
            cnt+=1
        v += p
    if cnt > 1:
        print('setwise coprime')
        exit(0)
print('pairwise coprime')

Buggy python submission (verdict: Time Limit Exceeded):
import math
from math import gcd
import sys
input = sys.stdin.readline
n = int(input())
a = list(map(int, input().split()))
a.sort()
used = [0] * (10**6+1)

def sieve_of_erastosthenes(num):
    input_list = [False if i % 2 == 0 or i % 3 == 0 or i % 5 == 0 else True for i in range(num)]
    input_list[0] = input_list[1] = False
    input_list[2] = input_list[3] = input_list[5] = True
    sqrt = math.sqrt(num)

    for serial in range(3, num, 2):

        if serial >= sqrt:
            return input_list

        for s in range(serial ** 2, num, serial): 
            input_list[s] = False

input_list = sieve_of_erastosthenes(int(-(-10**3//1))+1)
prime_list = [i for i, b in enumerate(input_list) if b == True]

def factorization(n):
    arr = []
    temp = n
    for i in prime_list:
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append(i)
    if temp!=1:
        arr.append(temp)
    if arr==[]:
        arr.append(n)
    return arr

a.sort(reverse=True)
g = a[0]
arr = factorization(a[0])
for i in arr:
    used[i] += 1

pair = True
max_used = 0
for i in range(n-1):
    # 一度でも互いに素でない組合せが出たらpariwise coprimeではない
    arr = factorization(a[i+1])
    for i in arr:
        if i == 1: continue
        if used[i]: pair=False
        used[i] += 1
        max_used = max(max_used, used[i])
    
if max_used == n:
    print('not coprime')
    exit(0)
if not pair:
    print('setwise coprime')
    exit(0)
else:
    print('pairwise coprime')


Fixed submission:
import math
import sys
import random

def gcd(x, y):
    if y == 0:
        return x
    return gcd(y, x % y)

input = sys.stdin.readline
n = int(input())
a = list(map(int, input().split()))

def sieve_of_erastosthenes(num):
    input_list = [False if i % 2 == 0 or i % 3 == 0 or i % 5 == 0 else True for i in range(num)]
    input_list[0] = input_list[1] = False
    input_list[2] = input_list[3] = input_list[5] = True
    sqrt = math.sqrt(num)

    for serial in range(3, num, 2):

        if serial >= sqrt:
            return input_list

        for s in range(serial ** 2, num, serial): 
            input_list[s] = False

input_list = sieve_of_erastosthenes(10**6+1)
prime_list = [i for i, b in enumerate(input_list) if b == True]

def factorization(n):
    arr = []
    temp = n
    for i in prime_list:
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append(i)
    if temp!=1:
        arr.append(temp)
    if arr==[]:
        arr.append(n)
    return arr
random.shuffle(a)
g = a[0]
arr = factorization(a[0])
used = set()
for i in arr:
    if i == 1: continue
    used.add(i)

# not coprimeか判定
for i in range(n-1):
    g = gcd(g, a[i+1])
if g > 1:
    print('not coprime')
    exit(0)

# pairwise coprimeか判定
used = [0] * (10**6+1)
pair = True
for _a in a:
    if _a == 1:
        continue
    if used[_a]:
        print('setwise coprime')
        exit(0)
    else:
        used[_a] = True

for p in prime_list:
    v = p
    cnt = 0
    while v < 10**6+1:
        if used[v]:
            cnt+=1
        v += p
    if cnt > 1:
        print('setwise coprime')
        exit(0)
print('pairwise coprime')

Buggy python submission (verdict: Time Limit Exceeded):
import math
from math import gcd
import sys
input = sys.stdin.readline
n = int(input())
a = list(map(int, input().split()))
a.sort()
used = [False] * (10**6+1)

def sieve_of_erastosthenes(num):
    input_list = [False if i % 2 == 0 or i % 3 == 0 or i % 5 == 0 else True for i in range(num)]
    input_list[0] = input_list[1] = False
    input_list[2] = input_list[3] = input_list[5] = True
    sqrt = math.sqrt(num)

    for serial in range(3, num, 2):

        if serial >= sqrt:
            return input_list

        for s in range(serial ** 2, num, serial): 
            input_list[s] = False

input_list = sieve_of_erastosthenes(int(-(-10**3//1))+1)
prime_list = [i for i, b in enumerate(input_list) if b == True]

def factorization(n):
    arr = []
    temp = n
    for i in prime_list:
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append(i)
    if temp!=1:
        arr.append(temp)
    if arr==[]:
        arr.append(n)
    return arr

# a.sort(reverse=True)
g = a[0]
arr = factorization(a[0])
for i in arr:
    used[i] = True

pair = True
for i in range(n-1):
    g = gcd(g, a[i+1])
    # 一度でも互いに素でない組合せが出たらpariwise coprimeではない
    if pair:
        arr = factorization(a[i+1])
        for i in arr:
            if i == 1: continue
            if used[i]: pair=False
            used[i] = True
if g > 1:
    print('not coprime')
    exit(0)
if not pair:
    print('setwise coprime')
    exit(0)
else:
    print('pairwise coprime')


Fixed submission:
import math
import sys
import random

def gcd(x, y):
    if y == 0:
        return x
    return gcd(y, x % y)

input = sys.stdin.readline
n = int(input())
a = list(map(int, input().split()))

def sieve_of_erastosthenes(num):
    input_list = [False if i % 2 == 0 or i % 3 == 0 or i % 5 == 0 else True for i in range(num)]
    input_list[0] = input_list[1] = False
    input_list[2] = input_list[3] = input_list[5] = True
    sqrt = math.sqrt(num)

    for serial in range(3, num, 2):

        if serial >= sqrt:
            return input_list

        for s in range(serial ** 2, num, serial): 
            input_list[s] = False

input_list = sieve_of_erastosthenes(10**6+1)
prime_list = [i for i, b in enumerate(input_list) if b == True]

def factorization(n):
    arr = []
    temp = n
    for i in prime_list:
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append(i)
    if temp!=1:
        arr.append(temp)
    if arr==[]:
        arr.append(n)
    return arr
random.shuffle(a)
g = a[0]
arr = factorization(a[0])
used = set()
for i in arr:
    if i == 1: continue
    used.add(i)

# not coprimeか判定
for i in range(n-1):
    g = gcd(g, a[i+1])
if g > 1:
    print('not coprime')
    exit(0)

# pairwise coprimeか判定
used = [0] * (10**6+1)
pair = True
for _a in a:
    if _a == 1:
        continue
    if used[_a]:
        print('setwise coprime')
        exit(0)
    else:
        used[_a] = True

for p in prime_list:
    v = p
    cnt = 0
    while v < 10**6+1:
        if used[v]:
            cnt+=1
        v += p
    if cnt > 1:
        print('setwise coprime')
        exit(0)
print('pairwise coprime')

Buggy python submission (verdict: Time Limit Exceeded):
import math
from math import gcd
n = int(input())
a = list(map(int, input().split()))
a.sort()
used = [False] * (10**6+1)

def sieve_of_erastosthenes(num):
    input_list = [False if i % 2 == 0 or i % 3 == 0 or i % 5 == 0 else True for i in range(num)]
    input_list[0] = input_list[1] = False
    input_list[2] = input_list[3] = input_list[5] = True
    sqrt = math.sqrt(num)

    for serial in range(3, num, 2):

        if serial >= sqrt:
            return input_list

        for s in range(serial ** 2, num, serial): 
            input_list[s] = False

input_list = sieve_of_erastosthenes(int(-(-10**3//1))+1)
prime_list = [i for i, b in enumerate(input_list) if b == True]

def factorization(n):
    arr = []
    temp = n
    for i in prime_list:
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append(i)
    if temp!=1:
        arr.append(temp)
    if arr==[]:
        arr.append(n)
    return arr

a.sort(reverse=True)
g = a[0]
arr = factorization(a[0])
for i in arr:
    used[i] = True

pair = True
for i in range(n-1):
    g = gcd(g, a[i+1])
    # 一度でも互いに素でない組合せが出たらpariwise coprimeではない
    if pair:
        arr = factorization(a[i+1])
        for i in arr:
            if i == 1: continue
            if used[i]: pair=False
            used[i] = True
if g > 1:
    print('not coprime')
    exit(0)
if not pair:
    print('setwise coprime')
    exit(0)
else:
    print('pairwise coprime')


Fixed submission:
import math
import sys
import random

def gcd(x, y):
    if y == 0:
        return x
    return gcd(y, x % y)

input = sys.stdin.readline
n = int(input())
a = list(map(int, input().split()))

def sieve_of_erastosthenes(num):
    input_list = [False if i % 2 == 0 or i % 3 == 0 or i % 5 == 0 else True for i in range(num)]
    input_list[0] = input_list[1] = False
    input_list[2] = input_list[3] = input_list[5] = True
    sqrt = math.sqrt(num)

    for serial in range(3, num, 2):

        if serial >= sqrt:
            return input_list

        for s in range(serial ** 2, num, serial): 
            input_list[s] = False

input_list = sieve_of_erastosthenes(10**6+1)
prime_list = [i for i, b in enumerate(input_list) if b == True]

def factorization(n):
    arr = []
    temp = n
    for i in prime_list:
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append(i)
    if temp!=1:
        arr.append(temp)
    if arr==[]:
        arr.append(n)
    return arr
random.shuffle(a)
g = a[0]
arr = factorization(a[0])
used = set()
for i in arr:
    if i == 1: continue
    used.add(i)

# not coprimeか判定
for i in range(n-1):
    g = gcd(g, a[i+1])
if g > 1:
    print('not coprime')
    exit(0)

# pairwise coprimeか判定
used = [0] * (10**6+1)
pair = True
for _a in a:
    if _a == 1:
        continue
    if used[_a]:
        print('setwise coprime')
        exit(0)
    else:
        used[_a] = True

for p in prime_list:
    v = p
    cnt = 0
    while v < 10**6+1:
        if used[v]:
            cnt+=1
        v += p
    if cnt > 1:
        print('setwise coprime')
        exit(0)
print('pairwise coprime')

Buggy python submission (verdict: Time Limit Exceeded):
import math
from math import gcd
n = int(input())
a = list(map(int, input().split()))
a.sort()
used = [False] * (10**6+1)

def sieve_of_erastosthenes(num):
    input_list = [False if i % 2 == 0 or i % 3 == 0 or i % 5 == 0 else True for i in range(num)]
    input_list[0] = input_list[1] = False
    input_list[2] = input_list[3] = input_list[5] = True
    sqrt = math.sqrt(num)

    for serial in range(3, num, 2):

        if serial >= sqrt:
            return input_list

        for s in range(serial ** 2, num, serial): 
            input_list[s] = False

input_list = sieve_of_erastosthenes(int(-(-10**3//1))+1)
prime_list = [i for i, b in enumerate(input_list) if b == True]

def factorization(n):
    arr = []
    temp = n
    for i in prime_list:
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append(i)
    if temp!=1:
        arr.append(temp)
    if arr==[]:
        arr.append(n)
    return arr

a.sort(reverse=True)
g = a[0]
arr = factorization(a[0])
for i in arr:
    used[i] = True

pair = True
for i in range(n-1):
    g = gcd(g, a[i+1])
    # 一度でも互いに素でない組合せが出たらpariwise coprimeではない
    if pair:
        arr = factorization(a[i+1])
        for i in arr:
            if i == 1: continue
            if used[i]: pair=False
            used[i] = True
if g > 1:
    print('not coprime')
    exit(0)
if not pair:
    print('setwise coprime')
    exit(0)
else:
    print('pairwise coprime')


Fixed submission:
import math
import sys
import random

def gcd(x, y):
    if y == 0:
        return x
    return gcd(y, x % y)

input = sys.stdin.readline
n = int(input())
a = list(map(int, input().split()))

def sieve_of_erastosthenes(num):
    input_list = [False if i % 2 == 0 or i % 3 == 0 or i % 5 == 0 else True for i in range(num)]
    input_list[0] = input_list[1] = False
    input_list[2] = input_list[3] = input_list[5] = True
    sqrt = math.sqrt(num)

    for serial in range(3, num, 2):

        if serial >= sqrt:
            return input_list

        for s in range(serial ** 2, num, serial): 
            input_list[s] = False

input_list = sieve_of_erastosthenes(10**6+1)
prime_list = [i for i, b in enumerate(input_list) if b == True]

def factorization(n):
    arr = []
    temp = n
    for i in prime_list:
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append(i)
    if temp!=1:
        arr.append(temp)
    if arr==[]:
        arr.append(n)
    return arr
random.shuffle(a)
g = a[0]
arr = factorization(a[0])
used = set()
for i in arr:
    if i == 1: continue
    used.add(i)

# not coprimeか判定
for i in range(n-1):
    g = gcd(g, a[i+1])
if g > 1:
    print('not coprime')
    exit(0)

# pairwise coprimeか判定
used = [0] * (10**6+1)
pair = True
for _a in a:
    if _a == 1:
        continue
    if used[_a]:
        print('setwise coprime')
        exit(0)
    else:
        used[_a] = True

for p in prime_list:
    v = p
    cnt = 0
    while v < 10**6+1:
        if used[v]:
            cnt+=1
        v += p
    if cnt > 1:
        print('setwise coprime')
        exit(0)
print('pairwise coprime')

Buggy python submission (verdict: Time Limit Exceeded):
import math
from math import gcd
n = int(input())
a = list(map(int, input().split()))
a.sort()
used = [False] * (10**6+1)

def sieve_of_erastosthenes(num):
    input_list = [False if i % 2 == 0 or i % 3 == 0 or i % 5 == 0 else True for i in range(num)]
    input_list[0] = input_list[1] = False
    input_list[2] = input_list[3] = input_list[5] = True
    sqrt = math.sqrt(num)

    for serial in range(3, num, 2):

        if serial >= sqrt:
            return input_list

        for s in range(serial ** 2, num, serial): 
            input_list[s] = False

input_list = sieve_of_erastosthenes(int(-(-10**3//1))+1)
prime_list = [i for i, b in enumerate(input_list) if b == True]

def factorization(n):
    arr = []
    temp = n
    for i in prime_list:
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append(i)
    if temp!=1:
        arr.append(temp)
    if arr==[]:
        arr.append(n)
    return arr

g = a[0]
arr = factorization(a[0])
for i in arr:
    used[i] = True

pair = True
for i in range(n-1):
    g = gcd(g, a[i+1])
    # 一度でも互いに素でない組合せが出たらpariwise coprimeではない
    if pair:
        arr = factorization(a[i+1])
        for i in arr:
            if i == 1: continue
            if used[i]: pair=False
            used[i] = True
if g > 1:
    print('not coprime')
    exit(0)
if not pair:
    print('setwise coprime')
    exit(0)
else:
    print('pairwise coprime')


Fixed submission:
import math
import sys
import random

def gcd(x, y):
    if y == 0:
        return x
    return gcd(y, x % y)

input = sys.stdin.readline
n = int(input())
a = list(map(int, input().split()))

def sieve_of_erastosthenes(num):
    input_list = [False if i % 2 == 0 or i % 3 == 0 or i % 5 == 0 else True for i in range(num)]
    input_list[0] = input_list[1] = False
    input_list[2] = input_list[3] = input_list[5] = True
    sqrt = math.sqrt(num)

    for serial in range(3, num, 2):

        if serial >= sqrt:
            return input_list

        for s in range(serial ** 2, num, serial): 
            input_list[s] = False

input_list = sieve_of_erastosthenes(10**6+1)
prime_list = [i for i, b in enumerate(input_list) if b == True]

def factorization(n):
    arr = []
    temp = n
    for i in prime_list:
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append(i)
    if temp!=1:
        arr.append(temp)
    if arr==[]:
        arr.append(n)
    return arr
random.shuffle(a)
g = a[0]
arr = factorization(a[0])
used = set()
for i in arr:
    if i == 1: continue
    used.add(i)

# not coprimeか判定
for i in range(n-1):
    g = gcd(g, a[i+1])
if g > 1:
    print('not coprime')
    exit(0)

# pairwise coprimeか判定
used = [0] * (10**6+1)
pair = True
for _a in a:
    if _a == 1:
        continue
    if used[_a]:
        print('setwise coprime')
        exit(0)
    else:
        used[_a] = True

for p in prime_list:
    v = p
    cnt = 0
    while v < 10**6+1:
        if used[v]:
            cnt+=1
        v += p
    if cnt > 1:
        print('setwise coprime')
        exit(0)
print('pairwise coprime')

Buggy python submission (verdict: Time Limit Exceeded):
import math
from math import gcd
n = int(input())
a = list(map(int, input().split()))
a.sort()
used = [False] * (10**6+1)

def sieve_of_erastosthenes(num):
    input_list = [False if i % 2 == 0 or i % 3 == 0 or i % 5 == 0 else True for i in range(num)]
    input_list[0] = input_list[1] = False
    input_list[2] = input_list[3] = input_list[5] = True
    sqrt = math.sqrt(num)

    for serial in range(3, num, 2):

        if serial >= sqrt:
            return input_list

        for s in range(serial ** 2, num, serial): 
            input_list[s] = False

input_list = sieve_of_erastosthenes(int(-(-10**3//1))+1)
prime_list = [i for i, b in enumerate(input_list) if b == True]

def factorization(n):
    arr = []
    temp = n
    for i in prime_list:
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append(i)
    if temp!=1:
        arr.append(temp)
    if arr==[]:
        arr.append(n)
    return arr

g = a[0]
arr = factorization(a[0])
for i in arr:
    used[i] = True

pair = True
for i in range(n-1):
    g = gcd(g, a[i+1])
    # 一度でも互いに素でない組合せが出たらpariwise coprimeではない
    arr = factorization(a[i+1])
    for i in arr:
        if i == 1: continue
        if used[i]: pair=False
        used[i] = True
if g > 1:
    print('not coprime')
    exit(0)
if not pair:
    print('setwise coprime')
    exit(0)
else:
    print('pairwise coprime')


Fixed submission:
import math
import sys
import random

def gcd(x, y):
    if y == 0:
        return x
    return gcd(y, x % y)

input = sys.stdin.readline
n = int(input())
a = list(map(int, input().split()))

def sieve_of_erastosthenes(num):
    input_list = [False if i % 2 == 0 or i % 3 == 0 or i % 5 == 0 else True for i in range(num)]
    input_list[0] = input_list[1] = False
    input_list[2] = input_list[3] = input_list[5] = True
    sqrt = math.sqrt(num)

    for serial in range(3, num, 2):

        if serial >= sqrt:
            return input_list

        for s in range(serial ** 2, num, serial): 
            input_list[s] = False

input_list = sieve_of_erastosthenes(10**6+1)
prime_list = [i for i, b in enumerate(input_list) if b == True]

def factorization(n):
    arr = []
    temp = n
    for i in prime_list:
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append(i)
    if temp!=1:
        arr.append(temp)
    if arr==[]:
        arr.append(n)
    return arr
random.shuffle(a)
g = a[0]
arr = factorization(a[0])
used = set()
for i in arr:
    if i == 1: continue
    used.add(i)

# not coprimeか判定
for i in range(n-1):
    g = gcd(g, a[i+1])
if g > 1:
    print('not coprime')
    exit(0)

# pairwise coprimeか判定
used = [0] * (10**6+1)
pair = True
for _a in a:
    if _a == 1:
        continue
    if used[_a]:
        print('setwise coprime')
        exit(0)
    else:
        used[_a] = True

for p in prime_list:
    v = p
    cnt = 0
    while v < 10**6+1:
        if used[v]:
            cnt+=1
        v += p
    if cnt > 1:
        print('setwise coprime')
        exit(0)
print('pairwise coprime')

Buggy python submission (verdict: Time Limit Exceeded):
import math
from math import gcd
n = int(input())
a = list(map(int, input().split()))
a.sort()
used = [False] * (10**6+1)

def sieve_of_erastosthenes(num):
    input_list = [False if i % 2 == 0 or i % 3 == 0 or i % 5 == 0 else True for i in range(num)]
    input_list[0] = input_list[1] = False
    input_list[2] = input_list[3] = input_list[5] = True
    sqrt = math.sqrt(num)

    for serial in range(3, num, 2):

        if serial >= sqrt:
            return input_list

        for s in range(serial ** 2, num, serial): 
            input_list[s] = False

input_list = sieve_of_erastosthenes(10**6+1)
prime_list = [i for i, b in enumerate(input_list) if b == True]

def factorization(n):
    arr = []
    temp = n
    for i in prime_list:
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append(i)
    if temp!=1:
        arr.append(temp)
    if arr==[]:
        arr.append(n)
    return arr

g = a[0]
arr = factorization(a[0])
for i in arr:
    used[i] = True

pair = True
for i in range(n-1):
    g = gcd(g, a[i+1])
    # 一度でも互いに素でない組合せが出たらpariwise coprimeではない
    arr = factorization(a[i+1])
    for i in arr:
        if i == 1: continue
        if used[i]: pair=False
        used[i] = True
if g > 1:
    print('not coprime')
    exit(0)
if not pair:
    print('setwise coprime')
    exit(0)
else:
    print('pairwise coprime')


Fixed submission:
import math
import sys
import random

def gcd(x, y):
    if y == 0:
        return x
    return gcd(y, x % y)

input = sys.stdin.readline
n = int(input())
a = list(map(int, input().split()))

def sieve_of_erastosthenes(num):
    input_list = [False if i % 2 == 0 or i % 3 == 0 or i % 5 == 0 else True for i in range(num)]
    input_list[0] = input_list[1] = False
    input_list[2] = input_list[3] = input_list[5] = True
    sqrt = math.sqrt(num)

    for serial in range(3, num, 2):

        if serial >= sqrt:
            return input_list

        for s in range(serial ** 2, num, serial): 
            input_list[s] = False

input_list = sieve_of_erastosthenes(10**6+1)
prime_list = [i for i, b in enumerate(input_list) if b == True]

def factorization(n):
    arr = []
    temp = n
    for i in prime_list:
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append(i)
    if temp!=1:
        arr.append(temp)
    if arr==[]:
        arr.append(n)
    return arr
random.shuffle(a)
g = a[0]
arr = factorization(a[0])
used = set()
for i in arr:
    if i == 1: continue
    used.add(i)

# not coprimeか判定
for i in range(n-1):
    g = gcd(g, a[i+1])
if g > 1:
    print('not coprime')
    exit(0)

# pairwise coprimeか判定
used = [0] * (10**6+1)
pair = True
for _a in a:
    if _a == 1:
        continue
    if used[_a]:
        print('setwise coprime')
        exit(0)
    else:
        used[_a] = True

for p in prime_list:
    v = p
    cnt = 0
    while v < 10**6+1:
        if used[v]:
            cnt+=1
        v += p
    if cnt > 1:
        print('setwise coprime')
        exit(0)
print('pairwise coprime')

Buggy python submission (verdict: Time Limit Exceeded):
from math import gcd
n = int(input())
a = list(map(int, input().split()))
a.sort()
used = [False] * (10**6+1)

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)
    if arr==[]:
        arr.append(n)
    return arr

g = a[0]
arr = factorization(a[0])
for i in arr:
    used[i] = True

pair = True
for i in range(n-1):
    g = gcd(g, a[i+1])
    # 一度でも互いに素でない組合せが出たらpariwise coprimeではない
    arr = factorization(a[i+1])
    for i in arr:
        if i == 1: continue
        if used[i]: pair=False
        used[i] = True
if g > 1:
    print('not coprime')
    exit(0)
if not pair:
    print('setwise coprime')
    exit(0)
else:
    print('pairwise coprime')


Fixed submission:
import math
import sys
import random

def gcd(x, y):
    if y == 0:
        return x
    return gcd(y, x % y)

input = sys.stdin.readline
n = int(input())
a = list(map(int, input().split()))

def sieve_of_erastosthenes(num):
    input_list = [False if i % 2 == 0 or i % 3 == 0 or i % 5 == 0 else True for i in range(num)]
    input_list[0] = input_list[1] = False
    input_list[2] = input_list[3] = input_list[5] = True
    sqrt = math.sqrt(num)

    for serial in range(3, num, 2):

        if serial >= sqrt:
            return input_list

        for s in range(serial ** 2, num, serial): 
            input_list[s] = False

input_list = sieve_of_erastosthenes(10**6+1)
prime_list = [i for i, b in enumerate(input_list) if b == True]

def factorization(n):
    arr = []
    temp = n
    for i in prime_list:
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append(i)
    if temp!=1:
        arr.append(temp)
    if arr==[]:
        arr.append(n)
    return arr
random.shuffle(a)
g = a[0]
arr = factorization(a[0])
used = set()
for i in arr:
    if i == 1: continue
    used.add(i)

# not coprimeか判定
for i in range(n-1):
    g = gcd(g, a[i+1])
if g > 1:
    print('not coprime')
    exit(0)

# pairwise coprimeか判定
used = [0] * (10**6+1)
pair = True
for _a in a:
    if _a == 1:
        continue
    if used[_a]:
        print('setwise coprime')
        exit(0)
    else:
        used[_a] = True

for p in prime_list:
    v = p
    cnt = 0
    while v < 10**6+1:
        if used[v]:
            cnt+=1
        v += p
    if cnt > 1:
        print('setwise coprime')
        exit(0)
print('pairwise coprime')