Problem:


Score : 500 points

Problem Statement

We have N integers. The i-th number is A_i.

\{A_i\} is said to be pairwise coprime when GCD(A_i,A_j)=1 holds for every pair (i, j) such that 1\leq i < j \leq N.

\{A_i\} is said to be setwise coprime when \{A_i\} is not pairwise coprime but GCD(A_1,\ldots,A_N)=1.

Determine if \{A_i\} is pairwise coprime, setwise coprime, or neither.

Here, GCD(\ldots) denotes greatest common divisor.

Constraints

2 \leq N \leq 10^6

1 \leq A_i\leq 10^6

Input

Input is given from Standard Input in the following format:

N
A_1 \ldots A_N

Output

If \{A_i\} is pairwise coprime, print pairwise coprime; if \{A_i\} is setwise coprime, print setwise coprime; if neither, print not coprime.

Sample Input 1

3
3 4 5

Sample Output 1

pairwise coprime

GCD(3,4)=GCD(3,5)=GCD(4,5)=1, so they are pairwise coprime.

Sample Input 2

3
6 10 15

Sample Output 2

setwise coprime

Since GCD(6,10)=2, they are not pairwise coprime. However, since GCD(6,10,15)=1, they are setwise coprime.

Sample Input 3

3
6 10 16

Sample Output 3

not coprime

GCD(6,10,16)=2, so they are neither pairwise coprime nor setwise coprime.



Sample input:
3
3 4 5


Sample output:
pairwise coprime

Submission status: Wrong Answer

Solution code:
from collections import defaultdict
import math

INF = 10 ** 6 + 1
is_prime = [1] * INF

def eratorasu():
    is_prime[0] = 0
    is_prime[1] = 0
    for i in range(2, INF):
        if is_prime[i] == 0:
            continue
        for j in range(i * 2, INF, i):
            is_prime[j] = 0
    return

def f(n):
    yakusu = []
    if is_prime[n]:
        yakusu.append(n)
    else:
        for i in range(2, int(n ** 0.5) + 1):
            if n % i == 0:
                yakusu.append(i)
                break

    for i in yakusu:
        if i != 1:
            d[i] += 1

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

tmp = A[0]
for i in range(1, N):
    tmp = math.gcd(tmp, A[i])
    f(A[i])

if tmp != 1:
    print('not coprime')
    exit()
eratorasu()
f(A[0])

for i, v in d.items():
    if v != 1:
        print('setwise coprime')
        exit()

print('setwise coprime')

Submission status: Wrong Answer

Solution code:
from collections import defaultdict
import math

INF = 10 ** 6 + 1
is_prime = [1] * INF

def eratorasu():
    is_prime[0] = 0
    is_prime[1] = 0
    for i in range(2, INF):
        if is_prime[i] == 0:
            continue
        for j in range(i * 2, INF, i):
            is_prime[j] = 0
    return

def f(n):
    yakusu = []
    if is_prime[n]:
        yakusu.append(n)
    else:
        for i in range(2, int(n ** 0.5) + 1):
            if n % i == 0:
                yakusu.append(i)
                break

    for i in yakusu:
        if i != 1:
            d[i] += 1

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

tmp = A[0]
for i in range(1, N):
    tmp = math.gcd(tmp, A[i])
    f(A[i])

if tmp != 1:
    print('not coprime')
    exit()
eratorasu()
f(A[0])

for i, v in d.items():
    if v != 1:
        print('setwise coprime')
        exit()

print('pairwise coprime')

Submission status: Wrong Answer

Solution code:
n=int(input())
a=[int(x) for x in input().split()]

def gcd(a,b):#最大公約数
  while b!=0:
    a,b=b,a%b
  return a

ans=0
now=a[0]
flag_1=0
flag_2=0
flag_all=0
for i in range(1,n):
  now=gcd(now,a[i])
  if now==1:
    flag_1+=1
  else:
    flag_2+=1
  


# print(now)
# print(flag_1,flag_2)
if flag_1!=0 and flag_2==0 and now==1:
  print("pairwise coprime")
elif now==1 and flag_2!=0 and flag_1==1:
  print("setwise coprime")
else:
  print("not coprime")

Submission status: Wrong Answer

Solution code:
import math
 
N = 1000001
 
spf = [*range(N)]
i = 2
while i * i < N:
  if spf[i] == i:
    for j in range(i * i, N, i):
      if spf[j] == j:
        spf[j] = i
  i += 1
  
r = 'pairwise'
 
input()
d = None
u = set()
for x in map(int, input().split()):
  d = math.gcd(d or x, x);
  s = set()
  while x > 1:
    p = spf[x]
    if p in u:
      r = 'setwise'
    s.add(p)
    x //= p
  u |= s
print(d > 1 and r or 'not', 'coprime')

Submission status: Wrong Answer

Solution code:
from collections import defaultdict

def f(n):
    yakusu = []
    tmp = (n ** 0.5) + 1
    for i in range(2, n):
        if tmp <= i:
            yakusu.append(n)
            break
        if n % i == 0:
            yakusu.append(i)
            break
    for i in yakusu:
        if i != 1:
            d[i] += 1

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

for i in range(N):
    f(A[i])

cnt = 1
for i, v in d.items():
    if v != 1:
        cnt = max(cnt, v)

if cnt == N:
    print('not coprime')
elif cnt == 1:
    print('pairwise coprime')
else:
    print('setwise coprime')

Submission status: Wrong Answer

Solution code:
from collections import defaultdict

INF = 10 ** 6 + 1
is_prime = [1] * INF

def eratorasu():
    is_prime[0] = 0
    is_prime[1] = 0
    for i in range(2, INF):
        if is_prime[i] == 0:
            continue
        for j in range(i * 2, INF, i):
            is_prime[j] = 0
    return

def f(n):
    yakusu = []
    for i in range(2, n):
        if n % i == 0 and is_prime[i]:
            yakusu.append(i)
            break
    for i in yakusu:
        if i != 1:
            d[i] += 1

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

for i in range(N):
    f(A[i])

cnt = 1
for i, v in d.items():
    if v != 1:
        cnt = max(cnt, v)

if cnt == N:
    print('not coprime')
elif cnt == 1:
    print('pairwise coprime')
else:
    print('setwise coprime')

Submission status: Wrong Answer

Solution code:
from collections import defaultdict
import math

def f(n):
    yakusu = []
    for i in range(2, int(n ** 0.5) + 1):
        if n % i == 0:
            yakusu.append(i)
            if i != n // i:
                yakusu.append(n // i)
    for i in yakusu:
        if i != 1:
            d[i] += 1

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

tmp = A[0]
for i in range(1, N):
    tmp = math.gcd(tmp, A[i])
if tmp != 1:
    print('not coprime')
    exit()

for i in A:
    f(i)

for i, v in d.items():
    if v != 1:
        print('setwise coprime')
        exit()

print('pairwise coprime')

Submission status: Wrong Answer

Solution code:
from collections import defaultdict
def f(n):
    yakusu = []
    for i in range(1, int(n ** 0.5) + 1):
        if n % i == 0:
            yakusu.append(i)
            break
    for i in yakusu:
        if i != 1:
            d[i] += 1

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

for i in range(N):
    f(A[i])

cnt = 1
for i, v in d.items():
    if v != 1:
        cnt = max(cnt, v)

if cnt == N:
    print('not coprime')
elif cnt == 1:
    print('pairwise coprime')
else:
    print('setwise coprime')

Submission status: Wrong Answer

Solution code:
from collections import defaultdict

INF = 10 ** 6 + 1
is_prime = [1] * INF

def eratorasu():
    is_prime[0] = 0
    is_prime[1] = 0
    for i in range(2, INF):
        if is_prime[i] == 0:
            continue
        for j in range(i * 2, INF, i):
            is_prime[j] = 0
    return

def f(n):
    yakusu = []
    for i in range(1, int(n ** 0.5) + 1):
        if n % i == 0 and is_prime[i]:
            yakusu.append(i)
            break
    for i in yakusu:
        if i != 1:
            d[i] += 1

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

for i in range(N):
    f(A[i])

cnt = 1
for i, v in d.items():
    if v != 1:
        cnt = max(cnt, v)

if cnt == N:
    print('not coprime')
elif cnt == 1:
    print('pairwise coprime')
else:
    print('setwise coprime')

Submission status: Wrong Answer

Solution code:
import math


def get_pseudo_input():
    N = 3
    A = [6, 10, 16]
    return N, A


def get_input():
    N = int(input())
    A = [int(x) for x in input().split()]
    return N, A


def sieve_of_eratosthenes(x: int):
    ret = [-1] * (x + 1)
    for i in range(1, x + 1):
        ret[i] = i
    p_max = int(math.sqrt(x))
    for p in range(2, p_max + 1):
        if ret[p] < p:  # p is not a prime number
            continue
        for i in range(p, x + 1, p):
            if ret[i] > p:
                ret[i] = p
    return ret


A_max = 10 ** 6
p_table = sieve_of_eratosthenes(A_max)

N, A = get_input()
# Store a number of unique Ais using the prime number
p_nums = [0] * (A_max + 1)
max_p_nums = 0
for a in A:
    # print(f"a={a}")
    while a > 1:
        p = p_table[a]
        while a % p == 0:
            a = int(a / p)
        # print(f"  a={a}")
        p_nums[p] += 1
        if max_p_nums < p_nums[p]:
            max_p_nums = p_nums[p]
# print(max_p_nums)
if max_p_nums == 1:
    print('pairwise coprime')
elif max_p_nums < N:
    print('setwise coprime')
else:
    print('not coprime')

Submission status: Wrong Answer

Solution code:
n=int(input())
a=[int(x) for x in input().split()]

def gcd(a,b):#最大公約数
  while b!=0:
    a,b=b,a%b
  return a

ans=0
now=a[0]
flag_1=0
flag_2=0
flag_all=0
for i in range(1,n):
  now=gcd(now,a[i])
  if now==1:
    flag_1+=1
  else:
    flag_2+=1
  
  if now==1 and i==n-1:
    flag_all=1


if flag_1!=0 and flag_2==0:
  print("pairwise coprime")
elif flag_all==1 and flag_1==1:
  print("setwise coprime")
else:
  print("not coprime")

Submission status: Wrong Answer

Solution code:
from collections import defaultdict

INF = 10 ** 6 + 1
is_prime = [1] * INF

def eratorasu():
    is_prime[0] = 0
    is_prime[1] = 0
    for i in range(2, INF):
        if is_prime[i] == 0:
            continue
        for j in range(i * 2, INF, i):
            is_prime[j] = 0
    return

def f(n):
    yakusu = []
    for i in range(2, int(n ** 0.5) + 1):
        if n % i == 0 and is_prime[i]:
            yakusu.append(i)
            break
    for i in yakusu:
        if i != 1:
            d[i] += 1

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

for i in range(N):
    f(A[i])

cnt = 1
for i, v in d.items():
    if v != 1:
        cnt = max(cnt, v)

if cnt == N:
    print('not coprime')
elif cnt == 1:
    print('pairwise coprime')
else:
    print('setwise coprime')

Submission status: Wrong Answer

Solution code:
from collections import defaultdict

INF = 10 ** 6 + 1
is_prime = [1] * INF

def eratorasu():
    is_prime[0] = 0
    is_prime[1] = 0
    for i in range(2, INF):
        if is_prime[i] == 0:
            continue
        for j in range(i * 2, INF, i):
            is_prime[j] = 0
    return

def f(n):
    yakusu = []
    for i in range(2, int(n ** 0.5) + 1):
        if n % i == 0 and is_prime[i]:
            yakusu.append(i)
            break
    for i in yakusu:
        if i != 1:
            d[i] += 1

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

for i in range(N):
    f(A[i])
if is_prime:
    print(is_prime[2])
cnt = 1
for i, v in d.items():
    if v != 1:
        cnt = max(cnt, v)

if cnt == N:
    print('not coprime')
elif cnt == 1:
    print('pairwise coprime')
else:
    print('setwise coprime')

Submission status: Wrong Answer

Solution code:
from math import gcd
N = int(input())
A = list(map(int,input().split()))

g = 0
for a in A:
    g = gcd(g,a)
if g > 1:
    print('not coprime')
    exit()

MAXA = 10**6
B = [0] * (MAXA+1)
for a in A:
    if B[a]:
        print('setwise coprime')
        exit()
    B[a] = 1

for n in range(2,MAXA+1):
    c = 0
    for m in range(n,MAXA+1,n):
        c += B[m]
        if c > 1:
            print('setwise coprime')
            exit()

print('pairwise coprime')

Submission status: Wrong Answer

Solution code:
import math


def get_pseudo_input():
    N = 3
    A = [6, 10, 16]
    return N, A


def get_input():
    N = int(input())
    A = [int(x) for x in input().split()]
    return N, A


def sieve_of_eratosthenes(x: int):
    ret = [-1] * (x + 1)
    for i in range(1, x + 1):
        ret[i] = i
    p_max = int(math.sqrt(x))
    for p in range(2, p_max + 1):
        if ret[p] < p:  # p is not a prime number
            continue
        for i in range(p, x + 1, p):
            if ret[i] > p:
                ret[i] = p
    return ret


A_max = 1000000
p_table = sieve_of_eratosthenes(A_max)

N, A = get_input()
# Store a number of unique Ais using the prime number
p_nums = [0] * (A_max + 1)
max_p_nums = 0
for a in A:
    # print(f"a={a}")
    while a > 1:
        p = p_table[a]
        while a % p == 0:
            a = int(a / p)
        # print(f"  a={a}")
        p_nums[p] += 1
        if max_p_nums < p_nums[p]:
            max_p_nums = p_nums[p]
# print(max_p_nums)
if max_p_nums == 1:
    print('pairwise coprime')
elif max_p_nums < N:
    print('setwise coprime')
else:
    print('not coprime')

Submission status: Wrong Answer

Solution code:
from collections import defaultdict


def f(n):
    yakusu = []
    for i in range(2, int(n ** 0.5) + 1):
        if n % i == 0:
            yakusu.append(i)
            break
    for i in yakusu:
        if i != 1:
            d[i] += 1


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

for i in range(N):
    f(A[i])

cnt = 1
for i, v in d.items():
    if v != 1:
        cnt = max(cnt, v)

if cnt == N:
    print('not coprime')
elif cnt == 1:
    print('pairwise coprime')
else:
    print('setwise coprime')

Submission status: Wrong Answer

Solution code:
import math

n = int(input())
a_array = list(map(int, input().split()))

def get_primenumber(number):#エラトステネスの篩
    prime_list = []
    search_list = list(range(2,number+1))
    #search_listの先頭の値が√nの値を超えたら終了
    while search_list[0] <= math.sqrt(number):
      #search_listの先頭の値が√nの値を超えたら終了
      #search_listの先頭をprime_listに入れて、先頭をリストに追加して削除
        head_num = search_list.pop(0)
        prime_list.append(head_num)
        #head_numの倍数を除去
        search_list = [num for num in search_list if num % head_num != 0]
    #prime_listにsearch_listを結合
    prime_list.extend(search_list)
    return prime_list


def factrization_prime(number, prime_list):
    factor = {}
    i = 0
    div = prime_list[i]
    s = math.sqrt(number)
    while div <= s:
        div_cnt = 0
        while number % div == 0:
            div_cnt += 1
            number //= div
        if div_cnt != 0:
            factor[div] = div_cnt
            ans_array[div] += 1
        i += 1
        div = prime_list[i]
    if number > 1:
        factor[number] = 1
        ans_array[number] += 1
    return factor


thre = pow(10, 6) + 1
ans_array = [0] * thre

prime_list = get_primenumber(thre)
for a in a_array:
    factrization_prime(a, prime_list)

max_ans_array = max(ans_array)
if max_ans_array == 1:
    print('pairwise coprime')
elif max_ans_array < n:
    print('setwise coprime')
else:
    print('not coprime')

Submission status: Wrong Answer

Solution code:
import sys

def enum_div(n):
    ir=int(n**(0.5))+1
    ret=[]
    for i in range(1,ir):
        if n%i == 0:
            ret.append(i)
            if (i!= 1) & (i*i != n):
                ret.append(n//i)
    return ret

p=[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 
   31, 37, 41, 43, 47, 53, 59, 61, 67, 71,
   73, 79, 83, 89, 97, 101, 103, 107, 109, 113,
   127, 131, 137, 139, 149, 151, 157, 163, 167,
   173, 179, 181, 191, 193, 197, 199, 211, 223,
   227, 229, 233, 239, 241, 251, 257, 263, 269,
   271, 277, 281, 283, 293, 307, 311, 313, 317,
   331, 337, 347, 349, 353, 359, 367, 373, 379,
   383, 389, 397, 401, 409, 419, 421, 431, 433, 
   439, 443, 449, 457, 461, 463, 467, 479, 487,
   491, 499, 503, 509, 521, 523, 541, 547, 557,
   563, 569, 571, 577, 587, 593, 599, 601, 607,
   613, 617, 619, 631, 641, 643, 647, 653, 659,
   661, 673, 677, 683, 691, 701, 709, 719, 727,
   733, 739, 743, 751, 757, 761, 769, 773, 787,
   797, 809, 811, 821, 823, 827, 829, 839, 853,
   857, 859, 863, 877, 881, 883, 887, 907, 911,
   919, 929, 937, 941, 947, 953, 967, 971, 977,
   983, 991, 997,1009]

n=int(input())
ap=list(map(int,input().split()))
amin=min(ap)

if amin!=1:
    bp=enum_div(amin)+[amin]
    bp=set(bp[1:])
    bp=list(bp&set(p))
    for bpi in bp:
#        if not bpi in p:
#            continue
        lap=0
        for ai in ap:
            if ai%bpi==0:
                lap+=1
#        lap=len([ai for ai in ap if ai%bpi==0])
        if lap==n:
            print("not coprime")
            sys.exit()

ptype="pairwise coprime"
for pp in p:
    lap=0
    for ai in ap:
        if  ai%pp==0:
            lap+=1
        if lap>=2:
            ptype="setwise coprime"
            print(ptype)    
            sys.exit()
#    lap=len([ai for ai in ap if ai%pp==0])
#    print("pp:",pp,lap)
#    if lap==n:
#        ptype="not coprime"
#        print("not coprime")
#        break
#    if lap>=2:
#        if ptype!="not coprime":
#        ptype="setwise coprime"

print(ptype)

Submission status: Wrong Answer

Solution code:
import math

n = int(input())
a_array = list(map(int, input().split()))

def get_primenumber(number):#エラトステネスの篩
    prime_list = []
    search_list = list(range(2,number+1))
    #search_listの先頭の値が√nの値を超えたら終了
    while search_list[0] <= math.sqrt(number):
      #search_listの先頭の値が√nの値を超えたら終了
      #search_listの先頭をprime_listに入れて、先頭をリストに追加して削除
        head_num = search_list.pop(0)
        prime_list.append(head_num)
        #head_numの倍数を除去
        search_list = [num for num in search_list if num % head_num != 0]
    #prime_listにsearch_listを結合
    prime_list.extend(search_list)
    return prime_list


def factrization_prime(number, prime_list):
    factor = {}
    i = 0
    div = prime_list[i]
    s = math.sqrt(number)
    while div <= s:
        div_cnt = 0
        while number % div == 0:
            div_cnt += 1
            number //= div
        if div_cnt != 0:
            factor[div] = div_cnt
            ans_array[div] += 1
        i += 1
        div = prime_list[i]
    if number > 1:
        factor[number] = 1
        ans_array[number] += 1
    return factor


thre = pow(10, 6) + 1
ans_array = [0] * thre

prime_list = get_primenumber(thre)
for a in a_array:
    factrization_prime(a, prime_list)

print(prime_list[0:10])
print(ans_array[:10])
max_ans_array = max(ans_array)
if max_ans_array == 1:
    print('pairwise coprime')
elif max_ans_array < n:
    print('setwise coprime')
else:
    print('not coprime')

Submission status: Wrong Answer

Solution code:
from collections import defaultdict
import math

def f(n):
    yakusu = []
    for i in range(1, int(n ** 0.5) + 1):
        if n % i == 0:
            yakusu.append(i)
            if i != 1:
                break
            if i != n // i:
                yakusu.append(n // i)
    for i in yakusu:
        if i != 1:
            d[i] += 1

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

tmp = A[0]
for i in range(1, N):
    tmp = math.gcd(tmp, A[i])
if tmp != 1:
    print('not coprime')
    exit()
A.sort(reverse=True)
for i in A:
    f(i)

for i, v in d.items():
    if v != 1:
        print('setwise coprime')
        exit()

print('pairwise coprime')

Submission status: Wrong Answer

Solution code:
from collections import defaultdict
import math

def f(n):
    yakusu = []
    for i in range(2, int(n ** 0.5) + 1):
        if n % i == 0:
            yakusu.append(i)
            if i != 1:
                break
            if i != n // i:
                yakusu.append(n // i)
    for i in yakusu:
        if i != 1:
            d[i] += 1

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

tmp = A[0]
for i in range(1, N):
    tmp = math.gcd(tmp, A[i])
if tmp != 1:
    print('not coprime')
    exit()
A.sort(reverse=True)
for i in A:
    f(i)

for i, v in d.items():
    if v != 1:
        print('setwise coprime')
        exit()

print('pairwise coprime')

Submission status: Wrong Answer

Solution code:
from collections import defaultdict
import math

def f(n):
    yakusu = []
    for i in range(1, int(n ** 0.5) + 1):
        if n % i == 0:
            yakusu.append(i)
            if i != 1:
                break
    for i in yakusu:
        if i != 1:
            d[i] += 1

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

tmp = A[0]
for i in range(1, N):
    tmp = math.gcd(tmp, A[i])
if tmp != 1:
    print('not coprime')
    exit()
A.sort(reverse=True)
for i in A:
    f(i)

for i, v in d.items():
    if v != 1:
        print('setwise coprime')
        exit()

print('pairwise coprime')

Submission status: Wrong Answer

Solution code:
from collections import defaultdict
import math

def f(n):
    yakusu = []
    for i in range(2, int(n ** 0.5) + 1):
        if n % i == 0:
            yakusu.append(i)
            break
    for i in yakusu:
        if i != 1:
            d[i] += 1

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

tmp = A[0]
for i in range(1, N):
    tmp = math.gcd(tmp, A[i])
if tmp != 1:
    print('not coprime')
    exit()
A.sort(reverse=True)
for i in A:
    f(i)

for i, v in d.items():
    if v != 1:
        print('setwise coprime')
        exit()

print('pairwise coprime')

Submission status: Wrong Answer

Solution code:
from collections import defaultdict
import math

def f(n):
    yakusu = []
    for i in range(2, int(n ** 0.5) + 1):
        if n % i == 0:
            yakusu.append(i)
            if i != n // i:
                yakusu.append(n // i)
    for i in yakusu:
        if i != 1:
            d[i] += 1

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

tmp = A[0]
for i in range(1, N):
    tmp = math.gcd(tmp, A[i])
if tmp != 1:
    print('not coprime')
    exit()
A.sort(reverse=True)
for i in A:
    f(i)

for i, v in d.items():
    if v != 1:
        print('setwise coprime')
        exit()

print('pairwise coprime')

Submission status: Wrong Answer

Solution code:
import math
ini = lambda : int(input())
inm = lambda : map(int,input().split())
inl = lambda : list(map(int,input().split()))
gcd = lambda x,y : gcd(y,x%y) if x%y else 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, cnt])
    if temp!=1:
        arr.append([temp, 1])
    if arr==[]:
        arr.append([n, 1])
    return arr
def make_divisors(n):
    divisors = []
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            divisors.append(i)
            if i != n // i:
                divisors.append(n//i)
    divisors.sort()
    return divisors
class UnionFind():
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self, x):
        return -self.parents[self.find(x)]

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def members(self, x):
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        return {r: self.members(r) for r in self.roots()}

    def __str__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())
mod = 10**9 + 7

#maincode-------------------------------------------------

n = ini()
a = inl()
b = [0] * (10 **6+1)
ans = "pairwise coprime"

for i in a:
    b[i] += 1

if max(b) >= 2:
    ans = "setwise coprime"
else:
    for i in range(2,10**6+1):
        cnt = 0
        for j in range(i,10**6+1,i):
            if b[j] != 0:
                cnt += 1
            if cnt >= 2:
                ans = "setwise coprime"
                break
        else:
            break


if ans == "setwise coprime":
    c = a[0]
    for i in range(1,n):
        c = gcd(a[i],c)
    if c != 1:
        ans = "not coprime"

print(ans)

Submission status: Wrong Answer

Solution code:
import math
ini = lambda : int(input())
inm = lambda : map(int,input().split())
inl = lambda : list(map(int,input().split()))
gcd = lambda x,y : gcd(y,x%y) if x%y else 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, cnt])
    if temp!=1:
        arr.append([temp, 1])
    if arr==[]:
        arr.append([n, 1])
    return arr
def make_divisors(n):
    divisors = []
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            divisors.append(i)
            if i != n // i:
                divisors.append(n//i)
    divisors.sort()
    return divisors
class UnionFind():
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            self.parents[x] = self.find(self.parents[x])
            return self.parents[x]

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self, x):
        return -self.parents[self.find(x)]

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def members(self, x):
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        return {r: self.members(r) for r in self.roots()}

    def __str__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())
mod = 10**9 + 7

#maincode-------------------------------------------------

n = ini()
a = inl()
b = [0] * (10 **6+1)
ans = "pairwise coprime"

for i in a:
    b[i] += 1

if max(b) >= 2:
    ans = "setwise coprime"
else:
    for i in range(2,10**6+1):
        cnt = 0
        for j in range(i+i,10**6+1,i):
            if b[j] != 0:
                cnt += 1
            if cnt >= 2:
                ans = "setwise coprime"
                break
        else:
            break


if ans == "setwise coprime":
    c = a[0]
    for i in range(1,n):
        c = gcd(a[i],c)
    if c != 1:
        ans = "not coprime"

print(ans)

Submission status: Wrong Answer

Solution code:
import sys

def enum_div(n):
    ir=int(n**(0.5))+1
    ret=[]
    for i in range(1,ir):
        if n%i == 0:
            ret.append(i)
            if (i!= 1) & (i*i != n):
                ret.append(n//i)
    return ret

p=[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 
   31, 37, 41, 43, 47, 53, 59, 61, 67, 71,
   73, 79, 83, 89, 97, 101, 103, 107, 109, 113,
   127, 131, 137, 139, 149, 151, 157, 163, 167,
   173, 179, 181, 191, 193, 197, 199, 211, 223,
   227, 229, 233, 239, 241, 251, 257, 263, 269,
   271, 277, 281, 283, 293, 307, 311, 313, 317,
   331, 337, 347, 349, 353, 359, 367, 373, 379,
   383, 389, 397, 401, 409, 419, 421, 431, 433, 
   439, 443, 449, 457, 461, 463, 467, 479, 487,
   491, 499, 503, 509, 521, 523, 541, 547, 557,
   563, 569, 571, 577, 587, 593, 599, 601, 607,
   613, 617, 619, 631, 641, 643, 647, 653, 659,
   661, 673, 677, 683, 691, 701, 709, 719, 727,
   733, 739, 743, 751, 757, 761, 769, 773, 787,
   797, 809, 811, 821, 823, 827, 829, 839, 853,
   857, 859, 863, 877, 881, 883, 887, 907, 911,
   919, 929, 937, 941, 947, 953, 967, 971, 977,
   983, 991, 997,1009]

n=int(input())
ap=list(map(int,input().split()))
amin=min(ap)

if amin!=1:
    bp=enum_div(amin)+[amin]
#bp.sort()
    bp=bp[1:]
    for bpi in bp:
        if not bpi in p:
            continue
#        if bpi==1:
#            continue
        lap=0
        for ai in ap:
            if ai%bpi==0:
                lap+=1
#        lap=len([ai for ai in ap if ai%bpi==0])
        if lap==n:
            print("not coprime")
            sys.exit()

ptype="pairwise coprime"
for pp in p:
    lap=0
    for ai in ap:
        if  ai%pp==0:
            lap+=1
        if lap>=2:
            ptype="setwise coprime"
            print(ptype)    
            sys.exit()
#    lap=len([ai for ai in ap if ai%pp==0])
#    print("pp:",pp,lap)
#    if lap==n:
#        ptype="not coprime"
#        print("not coprime")
#        break
#    if lap>=2:
#        if ptype!="not coprime":
#        ptype="setwise coprime"

print(ptype)

Submission status: Wrong Answer

Solution code:
from functools import reduce

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

m = max(a)
d = [0] * (m + 1)
d[1] = 1
for i in range(2, m + 1):
    for j in range(i, m + 1, i):
        if d[j] == 0:
            d[j] = i

def prime_factorize(n):
    if n == 1:
        return []
    if n == 2:
        return [2]
    res = []
    while n > 2:
        res.append(d[n])
        n //= d[n]
    return res

def is_pairwise_coprime():
    exists = [0] * (m + 1)
    for ai in a:
        for p in prime_factorize(ai):
            if exists[p]:
                return False
            exists[p] = 1
    return True

def gcd(a, b):
    if a == 0:
        return b
    return gcd(b % a, a)

def is_setwise_coprime():
    return reduce(gcd, a) == 1


if is_pairwise_coprime():
    print('pairwise coprime')
elif is_setwise_coprime():
    print('setwise coprime')
else:
    print('not coprime')

Submission status: Wrong Answer

Solution code:
import math

n = int(input())
a_array = list(map(int, input().split()))

def factrization_prime(number):
    factor = {}
    div = 2
    s = math.sqrt(number)
    while div <= s:
        div_cnt = 0
        while number % div == 0:
            div_cnt += 1
            number //= div
        if div_cnt != 0:
            factor[div] = div_cnt
            ans_array[div] += 1
        div += 1
    if number > 1:
        factor[number] = 1
        ans_array[number] += 1
    return factor

thre = pow(10, 6) + 1
ans_array = [0] * thre

for a in a_array:
    factrization_prime(a)

max_ans_array = max(ans_array)
if max_ans_array == 1:
    print('pairwise coprime')
elif max_ans_array < n:
    print('setwise coprime')
else:
    print('not coprime')

Submission status: Wrong Answer

Solution code:
import math
L = 10**6 + 1

N = int(input())
A = list(map(int, input().split()))
memo = [0] * L
flag = 0 # 0をpairwise coprime

for a in A:
    memo[a] = 1

for i in range(2, L):
    if sum(memo[i::i]) > 1:
        flag = 1
        break

g = 0
for i in range(N):
    g = math.gcd(g, A[i])

if flag == 0:
    answer = 'pairwise coprime'
elif flag == 1 and g == 1:
    answer = 'setwise coprime'
else:
    answer = 'not coprime'

print(answer)