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: Time Limit Exceeded

Solution code:
import bisect
import collections
import copy
import functools
import heapq
import math
import sys
from collections import deque
from collections import defaultdict
input = sys.stdin.readline
sys.setrecursionlimit(10**9)
MOD = 10**9+7

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

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 euclid(a, b):
    if b == 0:
        return a
    else:
        return euclid(b, a%b)

def multiple(a, b):
    return a*b // euclid(a, b)

def gcd(nums):
    return functools.reduce(euclid, nums)

if gcd(A) != 1:
    print("not coprime")

else:
    """
    flag = 0
    M = [False]*(10**6+1)
    for i in range(N):
        n = A[i]
        if M[n]:
            flag = 1
            break
        if n != 1:
            k = 1
            while n*k <= 10**6:
                M[n*k] = True
                k += 1
    """
    flag = 0
    M = [False]*(10**6+1)
    for i in range(N):
        n = A[i]
        if n == 1:
            continue
        l = factorization(n)
        for j in range(len(l)):
            p = l[j][0]
            if M[p]:
                flag = 1
                break
            M[p] = True
    
    if flag == 0:
        print("pairwise coprime")
    else:
        print("setwise coprime")

Submission status: Time Limit Exceeded

Solution code:
import sys
import bisect as bi
import math
from collections import defaultdict as dd
import heapq
import itertools
input=sys.stdin.readline
from random import randint
##import numpy as np
##sys.setrecursionlimit(10**7)
mo=10**9+7
def cin():
    return map(int,sin().split())
def ain():            
    return list(map(int,sin().split()))
def sin():
    return input()
def inin():
    return int(input())
import sys
import bisect as bi
import math
from collections import defaultdict as dd
import heapq
import itertools
input=sys.stdin.readline
##from random import randint
##import numpy as np
##sys.setrecursionlimit(10**7)
mo=10**9+7
def cin():
    return map(int,sin().split())
def ain():            
    return list(map(int,sin().split()))
def sin():
    return input()
def inin():
    return int(input())
##def gcd(a,b): 
##    if a == 0: 
##        return b 
##    return gcd(b % a, a)
prime1=[]
def SieveOfEratosthenes(n): #list of primes upto n
    global prime1
    prime1 = [True for i in range(n+1)] 
    p = 2
    while (p * p <= n): 
        if (prime1[p] == True): 
            for i in range(p * p, n+1, p): 
                prime1[i] = False
        p += 1
    f=[]
    for p in range(2, n): 
        if prime1[p]: 
            f.append(p)
    return f

def lcm(a,b): 
    return (a*b) // math.gcd(a,b) 
for _ in range(1):
    n=inin()
    l=ain()
    f1,f2=0,0
    gc=l[0]
    d=dd(int)
    if(l.count(1)>0):gc=1
    else:
      for i in range(1,n):
        gc=math.gcd(gc,l[i])
    if(gc!=1):print("not coprime")
    else:
        lp=SieveOfEratosthenes(max(l))
        for i in l:
          if(i!=1):
            for j in lp:
              if(i%j==0):
                if(d[j]==1):
                  f1=1
                  break
                d[j]=1
            if(f1):break
        if(f1):
            print("setwise coprime")
        else:
            print("pairwise coprime")
        
        
    
    
    

 
    
    
    
    
        
        
    
    
    
    


    




##def msb(n):n|=n>>1;n|=n>>2;n|=n>>4;n|=n>>8;n|=n>>16;n|=n>>32;n|=n>>64;return n-(n>>1) #2 ki power
##def pref(a,n,f):             
##    pre=[0]*n
##    if(f==0):         ##from beginning
##        pre[0]=a[0]
##        for i in range(1,n):
##            pre[i]=a[i]+pre[i-1]
##    else:              ##from end
##        pre[-1]=a[-1]
##        for i in range(n-2,-1,-1):
##            pre[i]=pre[i+1]+a[i]
##    return pre
##maxint=10**24 
##def kadane(a,size): 
##    max_so_far = -maxint - 1
##    max_ending_here = 0
##       
##    for i in range(0, size): 
##        max_ending_here = max_ending_here + a[i] 
##        if (max_so_far < max_ending_here): 
##            max_so_far = max_ending_here 
##  
##        if max_ending_here < 0: 
##            max_ending_here = 0   
##    return max_so_far
##def power(x, y):
##    if(y == 0):return 1
##    temp = power(x, int(y / 2))%mo
##    if (y % 2 == 0):return (temp * temp)%mo 
##    else:
##        if(y > 0):return (x * temp * temp)%mo 
##        else:return ((temp * temp)//x )%mo

            
        
        
        
            
    
        
        
    
    
    

 
    
    
    
    
        
        
    
    
    
    


    




##def msb(n):n|=n>>1;n|=n>>2;n|=n>>4;n|=n>>8;n|=n>>16;n|=n>>32;n|=n>>64;return n-(n>>1) #2 ki power
##def pref(a,n,f):             
##    pre=[0]*n
##    if(f==0):         ##from beginning
##        pre[0]=a[0]
##        for i in range(1,n):
##            pre[i]=a[i]+pre[i-1]
##    else:              ##from end
##        pre[-1]=a[-1]
##        for i in range(n-2,-1,-1):
##            pre[i]=pre[i+1]+a[i]
##    return pre
##maxint=10**24 
##def kadane(a,size): 
##    max_so_far = -maxint - 1
##    max_ending_here = 0
##       
##    for i in range(0, size): 
##        max_ending_here = max_ending_here + a[i] 
##        if (max_so_far < max_ending_here): 
##            max_so_far = max_ending_here 
##  
##        if max_ending_here < 0: 
##            max_ending_here = 0   
##    return max_so_far
##def power(x, y):
##    if(y == 0):return 1
##    temp = power(x, int(y / 2))%mo
##    if (y % 2 == 0):return (temp * temp)%mo 
##    else:
##        if(y > 0):return (x * temp * temp)%mo 
##        else:return ((temp * temp)//x )%mo

Submission status: Time Limit Exceeded

Solution code:
n = int(input())
A = tuple(map(int, input().split()))
U = 10**6
D = list(range(U+1))
i = 2
while i*i <= U:
  if D[i] != i:
    i += 1
    continue
  for j in range(i*i, U+1, i):
    D[j] = min(D[j], i)
  i += 1
C = [0]*(U+1)
is_pairwise = True
for a in A:
  while a > 1:
    d = D[a]
    while a%d == 0:
      a //= d
    if C[d]:
      is_pairwise = False
    C[d] += 1
if max(C) == n:
  print("not coprime")
else:
  if is_pairwise:
    print("pairwise coprime")
  else:
    print("setwise coprime")

Submission status: Time Limit Exceeded

Solution code:
import sys
import math
input = sys.stdin.readline

def prime_factor(n):
    factors = []
    while n%2==0:
        factors.append(2)
        n//=2
    f=3
    while f*f<=n:
        if n%f==0:
            factors.append(f)
            n//=f
        else:
            f+=2
    if n!=1:
        factors.append(n)
    return set(factors)


n=int(input())
L=list(map(int,input().split()))
val = L[0]
for i in range(1,n):
    val=math.gcd(val,L[i])
if val!=1:
    print('not coprime')
    sys.exit()

d={}
for i in range(n):
    factors = prime_factor(L[i])
    for j in factors:
        if j not in d.keys():
            d[j]=1
        else:
            print('setwise coprime')
            sys.exit()
print('pairwise coprime')

Submission status: Time Limit Exceeded

Solution code:
import sys
import math
input = sys.stdin.readline

def prime_factor(n):
    factors = []
    while n%2==0:
        factors.append(2)
        n//=2
    f=3
    while f*f<=n:
        if n%f==0:
            factors.append(f)
            n//=f
        else:
            f+=2
    if n!=1:
        factors.append(n)
    return set(factors)

def gcd(a,b):
    while b:
        a,b=b,a%b
    return a

n=int(input())
L=list(map(int,input().split()))
val = L[0]
for i in range(1,n):
    val=math.gcd(L[i],val)
if val!=1:
    print('not coprime')
    sys.exit()

d={}
for i in range(n):
    factors = prime_factor(L[i])
    for j in factors:
        if j not in d.keys():
            d[j]=1
        else:
            print('setwise coprime')
            sys.exit()
print('pairwise coprime')

Submission status: Time Limit Exceeded

Solution code:
def main():
    n, *a, = map(int, open(0).read().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 primes(x):
        ps = set()
        while x != 1:
            p = d[x]
            ps.add(p)
            x = x // d[x]
        return ps

    b = set()
    c = primes(a[0])
    f = 1
    for i in a:
        ps = set()
        while i != 1:
            p = d[i]
            ps.add(p)
            i = i // d[i]
        if f:
            if b & ps:
                f = 0
            b |= ps
        c &= ps

    if f:
        ans = "pairwise coprime"
    elif len(c) == 0:
        ans = "setwise coprime"
    else:
        ans = "not coprime"

    print(ans)


if __name__ == '__main__':
    main()

Submission status: Time Limit Exceeded

Solution code:
import sys
input = sys.stdin.readline

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

def prime_factor(n):
    factors = []
    while n%2==0:
        factors.append(2)
        n//=2
    f=3
    while f*f<=n:
        if n%f==0:
            factors.append(f)
            n//=f
        else:
            f+=2
    if n!=1:
        factors.append(n)
    return set(factors)

"""
def gcd(a,b):
    while b:
        a,b=b,a%b
    return a
"""
import math
val = L[0]
for i in range(1,n):
    val=math.gcd(L[i],val)
if val!=1:
    print('not coprime')
    sys.exit()

d={}
for i in range(n):
    factors = prime_factor(L[i])
    for j in factors:
        if j not in d.keys():
            d[j]=1
        else:
            print('setwise coprime')
            sys.exit()
print('pairwise coprime')

Submission status: Time Limit Exceeded

Solution code:
import sys
input = sys.stdin.readline

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

def prime_factor(n):
    factors = []
    while n%2==0:
        factors.append(2)
        n//=2
    f=3
    while f*f<=n:
        if n%f==0:
            factors.append(f)
            n//=f
        else:
            f+=2
    if n!=1:
        factors.append(n)
    return set(factors)

def gcd(a,b):
    while b:
        a,b=b,a%b
    return a
    
val = L[0]
for i in range(1,n):
    val=gcd(L[i],val)
if val!=1:
    print('not coprime')
    sys.exit()

d={}
for i in range(n):
    factors = prime_factor(L[i])
    for j in factors:
        if j not in d.keys():
            d[j]=1
        else:
            print('setwise coprime')
            sys.exit()
print('pairwise coprime')

Submission status: Time Limit Exceeded

Solution code:
import sys
input = sys.stdin.readline

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

def prime_factor(n):
    factors = []
    while n%2==0:
        factors.append(2)
        n//=2
    f=3
    while f*f<=n:
        if n%f==0:
            factors.append(f)
            n//=f
        else:
            f+=2
    if n!=1:
        factors.append(n)
    return set(factors)

def gcd(a,b):
    while b:
        a,b=b,a%b
    return a
    
val = L[0]
for i in range(1,n):
    val=gcd(L[i],val)
if val!=1:
    print('not coprime')
    sys.exit()

d={}
for i in range(n):
    factors = prime_factor(L[i])
    for j in factors:
        if j not in d:
            d[j]=1
        else:
            print('setwise coprime')
            sys.exit()
print('pairwise coprime')

Submission status: Time Limit Exceeded

Solution code:
def main():
    n, *a, = map(int, open(0).read().split())
    m = max(a)

    def minimum_prime(x):
        if x == 1:
            return 1
        for i in range(3, x + 1, 2):
            if x % i == 0:
                return i

    d = [minimum_prime(i) if i % 2 == 1 else 2 for i in range(m + 1)]

    def primes(x):
        ps = set()
        while x != 1:
            p = d[x]
            ps.add(p)
            x = x // d[x]
        return ps

    b = set()
    c = primes(a[0])
    f = 1
    for i in a:
        primes = set()
        while i != 1:
            p = d[i]
            primes.add(p)
            i = i // d[i]
        if f:
            if b & primes:
                f = 0
            b |= primes
        c &= primes

    if f:
        ans = "pairwise coprime"
    elif len(c) == 0:
        ans = "setwise coprime"
    else:
        ans = "not coprime"

    print(ans)


if __name__ == '__main__':
    main()

Submission status: Time Limit Exceeded

Solution code:
import fractions
import sys
sys.setrecursionlimit(10**9)

def mi(): return map(int,input().split())
def ii(): return int(input())
def isp(): return input().split()
def deb(text): print("-------\n{}\n-------".format(text))

INF=10**18
def solve(N,A):
    P = set()

    for i in range(N):
        n = A[i]
        if n % 2 == 0 and 2 in P: break
        while n % 2 == 0:
            P.add(2)
            n //= 2
            
        f = 3
        while f * f <= n:
            if n % f == 0:
                if f in P: break
                P.add(f)
                while n%f == 0:
                    n //= f
            else:
                f += 2
        else:
            if n != 1:
                if n in P: break
                P.add(n)
            
            continue
        break
    else:
        return 0
        
    return 1 

def get_gcd(X):
	gcd = X[0]
	for x in X[1:]:
	    gcd = fractions.gcd(x, gcd)
	return gcd

def main():
    N=ii()
    A=list(mi())

    flag = solve(N,A)
    if flag == 0:
        print("pairwise coprime")
    else:
        gcd = get_gcd(A)
        if gcd == 1:
            print("setwise coprime")
        else:
            print("not coprime")
       

if __name__ == '__main__':
    main()

Submission status: Time Limit Exceeded

Solution code:
def main():
    n, *a, = map(int, open(0).read().split())
    m = max(a)

    def minimum_prime(x):
        if x == 1:
            return 1
        for i in range(3, x + 1, 2):
            if x % i == 0:
                return i

    d = [minimum_prime(i) if i % 2 == 1 else 2 for i in range(m + 1)]

    def primes(x):
        ps = set()
        while x != 1:
            p = d[x]
            ps.add(p)
            x = x // d[x]
        return ps

    b = set()
    c = primes(a[0])
    f = 0
    for i in a:
        primes = set()
        while i != 1:
            p = d[i]
            primes.add(p)
            i = i // d[i]
        if b & primes:
            f = 1
        b |= primes
        c &= primes

    if f == 0:
        ans = "pairwise coprime"
    elif len(c) == 0:
        ans = "setwise coprime"
    else:
        ans = "not coprime"

    print(ans)


if __name__ == '__main__':
    main()

Submission status: Time Limit Exceeded

Solution code:
import numpy as np
import sys
sys.setrecursionlimit(10**9)

def mi(): return map(int,input().split())
def ii(): return int(input())
def isp(): return input().split()
def deb(text): print("-------\n{}\n-------".format(text))

INF=10**18
def solve(N,A):
    P = set()

    for i in range(N):
        n = A[i]
        if n % 2 == 0 and 2 in P: break
        while n % 2 == 0:
            P.add(2)
            n //= 2
            
        f = 3
        while f * f <= n:
            if n % f == 0:
                if f in P: break
                P.add(f)
                while n%f == 0:
                    n //= f
            else:
                f += 2
        else:
            if n != 1:
                if n in P: break
                P.add(n)
            
            continue
        break
    else:
        return 0
        
    return 1 



def main():
    N=ii()
    A=np.array(list(mi()))

    flag = solve(N,A)
    if flag == 0:
        print("pairwise coprime")
    else:
        gcd = np.gcd.reduce(A)
        if gcd == 1:
            print("setwise coprime")
        else:
            print("not coprime")
       

if __name__ == '__main__':
    main()

Submission status: Time Limit Exceeded

Solution code:
def main():
    n, *a, = map(int, open(0).read().split())
    m = max(a)

    def minimum_prime(x):
        if x == 1:
            return 1
        for i in range(2, x + 1):
            if x % i == 0:
                return i

    d = [minimum_prime(i) for i in range(m + 1)]

    def primes(x):
        ps = set()
        while x != 1:
            p = d[x]
            ps.add(p)
            x = x // d[x]
        return ps

    b = set()
    c = primes(a[0])
    f = 0
    for i in a:
        primes = set()
        while i != 1:
            p = d[i]
            primes.add(p)
            i = i // d[i]
        if b & primes:
            f = 1
        b |= primes
        c &= primes

    if f == 0:
        ans = "pairwise coprime"
    elif len(c) == 0:
        ans = "setwise coprime"
    else:
        ans = "not coprime"

    print(ans)


if __name__ == '__main__':
    main()

Submission status: Time Limit Exceeded

Solution code:
import math
def lcm(x, y):
    return (x * y) // math.gcd(x, y)

n = int(input())
a = list(map(int,input().split()))
b = [1] * (n + 1)
for i in range(n, 1, -1):
    b[i - 1] = lcm(b[i], a[i - 1])
flag = 1
for i in range(n - 1):
    if math.gcd(a[i], b[i + 1]) != 1:
        flag = 0
g = a[0]
for i in range(n):
    g = math.gcd(g, a[i])
if flag == 0:
    if g == 1:
        flag = 2
ans = "not coprime"
if flag == 1:
    ans = "pairwise coprime"
elif flag == 2:
    ans = "setwise coprime"
print(ans)

Submission status: Time Limit Exceeded

Solution code:
def primes(x):
    p = set()
    for i in range(2, x + 1):
        if x == 1:
            break
        if x % i != 0:
            continue
        while x % i == 0:
            x = x // i
        else:
            p.add(i)

    return p


def main():
    n, *a, = map(int, open(0).read().split())
    b = set()
    c = primes(a[0])
    f = True
    for i in a:
        p = primes(i)
        if f:
            if b & p:
                f = False
            b = b.union(p)
        c = c & p

    if f:
        ans = "pairwise coprime"
    elif len(c) == 0:
        ans = "setwise coprime"
    else:
        ans = "not coprime"

    print(ans)


if __name__ == '__main__':
    main()

Submission status: Time Limit Exceeded

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

import sys
import math
def setwise_coprime(a):
  ans=a[0]
  for i in range(1,n):
    ans=math.gcd(ans,a[i])
  return ans

def erast(n):
  num_set=set()
  prime_set=set()
  for i in range(2,n+1):
    if i not in num_set:
      prime_set.add(i)
      for j in range(i*i,n+1,i):
        num_set.add(j)
  s=list(prime_set)
  return s

check=set()
a_set=set(a)
if setwise_coprime(a)==1:
  t=erast(1000000)
  s=set()
  for i in t:
    if i<=1000:
      s.add(i)
    else:
      if i in a:
        s.add(i)
        
  a=list(a)
  s=list(s)
  for i in range(n):
    if a[i]!=1:
      for j in range(len(s)):
        if s[j]>a[i]:
          break
        if a[i]%s[j]==0:
          if s[j] in check:
            print("setwise coprime")
            sys.exit()
          else:
            check.add(s[j])
            
  print("pairwise coprime")    
else:
  print("not coprime")

Submission status: Time Limit Exceeded

Solution code:
from math import gcd
n=int(input())
A=list(map(int,input().split()))
m=max(A)
l=[0 for _ in range(m)]
fp=True
for a in A:
    l[a-1]+=1
for i in range(2,m):
    cnt=0
    for j in range(i-1,m,i):
        cnt+=l[j]
        if cnt>1:
            fp=False
            break
g=0
fs=False
for a in A:
    g=gcd(g,a)
if g==1:
    fs=True

if fp:
    print("pairwise coprime")
elif fs:
    print("setwise coprime")
else:
    print("not coprime")

Submission status: Time Limit Exceeded

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

import sys
import math
def setwise_coprime(a):
  ans=a[0]
  for i in range(1,n):
    ans=math.gcd(ans,a[i])
  return ans

def erast(n):
  num_set=set()
  prime_set=set()
  for i in range(2,n+1):
    if i not in num_set:
      prime_set.add(i)
      for j in range(i*i,n+1,i):
        num_set.add(j)
  s=list(prime_set)
  return s

check=set()

if setwise_coprime(a)==1:
  s=erast(1000000)
  s.sort()
  for i in range(n):
    if a[i]!=1:
      for j in range(len(s)):
        if s[j]>a[i]:
          break
        if a[i]%s[j]==0:
          if s[j] in check:
            print("setwise coprime")
            sys.exit()
          else:
            check.add(s[j])
            
  print("pairwise coprime")    
else:
  print("not coprime")

Submission status: Time Limit Exceeded

Solution code:
# E

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

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

def fast_factorization_init(N):
    res=list(range(N))
    for i in range(2,N):
        if i*i>N:
            break
        for j in range(i*i,N,i):
            if res[j]==j:
                res[j]=i
        if res[i]<i:
            continue
    return res            
    
min_factors=fast_factorization_init(10**6+10)
def fast_factorization(n):
    res=[]
    while n>1:
        res.append(min_factors[n])
        n//=min_factors[n]
    return res

res2=1
P=[]
for i in range(N):
    if i!=0:
        res1=gcd(A[i],res1)
    else:
        res1=A[0]
    fact=fast_factorization(A[i])
    if res2!=0:
        for p in P:
            if A[i]%p==0:
                res2=0
                break
    for p in fact:
        P.append(p)
if res2==1:
    print('pairwise coprime')
elif res1==1:
    print('setwise coprime')
else:
    print('not coprime')

Submission status: Time Limit Exceeded

Solution code:
from math import gcd

N = int(input())
A = list(map(int, input().split()))
MAX = 10**6


def prime_factor_sieve(n):
    """
    エラトステネスの篩で、
    2 ~ Nの各数に対して、その整数のもつ最小の素因数
    (その整数を篩落とした最小の素因数)を記録して返す
    O(nloglog(n))
    """
    res = [i for i in range(n+1)]
    for i in range(2, int(n**0.5)+1):
        if res[i] < i:
            continue
        for j in range(i*i, n+1, i):
            if res[j] == j:
                res[j] = i
    return res

def factorization(n, min_factor):
    """
    エラトステネスの篩で手に入れた、各整数の最小素因数のリスト
    からO(log(n))で素因数分解する
    """
    res = set()
    while n > 1:
        res.add(min_factor[n])
        n //= min_factor[n]
        # 割った後の素因数についてもO(1)で参照できる
    return res

# 素因数が重複しているかを調べる
min_factor = prime_factor_sieve(MAX)
res = set()
is_ok = 1

for a in A:
    tmp = factorization(a, min_factor)
    if res & tmp:
        is_ok = 0
        break
    res = res.union(tmp)
    
if is_ok:
    print("pairwise coprime")
else:
    g = A[0]
    for i in range(1, N):
        g = gcd(g, A[i])
    if g == 1:
        print("setwise coprime")
    else:
        print("not coprime")

Submission status: Time Limit Exceeded

Solution code:
from collections import Counter
import math
import random
n=int(input())
a=list(map(int,input().split()))
ma=max(a)
sa=set(a)
ans=[]
era=[1]*(10**6+1)
era[0]=0
ca=Counter(a)

k=2
while k<(10**6+1):
  if era[k]==1:
    for i in range(k,10**6+1,k):
      if i!=k:
        era[i]=0
      if i in sa:
        for t in range(ca[i]):
          ans.append(k)
  if k==2:
    k+=1
  else:
    k+=2

pflag=True
if len(ans)!=len(set(ans)):
  pflag=False
  
if pflag == False:
  setwise=a[0]
  for i in range(1,n):
    setwise=math.gcd(setwise,a[i])
  if setwise == 1:
    print("setwise coprime")
  else:
    print("not coprime")
else:
  print('pairwise coprime')

Submission status: Time Limit Exceeded

Solution code:
from math import gcd
from functools import lru_cache

@lru_cache(maxsize=None)
def mygcd(a):
    return gcd(a[0],a[1])
    
N=int(input())
A=list(map(int,input().split()))
for i in range(N-1):
    for j in range(i+1,N):
        g = mygcd((A[i],A[j]))
        if g != 1:
            break
    else:
        continue
    break
else:
    print("pairwise coprime")
    exit()
s=A.pop(0)
for i in A:
    s = mygcd((s,i))
    if s == 1:
        print("setwise coprime")
        break
else:
    print("not coprime")

Submission status: Time Limit Exceeded

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


def prime_factorize(n):
    r = set()
    if n % 2 == 0:
        r.add(2)
    f = 3
    while f * f <= n:
        if n % f == 0:
            r.add(f)
            n //= f
        else:
            f += 2
    if n != 1:
        r.add(n)
    return collections.Counter(r)


a1 = collections.Counter([])
a2 = prime_factorize(A[0])
for a in A:
    tmp = prime_factorize(a)
    a1 += tmp
    a2 &= tmp
if a2:
    print('not coprime')
elif a1.most_common()[0][1] >= 2:
    print('setwise coprime')
else:
    print('pairwise coprime')

Submission status: Time Limit Exceeded

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

import sys
import math
def setwise_coprime(a):
  ans=a[0]
  for i in range(1,n):
    ans=math.gcd(ans,a[i])
  return ans

def erast(n):
  num_set=set()
  prime_set=set()
  for i in range(2,n+1):
    if i not in num_set:
      prime_set.add(i)
      for j in range(i*i,n+1,i):
        num_set.add(j)
  s=prime_set
  return s

def is_prime(n):
  if n==1:
    return False
  if n==2:
    return True
  else:
    for i in range(2,int(math.sqrt(n))+1):
      if n%i==0:
        return False
    return True
  
check=set()


if setwise_coprime(a)==1:
  s=erast(1000)
  for i in range(n):
    if is_prime(a[i]):
      s.add(a[i])
  s=list(s)  
  s.sort()
  for i in range(n):
    if a[i]!=1:
      for j in range(len(s)):
        if a[i]%s[j]==0:
          if s[j] in check:
            print("setwise coprime")
            sys.exit()
          else:
            check.add(s[j])
            
  print("pairwise coprime")    
else:
  print("not coprime")

Submission status: Time Limit Exceeded

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


def prime_factorize(n):
    r = set()
    if n % 2 == 0:
        r.add(2)
    f = 3
    while f * f <= n:
        if n % f == 0:
            r.add(f)
            n //= f
        else:
            f += 2
    if n != 1:
        r.add(n)
    return collections.Counter(r)


a1 = collections.Counter([])
a2 = collections.Counter(prime_factorize(A[0]))
for a in A:
    tmp = prime_factorize(a)
    a1 += tmp
    a2 &= tmp
if a2:
    print('not coprime')
elif a1.most_common()[0][1] >= 2:
    print('setwise coprime')
else:
    print('pairwise coprime')

Submission status: Time Limit Exceeded

Solution code:
import math as m

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


D=[0]*(10**6+1)
for i in range(2,int(m.sqrt(10**6))+2):
    if D[i]!=0:
        continue
    j=2*i
    while j < 10**6+1:
        D[j]=i
        j+=i

P=[0]*10**6
pc=True
g=As[0]
for n in range(N):
    A=As[n]
    g=m.gcd(g,A)
    if A==1:
        continue
    ppre=1
    while True:
        p=D[A] if D[A]!=0 else A
        if ppre != p:
            if P[p] > 0:
                pc=False
            P[p]+=1
            ppre=p
        A=A//p
        if A==1:
            break

if pc:
    print('pairwise coprime')
elif g==1:
    print('setwise coprime')
else:
    print('not coprime')

Submission status: Time Limit Exceeded

Solution code:
def getN():
    return int(input())
def getNM():
    return map(int, input().split())
def getList():
    return list(map(int, input().split()))
def getArray(intn):
    return [int(input()) for i in range(intn)]
def input():
    return sys.stdin.readline().rstrip()
def rand_N(ran1, ran2):
    return random.randint(ran1, ran2)
def rand_List(ran1, ran2, rantime):
    return [random.randint(ran1, ran2) for i in range(rantime)]
def rand_ints_nodup(ran1, ran2, rantime):
  ns = []
  while len(ns) < rantime:
    n = random.randint(ran1, ran2)
    if not n in ns:
      ns.append(n)
  return sorted(ns)

def rand_query(ran1, ran2, rantime):
  r_query = []
  while len(r_query) < rantime:
    n_q = rand_ints_nodup(ran1, ran2, 2)
    if not n_q in r_query:
      r_query.append(n_q)
  return sorted(r_query)

from collections import defaultdict, deque, Counter
from sys import exit
from decimal import *
from heapq import heapify, heappop, heappush
import math
from fractions import gcd
import random
import string
import copy
from itertools import combinations, permutations, product
from operator import mul, itemgetter
from functools import reduce
from bisect import bisect_left, bisect_right

import sys
sys.setrecursionlimit(1000000000)
mod = 10 ** 9 + 7

#############
# Main Code #
#############

class Osa_k():
    def __init__(self, n):
        self.sieve = list(range(n + 1))
        self.sieve[0] = 1 #素数でない
        self.sieve[1] = 1 #素数でない
        m = int(math.sqrt(n))
        for i in range(2, m + 1):
            if self.sieve[i] < i:
                continue
            for j in range(i * i, n + 1, i):
                if self.sieve[j] == j:
                    self.sieve[j] = i

    def factorize(self, n):
        prime = defaultdict(int)
        if n == 0 or n == 1:
            return n
        opt = n
        while opt > 1:
            prime[self.sieve[opt]] += 1
            opt //= self.sieve[opt]
        return sorted(prime.items())

N = getN()
A = getList()
O = Osa_k(10 ** 6 + 1)

pair = True
primes = set()
x = A[0]
for a in A[1:]:
    x = gcd(x, a)
    if pair and a != 1:
        factor = set()
        for i in O.factorize(a):
            factor.add(i[0])
        if not primes.isdisjoint(factor):
            pair = False
        else:
            primes |= factor

if pair:
    print("pairwise coprime")
elif x == 1:
    print("setwise coprime")
else:
    print("not coprime")

Submission status: Time Limit Exceeded

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

import sys
import math
def setwise_coprime(a):
  ans=a[0]
  for i in range(1,n):
    ans=math.gcd(ans,a[i])
  return ans

def erast(n):
  num_set=set()
  prime_set=set()
  for i in range(2,n+1):
    if i not in num_set:
      prime_set.add(i)
      for j in range(i*i,n+1,i):
        num_set.add(j)
  s=list(prime_set)
  return s

def is_prime(n):
  if n==1:
    return False
  if n==2:
    return True
  else:
    for i in range(int(math.sqrt(n))+1):
      if n%i==0:
        return False
    return True
  
check=set()
if setwise_coprime(a)==1:
  s=erast(1000000)
  s.sort()
  for i in range(n):
    if a[i]!=1:
      for j in range(len(s)):
        if a[i]%s[j]==0:
          if s[j] in check:
            print("setwise coprime")
            sys.exit()
          else:
            check.add(s[j])
            
  print("pairwise coprime")    
else:
  print("not coprime")