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:
#abc177 e
import sys,math,collections,itertools
input = sys.stdin.readline

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

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

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


N=int(input())
A=list(map(int,input().split()))
num = [0]*(10**6+1)

fact = []

for a in A:
    fact += factorization(a)
mn= collections.Counter(fact).most_common()[0][1]

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

Submission status: Wrong Answer

Solution code:
def factorize(n, d):
  # if n == 0 or n == 1:
    # return []
    arr = []
    tmp = n
    while True:
      i = d[tmp]
      if i == 1:
        break
      #cnt=0
      while tmp%i==0:
        #cnt+=1
        tmp //= i
      arr.append(i)
    if tmp!=1:
      arr.append(tmp)
    if arr==[]:
      arr.append(n)
    return arr

def minimum_prime(n):
  # 試し割りをする際の最小の素数
  # エラトステネスの篩と同様の実装
    d = list(range(n+1))
    d[0] = 1
    for i in range(2, int(n**0.5) + 1):
        if d[i] != i:
          continue
        for j in range(i * 2, n + 1, i):
          if d[j] == j:
            d[j] = i
    return d  

def main():
  n = int(input())
  arr = list(map(int, input().split()))
  max_arr = max(arr)
  d = minimum_prime(max_arr)
  dp = [0]*(max_arr+1)
  is_pair = True
  is_set = True

  for a in arr:
    if a != 1:
      primes = factorize(a, d)
      for p in primes:
        dp[p] += 1

  max_dp = max(dp)
  if max_dp == 1:
    print('pairwise coprime')
  elif max_dp == n:
    print('not coprime')
  else:
    print('setwise coprime')
  
main()

Submission status: Wrong Answer

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

def get_prime(n):
  res = [1]*(n+1)
  x = 2
  for i in range(2,x):
    if res[i]:
      for j in range(i*2,n+1,i):
        res[j] = 0
  return [i for i in range(2,n+1) if res[i]]

prime_list = {x:0 for x in get_prime(10**6+1)}
def check(i):
  x = 2
  m = i
  ng = True
  while x < math.sqrt(i):
    if m%x == 0:
      if prime_list[x]:
        return 0
      while m % x == 0:
        m //= x
      prime_list[x] = 1
      continue
    else:
      x += 1
  return 1

allwise = 1
if len([x for x in a if x > 1]) > len(prime_list.keys()):
  allwise = 0
else:
  allwise = check(a[0])
setwise = a[0]

for ai in a[1:]:
  if allwise:
    allwise = check(ai)
  setwise = math.gcd(setwise,ai)
  #print(ai,allwise,setwise)
if allwise:
  print('pairwise coprime')
elif setwise == 1:
  print('setwise coprime')
else:
  print('not coprime')

Submission status: Wrong Answer

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

def get_prime(n):
  res = [1]*(n+1)
  x = 2
  for i in range(2,x):
    if res[i]:
      for j in range(i*2,n+1,i):
        res[j] = 0
  return [i for i in range(2,n+1) if res[i]]

prime_list = {x:0 for x in get_prime(10**6+1)}
def check(i):
  x = 2
  m = i
  ng = True
  while x < math.sqrt(i):
    if m%x == 0:
      if prime_list[x] and ng:
        return 0
      m //= x
      prime_list[x] = 1
      ng = False
      continue
    else:
      ng = True
      x += 1
  return 1

allwise = 1
if len([x for x in a if x > 1]) > len(prime_list.keys()):
  allwise = 0
else:
  allwise = check(a[0])
setwise = a[0]

for ai in a[1:]:
  if allwise:
    allwise = check(ai)
  setwise = math.gcd(setwise,ai)
  #print(ai,allwise,setwise)
if allwise:
  print('pairwise coprime')
elif setwise == 1:
  print('setwise coprime')
else:
  print('not coprime')

Submission status: Wrong Answer

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())
for _ in range(1):
    n=inin()
    l=ain()
    f1,f2=0,0
    gc=l[0]
    d=[0]*(10**6+1)
    d[gc]=1
    if(l.count(1)>0):gc=1
    else:
      for i in range(1,n):
        d[l[i]]+=1
        gc=math.gcd(gc,l[i])
    if(gc!=1):print("not coprime")
    else:
        m=max(l)
        for i in range(2,m+1):
            if(d[i]>1):
                f1=1
                break
            elif(d[i]==1):
                for j in range(i+i,m+1,i):
                    if(d[j]!=0):
                        f1=1
                        break
            if(f1):break
        if(f1):
            print("setwise coprime")
        else:
            print("setwise 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: Wrong Answer

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())
for _ in range(1):
    n=inin()
    l=ain()
    f1,f2=0,0
    gc=l[0]
    d=[0]*(10**6+1)
    d[gc]=1
    if(l.count(1)>0):gc=1
    else:
      for i in range(1,n):
        d[l[i]]+=1
        gc=math.gcd(gc,l[i])
    if(gc!=1):print("not coprime")
    else:
        m=max(l)
        for i in range(2,m+1):
            if(d[i]>1):
                f1=1
                break
            elif(d[i]==1):
                for j in range(i+i,m+1,i):
                    if(d[j]!=0):
                        f1=1
                        break
            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: Wrong Answer

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())
for _ in range(1):
    n=inin()
    l=ain()
    f1,f2=0,0
    gc=l[0]
    d=[0]*(10**6+1)
    d[gc]=1
    if(l.count(1)>0):gc=1
    else:
      for i in range(1,n):
        d[l[i]]+=1
        gc=math.gcd(gc,l[i])
    if(gc!=1):print("not coprime")
    else:
        m=max(l)
        for i in range(n):
            if(d[l[i]]>1):f1=1
            else:
                for j in range(2*l[i],m+1,l[i]):
                    if(d[j]>0):
                        f1=1
                        break
            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: Wrong Answer

Solution code:
from math import gcd

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

a.sort()
xs = [0] * (a[-1] + 1)
g = a[0]
for v in a:
    g = gcd(g, v)
    xs[v] += 1

if g != 1:
    print("not coprime")
    exit()

for v in a:
    if xs[v] > 1:
        print("setwise coprime")
        exit()
    j = 2
    while v * j <= a[-1]:
        if xs[v * j] > 0:
            print("setwise coprime")
            exit()
        xs[v * j] += 1
print("pairwise coprime")

Submission status: Wrong Answer

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())
for _ in range(1):
    n=inin()
    l=ain()
    f1,f2=0,0
    gc=l[0]
    d=[0]*(10**6+1)
    d[gc]=1
    if(l.count(1)>0):gc=1
    else:
      for i in range(1,n):
        d[l[i]]+=1
        gc=math.gcd(gc,l[i])
    if(gc!=1):print("not coprime")
    else:
        m=max(l)
        for i in range(2,m+1):
            if(d[i]==1):
                for j in range(2*i,m+1,i):
                    if(d[j]!=0):
                        f1=1
                        break
                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: Wrong Answer

Solution code:
from math import gcd

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

a.sort()
xs = [0] * (a[-1] + 1)
g = a[0]
for v in a:
    g = gcd(g, v)
    xs[v] += 1

if g != 1:
    print("not coprime")
    exit()

for v in a:
    j = 2
    while v * j <= a[-1]:
        if xs[v * j] > 0:
            print("setwise coprime")
            exit()
        xs[v * j] += 1
print("pairwise coprime")

Submission status: Wrong Answer

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())
for _ in range(1):
    n=inin()
    l=ain()
    f1,f2=0,0
    gc=l[0]
    d=[0]*(10**6+1)
    d[gc]=1
    if(l.count(1)>0):gc=1
    else:
      for i in range(1,n):
        d[l[i]]+=1
        gc=math.gcd(gc,l[i])
    if(gc!=1):print("not coprime")
    else:
        m=max(l)
        for i in range(2,m+1):
            for j in range(i+i,m+1,i):
                if(d[j]!=0):
                    f1=1
                    break
            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: Wrong Answer

Solution code:
def factorization(n, is_prime):
    arr = []
    temp = n
    for i in [i for i in range(int(n**0.5)+1) if is_prime[i]]:
        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

def search_prime(n):
    is_prime = [True] * (n + 1)
    is_prime[0] = False
    is_prime[1] = False
    for i in range(2, int(n**0.5) + 1):
        if not is_prime[i]:
            continue
        for j in range(i * 2, n + 1, i):
            is_prime[j] = False
    return is_prime
    return [i for i in range(n + 1) if is_prime[i]]  

def main():
  n = int(input())
  arr = list(map(int, input().split()))
  max_arr = max(arr)
  is_prime = search_prime(int(max_arr**0.5//1))
  dp = [0]*(max_arr+1)
  is_pair = True
  is_set = True

  for a in arr:
    primes = factorization(a, is_prime)
    for p in primes:
      dp[p] += 1

  max_dp = max(dp)
  if max_dp == 1:
    print('pairwise coprime')
  elif max_dp == n:
    print('not coprime')
  else:
    print('setwise coprime')
  
main()

Submission status: Wrong Answer

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())
for _ in range(1):
    n=inin()
    l=ain()
    f1,f2=0,0
    gc=l[0]
    d=[0]*(10**6+1)
    d[gc]=1
    if(l.count(1)>0):gc=1
    else:
      for i in range(1,n):
        d[l[i]]+=1
        gc=math.gcd(gc,l[i])
    if(gc!=1):print("not coprime")
    else:
        m=max(l)
        for i in range(2,m):
            for j in range(i,m,i):
                if(d[j]!=0):
                    f1=1
                    break
            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