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: Runtime Error

Solution code:
import math
import sys
from functools import lru_cache
sys.setrecursionlimit(10000000)

N = int(input())
A_list = [int(e) for e in input().split()]

#pairwise coprime …… 素因数分解したとき、共通のものが1個もない
#setwise coprime　…… 素因数分解したとき、全てで共通のものがない

#試し割の結果の辞書を求める
def make_trial_division_dict(n):
    #import math
    td_dict = dict()
    for i in range(2,n+1):
        if i not in td_dict:
            td_dict[i] = i
            for j in range(2,1+n//i):
                if j*i not in td_dict:
                    td_dict[j*i] = i
    return td_dict

#試し割結果の辞書を利用して素因数分解する
@lru_cache(maxsize=None)
def high_speed_prime_factorization(n):
    pf_list = list()
    pf_list.append(td_dict[n])
    
    if n//td_dict[n] == 1:
        return pf_list
    else:
        pf_list.extend(high_speed_prime_factorization(n//td_dict[n]))
        return pf_list

td_dict = make_trial_division_dict(max(A_list))

all_pf = set()    #含まれる素因数がすべて集約される
common_pf = set() #共通する素因数が集約される
all_pf |= set(high_speed_prime_factorization(A_list[0]))
common_pf |= set(high_speed_prime_factorization(A_list[0]))
is_pairwise = True

#print(A_list[0],set(high_speed_prime_factorization(A_list[0])))

for i in range(1,len(A_list)):
    A_pf = set(high_speed_prime_factorization(A_list[i]))
    common_pf &= A_pf 
    
    #print(A_list[i],set(high_speed_prime_factorization(A_list[i])))
    
    if is_pairwise and len(all_pf&A_pf)!=0:
        is_pairwise = False
    else:
        all_pf |= A_pf

if is_pairwise:
    print("pairwise coprime")
elif len(common_pf) == 0:
    print("setwise coprime")
else:
    print("not coprime")

Submission status: Runtime Error

Solution code:
import math
import sys
from functools import lru_cache
sys.setrecursionlimit(10000000000)

N = int(input())
A_list = [int(e) for e in input().split()]

#pairwise coprime …… 素因数分解したとき、共通のものが1個もない
#setwise coprime　…… 素因数分解したとき、全てで共通のものがない

#試し割の結果の辞書を求める
def make_trial_division_dict(n):
    #import math
    td_dict = dict()
    for i in range(2,n+1):
        if i not in td_dict:
            td_dict[i] = i
            for j in range(2,1+n//i):
                if j*i not in td_dict:
                    td_dict[j*i] = i
    return td_dict

#試し割結果の辞書を利用して素因数分解する
@lru_cache(maxsize=None)
def high_speed_prime_factorization(n):
    pf_list = list()
    pf_list.append(td_dict[n])
    
    if n//td_dict[n] == 1:
        return pf_list
    else:
        pf_list.extend(high_speed_prime_factorization(n//td_dict[n]))
        return pf_list

td_dict = make_trial_division_dict(max(A_list))

all_pf = set()    #含まれる素因数がすべて集約される
common_pf = set() #共通する素因数が集約される
all_pf |= set(high_speed_prime_factorization(A_list[0]))
common_pf |= set(high_speed_prime_factorization(A_list[0]))
is_pairwise = True

#print(A_list[0],set(high_speed_prime_factorization(A_list[0])))

for i in range(1,len(A_list)):
    A_pf = set(high_speed_prime_factorization(A_list[i]))
    common_pf &= A_pf 
    
    #print(A_list[i],set(high_speed_prime_factorization(A_list[i])))
    
    if is_pairwise and len(all_pf&A_pf)!=0:
        is_pairwise = False
    else:
        all_pf |= A_pf

if is_pairwise:
    print("pairwise coprime")
elif len(common_pf) == 0:
    print("setwise coprime")
else:
    print("not coprime")

Submission status: Runtime Error

Solution code:
import math
import sys
from functools import lru_cache
sys.setrecursionlimit(1000000)

N = int(input())
A_list = [int(e) for e in input().split()]

#pairwise coprime …… 素因数分解したとき、共通のものが1個もない
#setwise coprime　…… 素因数分解したとき、全てで共通のものがない

#試し割の結果の辞書を求める
def make_trial_division_dict(n):
    #import math
    td_dict = dict()
    for i in range(2,n+1):
        if i not in td_dict:
            td_dict[i] = i
            for j in range(2,1+n//i):
                if j*i not in td_dict:
                    td_dict[j*i] = i
    return td_dict

#試し割結果の辞書を利用して素因数分解する
@lru_cache(maxsize=None)
def high_speed_prime_factorization(n):
    pf_list = list()
    pf_list.append(td_dict[n])
    
    if n//td_dict[n] == 1:
        return pf_list
    else:
        pf_list.extend(high_speed_prime_factorization(n//td_dict[n]))
        return pf_list

td_dict = make_trial_division_dict(max(A_list))

all_pf = set()    #含まれる素因数がすべて集約される
common_pf = set() #共通する素因数が集約される
all_pf |= set(high_speed_prime_factorization(A_list[0]))
common_pf |= set(high_speed_prime_factorization(A_list[0]))
is_pairwise = True

#print(A_list[0],set(high_speed_prime_factorization(A_list[0])))

for i in range(1,len(A_list)):
    A_pf = set(high_speed_prime_factorization(A_list[i]))
    common_pf &= A_pf 
    
    #print(A_list[i],set(high_speed_prime_factorization(A_list[i])))
    
    if is_pairwise and len(all_pf&A_pf)!=0:
        is_pairwise = False
    else:
        all_pf |= A_pf

if is_pairwise:
    print("pairwise coprime")
elif len(common_pf) == 0:
    print("setwise coprime")
else:
    print("not coprime")

Submission status: Runtime Error

Solution code:
def find_gcd(x, y): 
    while (y): 
        x, y = y, x % y 
    return x 
def fun(l):
  num1=l[0] 
  num2=l[1] 
  gcd=find_gcd(num1,num2) 
  for i in range(len(l)-1):
    gcd=find_gcd(l[i],l[i+1])
    if gcd!=1:
      break;
  else:
    print("pairwise coprime")
    return 1
 
  for i in range(2,len(l)):
    gcd=find_gcd(gcd,l[i])
  if gcd==1:
    print("setwise coprime")
    return 1

n=int(input())
l=[int(x) for i in input().split()]

x=fun(l)
if x!=1:
  print("not coprime")

Submission status: Runtime Error

Solution code:

import math
search_list = []

def get_primenumber(search_list):#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
    number= search_list[-1]-1
    while search_list[0] <= math.sqrt(number):
#    while search_list[0]**2 <= 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


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

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

if amax==1:
    print("pairwise coprime")
    sys.exit()

if amin!=1:
    bp=enum_div(amin)+[amin]
    bp.sort()
    bp=bp[1:]
    if len(bp)>1:
        bp=get_primenumber(bp)
    for bpi in bp:
        yn=""
        for ai in ap:
            if ai%bpi!=0:
                yn="coprime"
                break
        if yn=="":
            print("not coprime")
            sys.exit()

if n>=78500 :
    print("setwise coprime")
    sys.exit()

aa=[0]*(amax+1)
for ai in ap:
    aa[ai]+=1
    
for pp in range(2,amax+1):
    psum=sum(aa[pp: :pp])
#    print("pp:",pp,psum)
    if psum>=2:
            print("setwise coprime")
            sys.exit()
## max_13.txt ... max_16.txt : "setwise coprime"
print("pairwise coprime")

Submission status: Runtime Error

Solution code:
import math
search_list = []

def get_primenumber(search_list):#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
    number= search_list[-1]-1
    while search_list[0] <= math.sqrt(number):
#    while search_list[0]**2 <= 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


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

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

if amax==1:
    print("pairwise coprime")
    sys.exit()

if amin!=1:
    bp=enum_div(amin)+[amin]
    bp=bp[1:]
    if len(bp)>1:
        bp=get_primenumber(bp)
    for bpi in bp:
        yn=""
        for ai in ap:
            if ai%bpi!=0:
                yn="coprime"
                break
        if yn=="":
            print("not coprime")
            sys.exit()

if n>=78500 :
    print("setwise coprime")
    sys.exit()

aa=[0]*(amax+1)
for ai in ap:
    aa[ai]+=1
    
for pp in range(2,amax+1):
    psum=sum(aa[pp: :pp])
#    print("pp:",pp,psum)
    if psum>=2:
            print("setwise coprime")
            sys.exit()
## max_13.txt ... max_16.txt : "setwise coprime"
print("pairwise coprime")

Submission status: Runtime Error

Solution code:

import math
search_list = []

def get_primenumber(search_list):#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
    number= search_list[-1]
    while search_list[0] <= math.sqrt(number):
#    while search_list[0]**2 <= 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


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

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

if amax==1:
    print("pairwise coprime")
    sys.exit()

if amin!=1:
    bp=enum_div(amin)+[amin]
    bp=bp[1:]
    if len(bp)>1:
        bp=get_primenumber(bp)
    for bpi in bp:
        yn=""
        for ai in ap:
            if ai%bpi!=0:
                yn="coprime"
                break
        if yn=="":
            print("not coprime")
            sys.exit()

if n>=78500 :
    print("setwise coprime")
    sys.exit()

aa=[0]*(amax+1)
for ai in ap:
    aa[ai]+=1
    
for pp in range(2,amax+1):
    psum=sum(aa[pp: :pp])
#    print("pp:",pp,psum)
    if psum>=2:
            print("setwise coprime")
            sys.exit()
## max_13.txt ... max_16.txt : "setwise coprime"
print("pairwise coprime")

Submission status: Runtime Error

Solution code:
search_list = []

def get_primenumber(search_list):#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):
    number= search_list[-1]+1
    while search_list[0]**2 <= 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


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

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

if amax==1:
    print("pairwise coprime")
    sys.exit()

if amin!=1:
    bp=enum_div(amin)+[amin]
    bp=bp[1:]
    if len(bp)>1:
        bp=get_primenumber(bp)
    for bpi in bp:
        yn=""
        for ai in ap:
            if ai%bpi!=0:
                yn="coprime"
                break
        if yn=="":
            print("not coprime")
            sys.exit()

if n>=78500 :
    print("setwise coprime")
    sys.exit()

aa=[0]*(amax+1)
for ai in ap:
    aa[ai]+=1
    
for pp in range(2,amax+1):
    psum=sum(aa[pp: :pp])
#    print("pp:",pp,psum)
    if psum>=2:
            print("setwise coprime")
            sys.exit()
## max_13.txt ... max_16.txt : "setwise coprime"
print("pairwise coprime")

Submission status: Runtime Error

Solution code:

search_list = []

def get_primenumber(search_list):#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):
    number= search_list[-1]
    while search_list[0]**2 <= 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


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

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

if amax==1:
    print("pairwise coprime")
    sys.exit()

if amin!=1:
    bp=enum_div(amin)+[amin]
    bp=bp[1:]
    if len(bp)>1:
        bp=get_primenumber(bp)
    for bpi in bp:
        yn=""
        for ai in ap:
            if ai%bpi!=0:
                yn="coprime"
                break
        if yn=="":
            print("not coprime")
            sys.exit()

if n>=78500 :
    print("setwise coprime")
    sys.exit()

aa=[0]*(amax+1)
for ai in ap:
    aa[ai]+=1
    
for pp in range(2,amax+1):
    psum=sum(aa[pp: :pp])
#    print("pp:",pp,psum)
    if psum>=2:
            print("setwise coprime")
            sys.exit()
## max_13.txt ... max_16.txt : "setwise coprime"
print("pairwise coprime")

Submission status: Runtime Error

Solution code:
search_list = []

def get_primenumber(search_list):#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):
    while search_list[0]**2 <= search_list[-1]:
      #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


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

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

if amax==1:
    print("pairwise coprime")
    sys.exit()

if amin!=1:
    bp=enum_div(amin)+[amin]
    bp=bp[1:]
    if len(bp)>1:
        bp=get_primenumber(bp)
    for bpi in bp:
        yn=""
        for ai in ap:
            if ai%bpi!=0:
                yn="coprime"
                break
        if yn=="":
            print("not coprime")
            sys.exit()

if n>=78500 :
    print("setwise coprime")
    sys.exit()

aa=[0]*(amax+1)
for ai in ap:
    aa[ai]+=1
    
for pp in range(2,amax+1):
    psum=sum(aa[pp: :pp])
#    print("pp:",pp,psum)
    if psum>=2:
            print("setwise coprime")
            sys.exit()
## max_13.txt ... max_16.txt : "setwise coprime"
print("pairwise coprime")

Submission status: Runtime Error

Solution code:

search_list = []

def get_primenumber(search_list):#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):
    while search_list[0]**2 <= search_list[-1]:
      #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


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

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

if amax==1:
    print("pairwise coprime")
    sys.exit()

if amin!=1:
    bp=enum_div(amin)+[amin]
    bp=bp[1:]
    if len(bp)>:
        bp=get_primenumber(bp)
    for bpi in bp:
        yn=""
        for ai in ap:
            if ai%bpi!=0:
                yn="coprime"
                break
        if yn=="":
            print("not coprime")
            sys.exit()

if n>=78500 :
    print("setwise coprime")
    sys.exit()

aa=[0]*(amax+1)
for ai in ap:
    aa[ai]+=1
    
for pp in range(2,amax+1):
    psum=sum(aa[pp: :pp])
#    print("pp:",pp,psum)
    if psum>=2:
            print("setwise coprime")
            sys.exit()
## max_13.txt ... max_16.txt : "setwise coprime"
print("pairwise coprime")

Submission status: Runtime Error

Solution code:

search_list = []

def get_primenumber(search_list):#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):
    while search_list[0]**2 <= search_list[-1]:
      #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


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

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

if amax==1:
    print("pairwise coprime")
    sys.exit()

if amin!=1:
    bp=enum_div(amin)+[amin]
    bp=bp[1:]
    bp=get_primenumber(bp)
    for bpi in bp:
        yn=""
        for ai in ap:
            if ai%bpi!=0:
                yn="coprime"
                break
        if yn=="":
            print("not coprime")
            sys.exit()

if n>=78500 :
    print("setwise coprime")
    sys.exit()

aa=[0]*(amax+1)
for ai in ap:
    aa[ai]+=1
    
for pp in range(2,amax+1):
    psum=sum(aa[pp: :pp])
#    print("pp:",pp,psum)
    if psum>=2:
            print("setwise coprime")
            sys.exit()
## max_13.txt ... max_16.txt : "setwise coprime"
print("pairwise coprime")

Submission status: Runtime Error

Solution code:
#!/usr/bin/env pypy3
# N,M = map(int,sys.stdin.readline().split())
# a = tuple(map(int,sys.stdin.readline().split())) # single line with multi param
# a = tuple(int(sys.stdin.readline()) for _ in range(N)) # multi line with single param
# a = tuple(tuple(map(int,sys.stdin.readline().rstrip().split())) for _ in range(N)) # multi line with multi param
# s = sys.stdin.readline().rstrip()
# N = int(sys.stdin.readline())
# INF = float("inf")
import math,sys

n = int(sys.stdin.readline())
a = tuple(map(int,sys.stdin.readline().split()))
#n = int(input())
#a = list(map(int,input().split()))
g = math.gcd(a[0],a[1])
for i in range(2,n):
    g = math.gcd(g,a[i])
M = max(a)
acc = a[0]
for i in range(n):
    acc = math.gcd(acc,a[i])
if acc != 1:
    print("not coprime")
    exit()

LIMIT=max(a)
minPrime = [0]*(LIMIT+1)
minPrime[1] = 1
def make():
    for i in range(2,LIMIT+1):
        if minPrime[i] == 0:
            minPrime[i] = i
            #print(i)
            for j in range(i+i,LIMIT+1,i):
                #print(i,j)
                if minPrime[j] == 0:
                    minPrime[j] = i
make()
def factrial(N):
     ret = []
     while minPrime[N] != N:
         ret.append(minPrime[N])
         N = N//minPrime[N]
     if N != 1:
         ret.append(N)
     return ret

judge = set([])
pc = True

for e in a:
    if not pairwise:
        break
    asf = set(factrial(e))
    if judge & asf != set():
        pc = False
    judge |= asf
    #judge = judge | asf #too slow
if pc:
    print("pairwise coprime")
elif g == 1:
    print("setwise coprime")
else:
    print("not coprime")

Submission status: Runtime Error

Solution code:
from math import gcd
n = int(input())
s = list(map(int, input().split()))
s.sort()
dp = [0] * ((10 ** 6) + 100)

res = s[0]
for ss in s:
    dp[ss] += 1
    lf res != 1:
      continue
    else:
      res = gcd(res, ss)

A = max(s)
pairwise = True
setwise = (res == 1)

for i in range(2, A + 1):
    cnt = 0
    for j in range(i, A + 1, i):
        cnt += dp[j]
    if cnt > 1:
        pairwise = False
        break

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

Submission status: Runtime Error

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


import math

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

#p=get_primenumber(79000)
p=get_primenumber(amax)

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

if amax==1:
    print("pairwise coprime")
    sys.exit()

if amin!=1:
    bp=enum_div(amin)+[amin]
    bp=bp[1:]
    for bpi in bp:
        yn=""
        for ai in ap:
            if ai%bpi!=0:
                yn="coprime"
                break
        if yn=="":
            print("not coprime")
            sys.exit()

if n>=78500 :
    print("setwise coprime")
    sys.exit()

aa=[0]*(amax+1)
for ai in ap:
    aa[ai]+=1
    
for pp in range(2,amax+1):
#for pp in p:
    psum=0
    for pi in range(pp,amax+1,pp):
        psum+=aa[pi]
#    psum=sum(aa[pp: :pp])
#    print("pp:",pp,psum)
    if psum>=2:
            print("setwise coprime")
            sys.exit()
## max_13.txt ... max_16.txt : "setwise coprime"
print("pairwise coprime")

Submission status: Runtime Error

Solution code:
import math
from functools import reduce
from collections import deque

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


def gcd_list(numbers):
    return reduce(math.gcd, numbers)


max_A = max(A)
# エラトステネスの篩により素数を高速で求める
# そのかんにある数値がふるい落とされたその素数をメモしておく

D = [0] * (max_A + 1)
primes = list(range(2, max_A + 1))
prime = deque()
for i in range(max_A):
    if len(primes) == 0:
        break
    first = primes[0]
    prime.append(first)
    new_prime = deque()
    for j in range(len(primes)):
        if primes[j] % first == 0:
            D[primes[j]] = first
            continue
        else:
            new_prime.append(primes[j])

    primes = new_prime

# print(prime)
# print(D)

pairwise = True
check = [0] * (max_A + 1)
new_A = A[:]
for i in range(N):
    min_prime = D[new_A[i]]
    check[min_prime] += 1
    while True:
        new_A[i] //= min_prime
        if new_A[i] == 1:
            break

    if max(check) > 1:
        pairwise = False
        break

if pairwise:
    print('pairwise coprime')
else:
    if gcd_list(A) == 1:
        print('setwise coprime')
    else:
        print('not coprime')

Submission status: Runtime Error

Solution code:
import fractions
from functools import reduce

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


def gcd_list(numbers):
    return reduce(fractions.gcd, numbers)


# print(gcd_list(A))

max_A = max(A)
# エラトステネスの篩により素数を高速で求める
# そのかんにある数値がふるい落とされたその素数をメモしておく

D = [0] * (max_A + 1)
primes = list(range(2, max_A + 1))
prime = []
for i in range(max_A):
    if len(primes) == 0:
        break
    first = primes[0]
    prime.append(first)
    new_prime = []
    for j in range(len(primes)):
        if primes[j] % first == 0:
            D[primes[j]] = first
            continue
        else:
            new_prime.append(primes[j])

    primes = new_prime

# print(prime)
# print(D)

pairwise = True
check = [0] * (max_A + 1)
new_A = A[:]
for i in range(N):
    min_prime = D[new_A[i]]
    check[min_prime] += 1
    while True:
        new_A[i] //= min_prime
        if new_A[i] == 1:
            break

    if max(check) > 1:
        pairwise = False
        break

if pairwise:
    print('pairwise coprime')
else:
    if gcd_list(A) == 1:
        print('setwise coprime')
    else:
        print('not coprime')

Submission status: Runtime Error

Solution code:
import math
from functools import reduce

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


def gcd_list(numbers):
    return reduce(math.gcd, numbers)


# print(gcd_list(A))

max_A = max(A)
# エラトステネスの篩により素数を高速で求める
# そのかんにある数値がふるい落とされたその素数をメモしておく

D = [0] * (max_A + 1)
primes = list(range(2, max_A + 1))
prime = []
for i in range(max_A):
    if len(primes) == 0:
        break
    first = primes[0]
    prime.append(first)
    new_prime = []
    for j in range(len(primes)):
        if primes[j] % first == 0:
            D[primes[j]] = first
            continue
        else:
            new_prime.append(primes[j])

    primes = new_prime

# print(prime)
# print(D)

pairwise = True
check = [0] * (max_A + 1)
new_A = A[:]
for i in range(N):
    min_prime = D[new_A[i]]
    check[min_prime] += 1
    while True:
        new_A[i] //= min_prime
        if new_A[i] == 1:
            break

    if max(check) > 1:
        pairwise = False
        break

if pairwise:
    print('pairwise coprime')
else:
    if gcd_list(A) == 1:
        print('setwise coprime')
    else:
        print('not coprime')

Submission status: Runtime Error

Solution code:
#!/usr/bin/env pypy3
# N,M = map(int,sys.stdin.readline().split())
# a = tuple(map(int,sys.stdin.readline().split())) # single line with multi param
# a = tuple(int(sys.stdin.readline()) for _ in range(N)) # multi line with single param
# a = tuple(tuple(map(int,sys.stdin.readline().rstrip().split())) for _ in range(N)) # multi line with multi param
# s = sys.stdin.readline().rstrip()
# N = int(sys.stdin.readline())
# INF = float("inf")
import math

n = int(sys.stdin.readline())
a = tuple(map(int,sys.stdin.readline().split()))
#n = int(input())
#a = list(map(int,input().split()))
g = math.gcd(a[0],a[1])
for i in range(2,n):
    g = math.gcd(g,a[i])
M = max(a)
acc = a[0]
for i in range(N):
    acc = math.gcd(acc,a[i])
if acc != 1:
    print("not coprime")
    exit()

LIMIT=max(a)
minPrime = [0]*(LIMIT+1)
minPrime[1] = 1
def make():
    for i in range(2,LIMIT+1):
        if minPrime[i] == 0:
            minPrime[i] = i
            #print(i)
            for j in range(i+i,LIMIT+1,i):
                #print(i,j)
                if minPrime[j] == 0:
                    minPrime[j] = i
make()
def factrial(N):
     ret = []
     while minPrime[N] != N:
         ret.append(minPrime[N])
         N = N//minPrime[N]
     if N != 1:
         ret.append(N)
     return ret

judge = set([])
pc = True

for i in a:
    if not pc:
        break
    asf = set(factrial(i))

    if judge & asf != set():
        pc = False
    judge |= asf
if pc:
    print("pairwise coprime")
elif g == 1:
    print("setwise coprime")
else:
    print("not coprime")

Submission status: Runtime Error

Solution code:
#!/usr/bin/env pypy3
# N,M = map(int,sys.stdin.readline().split())
# a = tuple(map(int,sys.stdin.readline().split())) # single line with multi param
# a = tuple(int(sys.stdin.readline()) for _ in range(N)) # multi line with single param
# a = tuple(tuple(map(int,sys.stdin.readline().rstrip().split())) for _ in range(N)) # multi line with multi param
# s = sys.stdin.readline().rstrip()
# N = int(sys.stdin.readline())
# INF = float("inf")
import sys,collections

N = int(sys.stdin.readline())
a = tuple(map(int,sys.stdin.readline().split())) # single line with multi param

from math import gcd
import math
acc = a[0]
LIMIT=max(a)
minPrime = [0]*(LIMIT+1)
#minPrime[1] = 1
count = 0
for i in range(2,LIMIT+1):
    if minPrime[i] == 0:
        count += 1
        j = i
        while j <= LIMIT:
            if minPrime[j] == 0:
                minPrime[j] = i
            j += i
#print(minPrime)
def factrial(N):
    ret = []
    while minPrime[N] != N:
        ret.append(minPrime[N])
        N = N//minPrime[N]
    if N != 1:
        ret.append(N)
    return ret

for i in range(N):
    acc = gcd(acc,a[i])
if acc != 1:
    print("not coprime")
    exit()

pairwise = True
# facts = [set(factrial(e)) for e in a]
p = set() #all prime
#s = set(factrial(a[0])) # pair prime
for e in a:
    if not pairwise:
        break
    f = set(factrial(e))
    # s = s & f
    if p & f != set():
        pairwise = False
    p = p | f
#print(p,s,pairwise)

if pairwise:
    print("pairwise coprime")
else:
    print("setwise coprime")
# for s:
#     acc = math.gcd(acc,a[i])
# if acc != 1:
#     print("not coprime")
#     exit()
# print("pairwise coprime")
# for i in range(N):
#     for j in range(i+1,N):
#         b = gcd(a[i],a[j])
#         if b != 1:
#             print("setwise coprime")
#             exit()
# if pairwise == True:
#     print("pairwise coprime")
# else:
#     print("not coprime")