qyliang/CodeNanoFix huggingface dataset:
Buggy code:
import math

def divisorGenerator(n):
    large_divisors = []
    for i in range(1, int(math.sqrt(n) + 1)):
        if n % i == 0:
            yield i
            if i*i != n:
                large_divisors.append(n // i)
    for divisor in reversed(large_divisors):
        yield divisor

if __name__ == '__main__':

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

    gcd_ = math.gcd(A[0], A[1])
    for i in range(2, len(A)):
        gcd_ = math.gcd(gcd_, A[i])

    set_wise = False
    if gcd_ == 1:
        set_wise = True
    if not(set_wise):
        print("not coprime")
    else:
        pairwise = False
        divs = dict()
        for i in A:
            res = list(divisorGenerator(i))
            for el in res:
                if el != 1:
                    if not(el in divs):
                        divs[el] = 0
                    divs[el] += 1
        for value in divs.values():
            if value == 1:
                pairwise = True
        if pairwise:
            print("pairwise coprime")
        else:
            print("set coprime")




Fixed code:
import math


def divisorGenerator(n):

    large_divisors = []
    for i in range(1, int(math.sqrt(n) + 1)):
        if n % i == 0:
            yield i
            if i*i != n:
                large_divisors.append(n // i)
    for divisor in reversed(large_divisors):
        yield divisor

if __name__ == '__main__':

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

    gcd_ = math.gcd(A[0], A[1])
    for i in range(2, len(A)):
        gcd_ = math.gcd(gcd_, A[i])

    set_wise = False
    if gcd_ == 1:
        set_wise = True
    if not(set_wise):
        print("not coprime")
    else:
        pairwise = True
        divs = dict()
        for i in A:
            res = list(divisorGenerator(i))
            for el in res:
                if el != 1:
                    if not(el in divs):
                        divs[el] = 0
                    divs[el] += 1
                    if divs[el] > 1:
                        print("setwise coprime")
                        exit()
        print("pairwise coprime")
        # for value in divs.values():
        #     if value > 1:
        #         pairwise = False
        #         break
        # if pairwise:
        #     print("pairwise coprime")
        # else:
        #
        #
Buggy code:
import math

def eratosthenes():
    erat = [0 for _ in range(max_a+1)]
    lim = int(math.sqrt(max_a))
    pair = True
    for i in range(2, lim+1):
        cnt = 0
        if not erat[i]:
            for res in range(i, max_a+1, i):
                if res in set_a:
                    cnt += 1
                erat[res] = i
                if cnt > 1:
                    pair = False
                    break
        if not pair:
            break
    return pair


n = int(input())
a = [int(x) for x in input().split()]
max_a = max(a)
set_a = set(a)

if eratosthenes() and len(set_a) == n - (a.count(1)-1):
    print('pairwise coprime')
else:
    res = a[0]
    for i in range(n):
        res = math.gcd(res, a[i])
    if res == 1:
        print('setwise coprime')
    else:
        print('not coprime')

Fixed code:
import math

def eratosthenes():
    erat = [0 for _ in range(max_a+1)]
    #lim = int(math.sqrt(max_a))
    pair = True
    #for i in range(2, lim+1):
    for i in range(2, max_a+1):
        cnt = 0
        if not erat[i]:
            for res in range(i, max_a+1, i):
                if res in set_a:
                    cnt += 1
                erat[res] = i
                if cnt > 1:
                    pair = False
                    break
        if not pair:
            break
    return pair


n = int(input())
a = [int(x) for x in input().split()]
max_a = max(a)
set_a = set(a)

if eratosthenes() and len(set_a) == n - max(0, a.count(1)-1):
    print('pairwise coprime')
else:
    res = a[0]
    for i in range(n):
        res = math.gcd(res, a[i])
    if res == 1:
        print('setwise coprime')
    else:
        print('not coprime')
Buggy code:
from collections import *
def gcd(a,b):
    if a%b==0:return(b)
    else:return(gcd(b,a%b))

def soinsuu(n):
    visited=defaultdict(int)
    for i in range(2,round(n**.5)+1):
        while n%i==0:
            n//=i
            visited[i]+=1
    if n>1:
        visited[n]+=1
    return(visited)

N=int(input())
A=list(map(int,input().split()))
A=[soinsuu(a) for a in A]
visited=set()
flg=False
for a in A:
    for i in a:
        if i in visited:
            flg=True
            break
        else:
            visited.add(i)

    if flg:
        break
else:
    print("pairwise coprime")
    exit()

visited=soinsuu(A[0])
for a in A[1:]:
    for i in a:
        visited[i]-=data[i]

if [i for i in visited if visited[i]>0]:
    print("not coprime")
else:
    print("setwise coprime")


Fixed code:
from collections import *
def gcd(a,b):
    if a%b==0:return(b)
    else:return(gcd(b,a%b))

def soinsuu(n):
    visited=defaultdict(int)
    for i in range(2,round(n**.5)+1):
        while n%i==0:
            n//=i
            visited[i]+=1
    if n>1:
        visited[n]+=1
    return(visited)

N=int(input())
A=list(map(int,input().split()))
visited=set()
flg=False
for a in A:
    for i in soinsuu(a):
        if i in visited:
            flg=True
            break
        else:
            visited.add(i)

    if flg:
        break
else:
    print("pairwise coprime")
    exit()

n=A[0]
for a in A[1:]:
    n=gcd(n,a)



if n>1:
    print("not coprime")
else:
    print("setwise coprime")
Buggy code:
n=int(input())
A=[int(x) for x in input().split()]

u=10**6+1
C=[0]*u
D=[0]*2+[1]*(u-2)

def e():
  n=4
  while n<u:
    D[n]=0
    n+=2
  i=3
  while i*i<u:
    if D[i]:
      n=i*2
      while n<u:
        D[n]=0
        n+=i
    i+=2

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

for a in A:
  C[a]+=1
e()
for i in [x for x in range(2,u) if D[x]==1]:
  if sum(C[i::i])>1:
    break
else:
  print('pairwise coprime')
  exit()

c=A[0]
for a in A:
  c=gcd(c,a)
  if c==1:
    break
else:
  print('not coprime')
  exit()

print('setwise comprime')


Fixed code:
n=int(input())
A=[int(x) for x in input().split()]

u=10**6+1
C=[0]*u
D=[0]*2+[1]*(u-2)

def e():
  n=4
  while n<u:
    D[n]=0
    n+=2
  i=3
  while i*i<u:
    if D[i]:
      n=i*2
      while n<u:
        D[n]=0
        n+=i
    i+=2

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

for a in A:
  C[a]+=1
e()
for i in [x for x in range(2,u) if D[x]==1]:
  if sum(C[i::i])>1:
    break
else:
  print('pairwise coprime')
  exit()

c=A[0]
for a in A:
  c=gcd(c,a)
  if c==1:
    break
else:
  print('not coprime')
  exit()

print('setwise coprime')
Buggy code:
import sys, math

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 == [] and n != 1:
        arr.append([n, 1])

    return arr

N = int(input())
A = list(map(int, sys.stdin.readline().rsplit()))

ok = True
S = set()
for a in A:
    arr = factorization(a)
    print(arr)
    for b, _ in arr:
        if b in S:
            ok = False
            break
        else:
            S.add(b)
    if ok is False:
        break
if ok:
    print("pairwise coprime")
else:
    tmp = A[0]
    for a in A[1:]:
        tmp = math.gcd(a, tmp)
    if tmp != 1:
        print("not coprime")
    else:
        print("setwise coprime")


Fixed code:
import sys, math

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 == [] and n != 1:
        arr.append([n, 1])

    return arr

N = int(input())
A = list(map(int, sys.stdin.readline().rsplit()))

ok = True
S = set()
for a in A:
    arr = factorization(a)
    # print(arr)
    for b, _ in arr:
        if b in S:
            ok = False
            break
        else:
            S.add(b)
    if ok is False:
        break
if ok:
    print("pairwise coprime")
else:
    tmp = A[0]
    for a in A[1:]:
        tmp = math.gcd(a, tmp)
    if tmp != 1:
        print("not coprime")
    else:
        print("setwise coprime")
Buggy code:
def sieve(n):
  is_prime = [True for _ in range(n+1)]
  is_prime[0] = False
  for i in range(2, n+1):
    if is_prime[i-1]:
      j = 2 * i
      while j <= n:
        is_prime[j-1] = False
        j += i
  table = [i for i in range(1, n+1) if is_prime[i-1]]
  return table

N = int(input())
A = list(map(int, input().split()))
Amax = max(A)
lis = [0]*(Amax+1)
for i in range(N):
  lis[A[i]] += 1
table = sieve(Amax)
setwise = False
for t in table:
  p = t
  cnt = 0
  while p<=Amax:
    cnt += lis[p]
    p += t
  if cnt==N:
    print('not comprime')
    break
  if 2<=cnt<N:
    setwise=True
else:
  if setwise==True:
    print('setwise coprime')
  else:
    print('pairwise coprime')


Fixed code:
def sieve(n):
  is_prime = [True for _ in range(n+1)]
  is_prime[0] = False
  for i in range(2, n+1):
    if is_prime[i-1]:
      j = 2 * i
      while j <= n:
        is_prime[j-1] = False
        j += i
  table = [i for i in range(1, n+1) if is_prime[i-1]]
  return table

N = int(input())
A = list(map(int, input().split()))
Amax = max(A)
lis = [0]*(Amax+1)
for i in range(N):
  lis[A[i]] += 1
table = sieve(Amax)
setwise = False
for t in table:
  p = t
  cnt = 0
  while p<=Amax:
    cnt += lis[p]
    p += t
  if cnt==N:
    print('not coprime')
    break
  if 2<=cnt<N:
    setwise=True
else:
  if setwise==True:
    print('setwise coprime')
  else:
    print('pairwise coprime')
Buggy code:
n,a=int(input()),list(map(int,input().split()))
g=0
from math import gcd
for i in a:g=gcd(i,g)
if g!=1:print("not coprime")
else:

    primes=list(range(10**6))
    primes[0]=primes[1]=0
    for i in range(2,10**6):
        if primes[i]==i:
            for j in range(2*i,10**6,i):primes[j]=i
    ps=set()
    for x in a:
        while x !=1:
            t=primes[x]
            if t in ps:print("setwise coprime");exit()
            ps.add(t)
            x//=t
    print("pairwise coprime")

Fixed code:
n,a=int(input()),list(map(int,input().split()))
g=0
from math import gcd
for i in a:g=gcd(i,g)
if g!=1:print("not coprime")
else:

    primes=list(range(10**6+1))
    primes[0]=primes[1]=0
    for i in range(2,10**6+1):
        if primes[i]==i:
            for j in range(2*i,10**6,i):primes[j]=i
    ps=set()
    for x in a:
        while x !=1:
            t=primes[x]
            if t in ps:print("setwise coprime");exit()
            ps.add(t)
            while x%t==0:x//=t
    print("pairwise coprime")
Buggy code:
import sys


def input():
    return sys.stdin.readline().rstrip()

def euc(a,b):

    while b!=0:
        a,b =b,a%b

    return a

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

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

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



def main():

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

    PS =set()

    current =A[0]
    for i in range(N-1):
        current =euc(current,A[i+1])
        if current ==1:
            break

    else:
        print("not coprime")
        exit()
    exit()



    for i in range(N):
        if A[i]==1:
            continue
        aa =factorization(A[i])
        for i in aa:
            if i in PS:
                print("setwise coprime")
                exit()
            else:
                PS.add(i)

    print("pairwise coprime")
    exit()



if __name__ == "__main__":
    main()


Fixed code:
import sys


def input():
    return sys.stdin.readline().rstrip()

def euc(a,b):

    while b!=0:
        a,b =b,a%b

    return a

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

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

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



def main():

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

    PS =set()

    current =A[0]
    for i in range(N-1):
        current =euc(current,A[i+1])
        if current ==1:
            break

    else:
        print("not coprime")
        exit()


    for i in range(N):
        if A[i]==1:
            continue
        aa =factorization(A[i])
        for i in aa:
            if i in PS:
                print("setwise coprime")
                exit()
            else:
                PS.add(i)

    print("pairwise coprime")
    exit()



if __name__ == "__main__":
    main()
Buggy code:
import math as mt
n=int(input())
l=list(map(int,input().split()))
gd=l[0]
sv=[0]*(10**6+1)
for i in range(2,len(sv)+1):
  if not sv[i]:
    sv[i]=i
    for j in range(2*i,len(sv),i):
      sv[j]=i
an="not coprime"
for i in range(n):
      gd=mt.gcd(gd,l[i])
if gd!=1:
	print(an)
else:
    an="setwise coprime"
    pos=1
    vis=[0]*(10**6+2)
    for i in range(n):
      cr=l[i]
      while cr>1:
          dv=sv[cr]
          if vis[dv]:
            pos=0;break
          while cr%dv==0:
            cr//=dv
          vis[dv]=1
    if pos:
      an="pairwise coprime"
    print(an)


Fixed code:
import math as mt
n=int(input())
l=list(map(int,input().split()))
gd=l[0]
sv=[0]*(10**6+1)
for i in range(2,len(sv)):
  if not sv[i]:
    sv[i]=i
    for j in range(2*i,len(sv),i):
      sv[j]=i
an="not coprime"
for i in range(n):
      gd=mt.gcd(gd,l[i])
if gd!=1:
	print(an)
else:
    an="setwise coprime"
    pos=1
    vis=[0]*(10**6+2)
    for i in range(n):
      cr=l[i]
      while cr>1:
          dv=sv[cr]
          if vis[dv]:
            pos=0;break
          while cr%dv==0:
            cr//=dv
          vis[dv]=1
    if pos:
      an="pairwise coprime"
    print(an)
Buggy code:
import math
from functools import reduce

n = int(input())
a_list = list(map(int, input().split()))
max = a_list[n - 1]
memo = [0] * max

for a in a_list:
    memo[a] += 1

for i in range(2, max):
    if sum(memo[i::i]) > 1:
        if reduce(math.gcd, a_list) == 1:
            print("setwise coprime")
            exit()
        else:
            print("not coprime")
            exit()

print("pairwise coprime")


Fixed code:
import math
from functools import reduce

n = int(input())
a_list = list(map(int, input().split()))
max = 10 ** 6 + 1
memo = [0] * max

for a in a_list:
    memo[a] += 1

for i in range(2, max):
    if sum(memo[i::i]) > 1:
        if reduce(math.gcd, a_list) == 1:
            print("setwise coprime")
            exit()
        else:
            print("not coprime")
            exit()

print("pairwise coprime")
Buggy code:
def arrayF(n): 
    F=[0]*(n+1) 
    i=2 
    while i*i<=n:
        if F[i] == 0: 
            k=i*i
            while k <= n:
                if F[k] == 0:
                    F[k] = i
                k += i
        i += 1 
    return F


def factorization(x, F): 
    primeFactors = []
    while F[x] > 0:
        primeFactors.append(F[x])
        x //= F[x] 
    if x != 1:
        primeFactors.append(x)
    return set(primeFactors)

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

amax = max(A)
F  = arrayF(amax)

P = Counter()
P = [0] *  (amax+1)
for a in A:
    for p in factorization(a,  F):
        P[p] += 1
p_max = max(P)
if  p_max <= 1:
    print('pairwise coprime')
elif  p_max <  n:
    print('setwise coprime')
else:
    print('not coprime')

Fixed code:
def arrayF(n): 
    F=[0]*(n+1) 
    i=2 
    while i*i<=n:
        if F[i] == 0: 
            k=i*i
            while k <= n:
                if F[k] == 0:
                    F[k] = i
                k += i
        i += 1 
    return F


def factorization(x, F): 
    primeFactors = []
    while F[x] > 0:
        primeFactors.append(F[x])
        x //= F[x] 
    if x != 1:
        primeFactors.append(x)
    return set(primeFactors)

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

amax = max(A)
F  = arrayF(amax)

P = [0] *  (amax+1)
for a in A:
    for p in factorization(a,  F):
        P[p] += 1
p_max = max(P)
if  p_max <= 1:
    print('pairwise coprime')
elif  p_max <  n:
    print('setwise coprime')
else:
    print('not coprime')
Buggy code:
def main():
    from math import gcd
    from functools import reduce
    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()
    f = 0
    for i in a:
        ps = primes(i)
        if f == 0:
            if b & ps:
                f = 1
                break
    if f > 0 and reduce(gcd, a) != 1:
        f = 2
    
    ans = ["pairwise coprime", "setwise coprime", "not coprime"][f]
    print(ans)


if __name__ == '__main__':
    main()


Fixed code:
def main():
    from math import gcd
    from functools import reduce
    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()
    f = 0
    for i in a:
        ps = primes(i)
        if b & ps:
            f = 1
            break
        b |= ps
    if f > 0 and reduce(gcd, a) != 1:
        f = 2

    ans = ["pairwise coprime", "setwise coprime", "not coprime"][f]
    print(ans)


if __name__ == '__main__':
    main()
Buggy code:
def main():
    n, *a, = map(int, open(0).read().split())
    m = max(a)

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


Fixed 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()
Buggy code:
from collections import defaultdict
from numba import njit

@njit
def get_prime_factors(x):
    out = set()
    if x < 1:
        return out
    while not x%2:
        out.add(2)
        x //= 2
    i = 3
    while i*i <= x:
        if not x%i:
            out.add(i)
            x //= i
        else:
            i += 2
    if x != 1:
        out.add(x)
    return out

@njit
def main():
    n = int(input())
    a = list(map(int, input().split()))
    df = defaultdict(lambda : 0)
    
    
    for ai in a:
        primes = get_prime_factors(ai)
        for prime in primes:
            df[prime] += 1
    if df.values():
        val = max(df.values())
        if val == 1:
            print("pairwise coprime")
        elif val == n:
            print("not coprime")
        else:
            print("setwise coprime")
    else:
        print("pairwise coprime")

if __name__ == "__main__":
    main()


Fixed code:
from collections import defaultdict


def get_prime_factors(x):
    out = set()
    if x < 1:
        return out
    while not x%2:
        out.add(2)
        x //= 2
    i = 3
    while i*i <= x:
        if not x%i:
            out.add(i)
            x //= i
        else:
            i += 2
    if x != 1:
        out.add(x)
    return out


def main():
    n = int(input())
    a = list(map(int, input().split()))
    df = defaultdict(lambda : 0)
    for ai in a:
        primes = get_prime_factors(ai)
        for prime in primes:
            df[prime] += 1
    if df.values():
        val = max(df.values())
        if val == 1:
            print("pairwise coprime")
        elif val == n:
            print("not coprime")
        else:
            print("setwise coprime")
    else:
        print("pairwise coprime")

if __name__ == "__main__":
    main()
Buggy code:
import collections
import sys
input=sys.stdin.readline

def divisors(n):
  ret=[]
  for i in range(2,int(n**0.5)+1):
    if n%i==0:
      ret.append(i)
      while n%i==0:
        n//=i
  return ret

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

n=int(input())
arr=list(map(int,input().split()))
cnt=collections.defaultdict(int)
tmp=arr[0]
for val in arr:
  tmp=gcd(tmp,val)
if tmp==1:
  is_setwise=True
else:
  is_setwise=False
is_pairwise=True
for val in arr:
  divisor=divisors(val)
  for val2 in divisor:
    cnt[val]+=1
    if cnt[val]==2:
      is_pairwise=False
      break
if is_pairwise==True:
  print('pairwise coprime')
elif is_setwise==True:
  print('setwise coprime')
else:
  print('not coprime')

Fixed code:
import collections
import sys
input=sys.stdin.readline

def divisors(n):
  ret=[]
  for i in range(2,int(n**0.5)+1):
    if n%i==0:
      ret.append(i)
      while n%i==0:
        n//=i
  if n!=1:
    ret.append(n)
  return ret

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

n=int(input())
arr=list(map(int,input().split()))
cnt=[False]*(max(arr)+1)
is_pairwise=True
tmp=arr[0]
for val in arr:
  tmp=gcd(tmp,val)
  if is_pairwise==False:
    continue
  divisor=divisors(val)
  for val2 in divisor:
    if cnt[val2]==True:
      is_pairwise=False
      break
    cnt[val2]=True
if tmp==1:
  is_setwise=True
else:
  is_setwise=False
if is_pairwise==True:
  print('pairwise coprime')
elif is_setwise==True:
  print('setwise coprime')
else:
  print('not coprime')