qyliang/CodeNanoFix huggingface dataset:
Buggy code:
import sys
import math

def soinsu(dic, x):
  i = 2
  while i*i <= x:
    if x % i == 0 and i in dic.keys():
      print(i, dic)
      return False
    
    while x % i == 0:
      dic.setdefault(i, 0)
      dic[i] += 1
      x //= i
      
    i += 1
      
      
  if x == 1:
    return True
  
  if x in dic.keys():
    return False
  
  dic.setdefault(x, 1)
  return True
    

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

flag = False
for i in range(n):
  if not soinsu(dic, a[i]):
    flag = True
    break

if not flag:
  print("pairwise coprime")
  sys.exit()
  
tmp = a[0]
for i in range(1,n):
  tmp = math.gcd(tmp, a[i])
  
if tmp == 1:
  print("setwise coprime")
else:
  print("not coprime")

Fixed code:
import sys
import math

def soinsu(dic, x):
  i = 2
  while i*i <= x:
    if x % i == 0 and i in dic.keys():
      return False
    
    while x % i == 0:
      dic.setdefault(i, 0)
      dic[i] += 1
      x //= i
      
    i += 1
      
      
  if x == 1:
    return True
  
  if x in dic.keys():
    return False
  
  dic.setdefault(x, 1)
  return True
    

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

flag = False
for i in range(n):
  if not soinsu(dic, a[i]):
    flag = True
    break

if not flag:
  print("pairwise coprime")
  sys.exit()
  
tmp = a[0]
for i in range(1,n):
  tmp = math.gcd(tmp, a[i])
  
if tmp == 1:
  print("setwise coprime")
else:
  print("not coprime")
Buggy code:
from math import gcd
N = 1000001
sieve = [-1] * (N + 1)
sieve[0] = sieve[1] = 0
for i in range(N + 1):
    if sieve[i] != -1:
        continue
    else:
        index = i * i
        while True:
            if index > N:
                break
            sieve[index] = i
            index += i

isCounted = [0] * 1000001
isPairwiseCoprime = True
M = int(input())
A = map(int,input().split())
for i in range(M):
    elem = M[i]
    if elem == 1:
        continue
    primeList = []
    while sieve[elem] != -1:
        primeList.append(sieve[elem])
        elem //= sieve[elem]
    primeList.append(elem)
    for elem1 in primeList:
        if isCounted[elem1] != 0:
            isPairwiseCoprime = False
            break
    if not isPairwiseCoprime:
        break
    for elem1 in primeList:
        isCounted[elem1] += 1
if isPairwiseCoprime:
    print("pairwise coprime")
else:
    curGcd = A[0]
    for elem in A:
        curGcd = gcd(elem,curGcd)
    if curGcd == 1:
        print("setwise coprime")
    else:
        print("not coprime")


Fixed code:
from math import gcd
N = 1000001
sieve = [-1] * (N + 1)
sieve[0] = sieve[1] = 0
for i in range(N + 1):
    if sieve[i] != -1:
        continue
    else:
        index = i * i
        while True:
            if index > N:
                break
            sieve[index] = i
            index += i

isCounted = [0] * 1000001
isPairwiseCoprime = True
M = int(input())
A = list(map(int,input().split()))
for i in range(M):
    elem = A[i]
    if elem == 1:
        continue
    primeList = []
    while sieve[elem] != -1:
        primeList.append(sieve[elem])
        elem //= sieve[elem]
    primeList.append(elem)
    for elem1 in primeList:
        if isCounted[elem1] != 0:
            isPairwiseCoprime = False
            break
    if not isPairwiseCoprime:
        break
    for elem1 in primeList:
        isCounted[elem1] += 1
if isPairwiseCoprime:
    print("pairwise coprime")
else:
    curGcd = A[0]
    for elem in A:
        curGcd = gcd(elem,curGcd)
    if curGcd == 1:
        print("setwise coprime")
    else:
        print("not coprime")
Buggy code:
import math
N = int(input())
A = list(map(int, input().split()))

maxA = max(A) + 1

C = [0] * maxA

g = 0

for a in A:
    C[a] += 1
    g = math.gcd(g, a)

pairwise = True

for i in range(2, maxA):
    cnt = 0
    for j in range(i, maxA, i):
        cnt += C[j]

    if cnt > 1:
        pairwise = False

if pairwise:
    print("pairwise comrime")
    exit()

if g == 1:
    print("setwise coprime")

else:
    print("not coprime")

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

maxA = max(A) + 1

C = [0] * maxA

g = 0

for a in A:
    C[a] += 1
    g = math.gcd(g, a)

pairwise = True

for i in range(2, maxA):
    cnt = 0
    for j in range(i, maxA, i):
        cnt += C[j]

    if cnt > 1:
        pairwise = False

if pairwise:
    print("pairwise coprime")
    exit()

if g == 1:
    print("setwise coprime")

else:
    print("not coprime")
Buggy code:
from collections import Counter
def prime_factorize(n):
    a = set()
    while n % 2 == 0:
        a.add(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.add(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.add(n)
    return a
n = int(input())
input_list = list(map(int,input().split()))
num_count = Counter([prime for num in input_list for prime in prime_factorize(num)])
if len(num_count.values())==0:
    print("pairwise coprime")
    exit()
max_appear = max(num_count.values())
if max_appear == 1:
    print("pairwise coprime")
elif max_appear != n:
    print("setwise_coprime")
else:
    print("not coprime")

Fixed code:
from collections import Counter
def prime_factorize(n):
    a = set()
    while n % 2 == 0:
        a.add(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.add(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.add(n)
    return a
n = int(input())
input_list = list(map(int,input().split()))
num_count = Counter([prime for num in input_list for prime in prime_factorize(num)])
if len(num_count.values())==0:
    print("pairwise coprime")
    exit()
max_appear = max(num_count.values())
if max_appear == 1:
    print("pairwise coprime")
elif max_appear != n:
    print("setwise coprime")
else:
    print("not coprime")
Buggy code:
def divplis(N):
    lis = [i for i in range(N+1)]
    for i in range(int(N**0.5+1),1,-1):
        if lis[i] == i:
            lis[i::i] = [i]*(N//i)
    return lis

divp = divplis(10**6+1)
print(divp[:10])
print(divp[-10:])
print(len(divp)-1)
print((len(divp)-1)/divp[-1])
N = int(input())
d = [0]*(10**6+1)
A = [int(i) for i in input().split()]


def pfact(N):
    b = 0
    while N != 1:
        n = divp[N]
        if b != n:
            d[n] += 1
        b = n
        N = N // n
    return 0
    
for a in A:
    pfact(a)
m = max(d)
if m == 1:
    print("pairwise coprime")
elif m == N:
    print("not coprime")
else:
    print("setwise coprime")


Fixed code:
def divplis(N):
    lis = [i for i in range(N+1)]
    for i in range(int(N**0.5+1),1,-1):
        if lis[i] == i:
            lis[i::i] = [i]*(N//i)
    return lis

divp = divplis(10**6+1)
N = int(input())
d = [0]*(10**6+1)
A = [int(i) for i in input().split()]


def pfact(N):
    b = 0
    while N != 1:
        n = divp[N]
        if b != n:
            d[n] += 1
        b = n
        N = N // n
    return 0
    
for a in A:
    pfact(a)
m = max(d)
if m <= 1:
    print("pairwise coprime")
elif m == N:
    print("not coprime")
else:
    print("setwise coprime")
Buggy code:
n=int(input())
a=list(map(int,input().split()))

import math 

ans = a[0]
for i in range(1, n):
    ans = math .gcd(ans, a[i])

if ans!=1:
    print("not coprime")
    exit()
else:
    checked=[0]*(int(max(a)**(0.5))+100)

    for item in a:

        for j in range(2,int(item**0.5)+1):
            if item%j==0 and j*j<=item:
                if checked[j]==0:
                    checked[j]+=1
                else:
                    print(item,j,checked)
                    #print("setwise coprime")
                    exit()
print("pairwise coprime")





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

import math 

ans = a[0]
for i in range(1, n):
    ans = math .gcd(ans, a[i])

if ans!=1:
    #print(ans)
    print("not coprime")
    exit()
else:
    checked=[0]*(int(max(a))+1)
    #print(checked)
    for item in a:
        for j in range(1,int(item**0.5)+1):
            if item%j==0 and j*j<=item:
                if checked[j]==0:
                    if j!=1:
                        checked[j]+=1
                    
                    if j*j!=item:
                        if checked[item//j]==0:
                            checked[item//j]+=1
                        else:
                            #print(item,j,checked)
                            print("setwise coprime")
                            exit() 
                else:
                    #print(item,j,checked)
                    print("setwise coprime")
                    exit()
print("pairwise coprime")
Buggy code:
def gcd(x, y):
    if x < y:
        x, y = y, x
    while x % y != 0:
        x, y = y, x % y
    return y


def gcd3(ll):
    ans = ll[0]
    for i in range(1, len(ll)):
        ans = gcd(ans, ll[i])
    return ans


D = {}
def prime_div(n, A):
    if len(D) == 0:
        for a in range(2, A + 1, 2):
            D[a] = 2
        for a in range(3, A + 1):
            if a in D:
                continue
            now = a
            while now <= A:
                if now not in D:
                    D[now] = a
                now += a * 2
    result = []
    while n > 1:
        result.append(D[n])
        n = n // D[n]
    return result
    

def checkPairwise(ll):
    dic = {}
    for n in ll:
        primes = prime_div(n, 1000000)
        for p in primes:
            if p not in dic:
                dic[p] = 1
            else:
                return False
    return True


def main():
    N = int(input())
    A = [int(n) for n in input().split(" ")]
    a1 = checkPairwise(A)
    if a1:
        print("pairwise coprime")
    else:
        a2 = gcd3(A)
        if a2 == 1:
            print("setwise coprime")
        else:
            print("not coprime")


if __name__ == "__main__":
    main()

Fixed code:
def gcd(x, y):
    if x < y:
        x, y = y, x
    while x % y != 0:
        x, y = y, x % y
    return y


def gcd3(ll):
    ans = ll[0]
    for i in range(1, len(ll)):
        ans = gcd(ans, ll[i])
    return ans


D = {}
def prime_div(n, A):
    if len(D) == 0:
        for a in range(2, A + 1, 2):
            D[a] = 2
        for a in range(3, A + 1):
            if a in D:
                continue
            now = a
            while now <= A:
                if now not in D:
                    D[now] = a
                now += a * 2
    result = []
    while n > 1:
        result.append(D[n])
        n = n // D[n]
    return result
    

def checkPairwise(ll):
    dic = {}
    for n in ll:
        primes = list(set(prime_div(n, 1000000)))
        # print(n, primes)
        for p in primes:
            if p not in dic:
                dic[p] = 1
            else:
                return False
    return True


def main():
    N = int(input())
    A = [int(n) for n in input().split(" ")]
    a1 = checkPairwise(A)
    if a1:
        print("pairwise coprime")
    else:
        a2 = gcd3(A)
        if a2 == 1:
            print("setwise coprime")
        else:
            print("not coprime")


if __name__ == "__main__":
    main()
Buggy code:
from math import gcd
MAX = 10**6

sieve = [i for i in range(MAX+1)]

p = 2
while p * p <= MAX:
    if sieve[p] == p:
        for i in range(p*2, MAX+1, p):
            if sieve[i] == i:
                sieve[i] = p
    p += 1


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

for a in A:
    tmp = set()
    b = a
    while b != 1:
        tmp.add(sieve[b])
        b //= sieve[b]
    pf.append(tmp)


soin = [0] * (10 ** 6 + 1)
for f in pf:
    for n in f:
        soin[n] += 1

if max(soin[2:]) <= 1:
    print('pairwise coprime')
    exit()


setwise = a[0]

for a in A:
    setwise = gcd(setwise, a)
    
if setwise == 1:
    print('setwise coprime')
else:
    print('not coprime')

Fixed code:
from math import gcd
MAX = 10**6

sieve = [i for i in range(MAX+1)]

p = 2
while p * p <= MAX:
    if sieve[p] == p:
        for i in range(p*2, MAX+1, p):
            if sieve[i] == i:
                sieve[i] = p
    p += 1


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

for a in A:
    tmp = set()
    b = a
    while b != 1:
        tmp.add(sieve[b])
        b //= sieve[b]
    pf.append(tmp)


soin = [0] * (10 ** 6 + 1)
for f in pf:
    for n in f:
        soin[n] += 1

if max(soin[2:]) <= 1:
    print('pairwise coprime')
    exit()


setwise = A[0]

for a in A:
    setwise = gcd(setwise, a)
    
if setwise == 1:
    print('setwise coprime')
else:
    print('not coprime')
Buggy code:
import math
import numpy as np

class SieveOfEratosthenes:
    def __init__(self, V):
        self.is_prime = np.ones(V + 1, dtype=bool)
        self.is_prime[4::2] = False
        self.is_prime[9::3] = False
        self.is_prime[25::5] = False
        self.primes = [2, 3, 5]
        for i in range(7, V + 1, 2):
            if self.is_prime[i]:
                self.primes.append(i)
                self.is_prime[i * i::i] = False
    
    def factorize(self, x):
        assert x >= 1
        if x == 1:
            return [(1, 1)]
        result = []
        for p in self.primes:
            exp = 0
            while x % p == 0:
                exp += 1
                x = x // p
            if exp > 0:
                result.append((p, exp))
            if p * p > x:
                break
        if x > 1:
            result.append((x, 1))
        return result


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

    if all(a == 1 for a in A):
        return 'pairwise coprime'

    gcd_all = 0
    for a in A:
        gcd_all = math.gcd(gcd_all, a)

    if gcd_all > 1:
        return 'not coprime'
    
    sieve = SieveOfEratosthenes(max(A))
    used_primes = set()
    for a in A:
        if a != 1:
            factors = sieve.factorize(a)
            for (p, e) in factors:
                if p in used_primes:
                    return 'set coprime'
                used_primes.add(p)
    
    return 'pairwise coprime'

print(solve())

Fixed code:
import math
import numpy as np

class SieveOfEratosthenes:
    def __init__(self, V):
        self.is_prime = np.ones(V + 1, dtype=bool)
        self.is_prime[4::2] = False
        self.is_prime[9::3] = False
        self.is_prime[25::5] = False
        self.primes = [2, 3, 5]
        for i in range(7, V + 1, 2):
            if self.is_prime[i]:
                self.primes.append(i)
                self.is_prime[i * i::i] = False
    
    def factorize(self, x):
        assert x >= 1
        if x == 1:
            return [(1, 1)]
        result = []
        for p in self.primes:
            exp = 0
            while x % p == 0:
                exp += 1
                x = x // p
            if exp > 0:
                result.append((p, exp))
            if p * p > x:
                break
        if x > 1:
            result.append((x, 1))
        return result


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

    if all(a == 1 for a in A):
        return 'pairwise coprime'

    gcd_all = 0
    for a in A:
        gcd_all = math.gcd(gcd_all, a)

    if gcd_all > 1:
        return 'not coprime'
    
    sieve = SieveOfEratosthenes(max(A))
    used_primes = set()
    for a in A:
        if a != 1:
            factors = sieve.factorize(a)
            for (p, e) in factors:
                if p in used_primes:
                    return 'setwise coprime'
                used_primes.add(p)
    
    return 'pairwise coprime'

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

g = A[0]
for i in range(1,N):
    g = gcd(g,A[i])

if g>1:
    print("not comprime")
    exit()

MAXN = 10**6 + 9
D = [i for i in range(MAXN+1)]
p = 2
while(p*p <=MAXN):
    if D[p]==p:
        for q in range(2*p,MAXN+1,p):
            if D[q]==q:
                D[q]=p
    p+=1

st = set()
for a in A:
    tmp = set()
    while(a>1):
        tmp.add(D[a])
        a //=D[a]
    for p in tmp:
        if p in st:
            print("setwise coprime")
            exit()
        st.add(p)

print("pairwise coprime") 

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

g = A[0]
for i in range(1,N):
    g = gcd(g,A[i])

if g>1:
    print("not coprime")
    exit()

MAXN = 10**6 + 9
D = [i for i in range(MAXN+1)]
p = 2
while(p*p <=MAXN):
    if D[p]==p:
        for q in range(2*p,MAXN+1,p):
            if D[q]==q:
                D[q]=p
    p+=1

st = set()
for a in A:
    tmp = set()
    while(a>1):
        tmp.add(D[a])
        a //=D[a]
    for p in tmp:
        if p in st:
            print("setwise coprime")
            exit()
        st.add(p)

print("pairwise coprime")
Buggy code:
n = int(input())
a = list(map(int, input().split()))
                                                                                              M = max(a)
biggest_prime = [0] * (M+10)
for i in range(2, M+10):
    if biggest_prime[i] == 0:
        biggest_prime[i] = i
        for j in range(i*i, M+1, i):
            biggest_prime[j] = i

from collections import defaultdict
cntd=defaultdict(int)
for i in range(len(a)):
    num = a[i]
    while num>1:
        p=biggest_prime[num]
        cntd[p]+=1
        while num % p == 0:
            num//=p

flg=False
for c in cntd.values():
    if c==n:
        print("not coprime")
        exit()
    if c>1:
        flg=True
if flg:
    print("setwise coprime")
else:
    print("pairwise coprime")

Fixed code:
n = int(input())
a = list(map(int, input().split()))
M=max(a)
biggest_prime = [0] * (M+10)
for i in range(2, M+10):
    if biggest_prime[i] == 0:
        biggest_prime[i] = i
        for j in range(i*i, M+1, i):
            biggest_prime[j] = i

from collections import defaultdict
cntd=defaultdict(int)
for i in range(len(a)):
    num = a[i]
    while num>1:
        p=biggest_prime[num]
        cntd[p]+=1
        while num % p == 0:
            num//=p

flg=False
for c in cntd.values():
    if c==n:
        print("not coprime")
        exit()
    if c>1:
        flg=True
if flg:
    print("setwise coprime")
else:
    print("pairwise coprime")
Buggy code:
import sys
input = lambda: sys.stdin.readline().rstrip("\r\n")

from math import gcd

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

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

primes = set()

flag = 1

for i in a:
    prime_factors = prime_factorize(i)
    for j in prime_factors:
        if j in primes:
            flag = 0
            break

if flag:
    print('pairwise coprime')
    sys.exit()
            
 
import math
from functools import reduce
 
def gcd(*numbers):
    return abs(reduce(math.gcd, numbers))
 
if gcd(*a) == 1:
    print('setwise coprime')
else:
    print('not coprime')

Fixed code:
import sys
input = lambda: sys.stdin.readline().rstrip("\r\n")

from math import gcd

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

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

primes = set()

flag = 1

for i in a:
    prime_factors = set(prime_factorize(i))
    for j in prime_factors:
        if j in primes:
            flag = 0
        else:
            primes.add(j)


if flag:
    print('pairwise coprime')
    sys.exit()
            
 
import math
from functools import reduce
 
def gcd(*numbers):
    return abs(reduce(math.gcd, numbers))
 
if gcd(*a) == 1:
    print('setwise coprime')
else:
    print('not coprime')
Buggy 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")


Fixed 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
    res = gcd(res, ss)

A = max(s)
pairwise = True

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

if pairwise:
    print("pairwise coprime")
elif res == 1:
    print("setwise coprime")
else:
    print("not coprime")
Buggy code:
max_num = 10**6 + 1
prime = [i for i in range(max_num)]
r2_num = int(max_num**(1/2))+1
for i in range(2, r2_num):
  if prime[i] == i:
    for j in range(i**2, max_num, i):
      if prime[j] == j:
        prime[j] = i
def gcd(a, b): # a >= b
  if a%b == 0:
    return b
  else:
    return gcd(b, a%b)

flg_pairwise = True
flg_setwise = False

n = int(input().rstrip())
a_ls = list(map(int, input().rstrip().split(" ")))
gcd_a = 0
primes_a = []
count_prime = [0 for i in range(max_num)]
for a in a_ls:
  gcd_a = gcd(gcd_a, a)
  if gcd_a == 1:
    flg_setwise = True
  tmp_prime = []
  if flg_pairwise:
    while a > 1:
      p = prime[a]
      if tmp_prime == [] or tmp_prime[-1] != p:
        tmp_prime.append(p)
        a = a//p
    for tp in tmp_prime:
      for pa in primes_a:
        if pa == tp:
          flg_pairwise = False
          break
      if flg_pairwise:
        primes_a.append(tp)
      else:
        break
  if flg_setwise and not flg_pairwise:
    break
if flg_pairwise:
  print("pairwise coprime")
elif flg_setwise:
  print("setwise coprime")
else:
  print("not coprime")

Fixed code:
max_num = 10**6 + 1
prime = [i for i in range(max_num)]
r2_num = int(max_num**(1/2))+1
for i in range(2, r2_num):
  if prime[i] == i:
    for j in range(i**2, max_num, i):
      if prime[j] == j:
        prime[j] = i
def gcd(a, b): # a >= b
  if a%b == 0:
    return b
  else:
    return gcd(b, a%b)

flg_pairwise = True
flg_setwise = False

n = int(input().rstrip())
a_ls = list(map(int, input().rstrip().split(" ")))
gcd_a = 0
primes_a = []
count_prime = [0 for i in range(max_num)]
for a in a_ls:
  gcd_a = gcd(gcd_a, a)
  if gcd_a == 1:
    flg_setwise = True
  tmp_prime = 0
  while a > 1:
    p = prime[a]
    pp = prime[p]
    if p == 0 or pp == 0:
      flg_pairwise = False
      break
    if tmp_prime != p:
      prime[tmp_prime] = 0
      tmp_prime = p
    a = a//p
  if flg_pairwise:
    prime[tmp_prime] = 0
  if flg_setwise and not flg_pairwise:
    break
if flg_pairwise:
  print("pairwise coprime")
elif flg_setwise:
  print("setwise coprime")
else:
  print("not coprime")