qyliang/CodeNanoFix huggingface dataset:
Buggy code:
def main():
    import sys
    input = sys.stdin.buffer.readline
    from math import gcd
    N = int(input())
    A = list(map(int, input().split()))
    g = A[0]
    M = max(A)
    X = [i for i in range(M+1)]
    S = [True for i in range(M+1)]
    S[0] = False
    S[1] = False

    for i in range(1, M+1):
        if S[i]:
            for j in range(i, M+1, i):
                if S[j]:
                    S[j] = False
                    X[j] = i
    flag = True
    s = set()
    for x in A:
        while(X[x] != x):
            if X[x] in s:
                flag = False
                break
            else:
                s.add(X[x])
            x //= X[x]

        if x != 1:
            if x in s:
                flag = False
                break
            s.add(x)
        if flag:
            continue
        else:
            break

    if flag:
        print("pairwise coprime")
    else:
        for x in A[1:]:
            g = gcd(g, x)
        if g == 1:
            print("setwise coprime")

        else:
            print("not coprime")


main()


Fixed code:
def main():
    import sys
    input = sys.stdin.buffer.readline
    from math import gcd
    N = int(input())
    A = list(map(int, input().split()))
    g = A[0]
    M = max(A)
    X = [i for i in range(M+1)]
    S = [True for i in range(M+1)]
    S[0] = False
    S[1] = False

    for i in range(1, M+1):
        if S[i]:
            for j in range(i, M+1, i):
                if S[j]:
                    S[j] = False
                    X[j] = i
    flag = True
    s = set()
    ls = 0
    for x in A:
        tmp = set()
        while(X[x] != 1):
            tmp.add(X[x])
            x //= X[x]
        l = len(tmp)
        s |= tmp
        if len(s) == ls + l:
            ls += l
            continue
        else:
            flag = False
            break

    if flag:
        print("pairwise coprime")
    else:
        for x in A[1:]:
            g = gcd(g, x)
        if g == 1:
            print("setwise coprime")

        else:
            print("not coprime")


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

g = 0
for a in A:
    g = gcd(g,a)
if g > 1:
    print('not coprime')
    exit()

sa = set(A)
if len(sa) < N:
    print('setwise coprime')
    exit()

MAXN = 10**6+10
sieve = [0,0] + [1]*MAXN
p = 2
small_primes = []
while p*p <= MAXN:
    if sieve[p]:
        small_primes.append(p)
        for q in range(2*p,MAXN+1,p):
            sieve[q] = 0
    p += 1

st = set()
for a in A:
    for p in small_primes:
       found = False
        while a%p==0:
            a //= p
            found = True
        if found:
            if p in st:
                print('setwise coprime')
                exit()
            st.add(p)
        if a==1: break
    else:
        if a in st:
            print('setwise coprime')
            exit()
        st.add(a)

print('pairwise coprime')

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

g = 0
for a in A:
    g = gcd(g,a)
if g > 1:
    print('not coprime')
    exit()

sa = set()
for a in A:
    if a==1: continue
    if a in sa:
        print('setwise coprime')
        exit()
    sa.add(a)

MAXN = 10**6+10
sieve = [0,0] + [1]*MAXN
p = 2
small_primes = []
while p*p <= MAXN:
    if sieve[p]:
        small_primes.append(p)
        for q in range(2*p,MAXN+1,p):
            sieve[q] = 0
    p += 1

st = set()
for a in A:
    for p in small_primes:
        found = False
        while a%p==0:
            a //= p
            found = True
        if found:
            if p in st:
                print('setwise coprime')
                exit()
            st.add(p)
        if a==1: break
    else:
        if a in st:
            print('setwise coprime')
            exit()
        st.add(a)

print('pairwise coprime')
Buggy code:
import sys
n = int(input())
a = list(map(int, input().split()))

def prime_decomposition(n):
    i = 2
    table = []
    while i**2 <= n:
        while n % i == 0:
            n //= i
            table.append(i)
        i += 1
    if n > 1: table.append(n)
    return set(table)

pri_0 = prime_decomposition(a[0])
pri_1 = prime_decomposition(a[1])

if len(pri_0&pri_1):
    for i in range(2, n):
        res = prime_decomposition(a[i])
        ans &= res
        if not ans:
            print('setwise coprime')
            sys.exit()
    print('not coprime')

else:
    ans = pri_0 | pri_1
    for i in range(2, n):
        res = prime_decomposition(a[i])
        for i in res:
            if i in ans:
                print('setwise coprime')
                sys.exit()
        ans |= res
    print('pairwise coprime')

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

def prime_decomposition(n):
    i = 2
    table = []
    while i**2 <= n:
        while n % i == 0:
            n //= i
            table.append(i)
        i += 1
    if n > 1: table.append(n)
    return set(table)

pri_0 = prime_decomposition(a[0])
pri_1 = prime_decomposition(a[1])
ans = pri_0&pri_1

if len(ans):
    for i in range(2, n):
        res = prime_decomposition(a[i])
        ans &= res
        if not ans:
            print('setwise coprime')
            sys.exit()
    print('not coprime')

else:
    ans = pri_0 | pri_1
    for i in range(2, n):
        res = prime_decomposition(a[i])
        for i in res:
            if i in ans:
                print('setwise coprime')
                sys.exit()
        ans |= res
    print('pairwise coprime')
Buggy code:
import math
n=int(input())
a=list(map(int,input().split()))
m=max(a)+1
g=a[0]
d=dict()
for i in a:
    g=math.gcd(g,i)
    if i in d:
        d[i]+=1
    else:
        d[i]=1
if g>1:
    print("not coprime")
else:
    p=[0]*(m)
    ch=0
    for i in range (2,m):
        if p[i]==1:
            continue
        p[i]=1
        ans=0
        for j in range (i,m,i):
            ans+=d[j]
        if ans>1:
            ch=1
            break
    if ch==1:
        print("setwise coprime")
    else:
        print("pairwise coprime")

Fixed code:
import math
mod=10**9+7
n=int(input())
a=list(map(int,input().split()))
m=max(a)+1
g=a[0]
d=dict()
for i in a:
    g=math.gcd(g,i)
    if i in d:
        d[i]+=1
    else:
        d[i]=1
if g>1:
    print("not coprime")
else:
    p=[0]*(m)
    ch=0
    for i in range (2,m):
        if p[i]==1:
            continue
        p[i]=1
        ans=0
        for j in range (i,m,i):
            if j in d:
                ans+=d[j]
        if ans>1:
            ch=1
            break
    if ch==1:
        print("setwise coprime")
    else:
        print("pairwise coprime")
Buggy code:
import math
from functools import reduce
k=10**6+1
def judge(n,a):
  c=[0]**k
  for x in a:
    c[x]=+1
  t=any(sum(c[i::i])>1 for i in range(2,k))
  t+=reduce(gcd,a)>1
  return ['pairwise','setwise','not'][t]+' coprime'
n=int(input())
a=list(map(int,input().split()))
print(judge(n,a))

Fixed code:
from math import gcd
from functools import reduce
NUM_MAX = 10**6 + 1
def solve(n, a):
    c = [0] * NUM_MAX
    for x in a:
        c[x] += 1
    t = any(sum(c[i::i]) > 1 for i in range(2, NUM_MAX))
    t += reduce(gcd, a) > 1
    return ["pairwise", "setwise", "not"][t] + " coprime"

n = int(input())
a = list(map(int, input().split()))
print(solve(n, a))
Buggy code:
import bisect, copy, heapq, math, sys
from collections import *
from functools import lru_cache
from itertools import accumulate, combinations, permutations, product
def input():
    return sys.stdin.readline()[:-1]
def ruiseki(lst):
    return [0]+list(accumulate(lst))
def celi(a,b):
    return -(-a//b)
sys.setrecursionlimit(5000000)
mod=pow(10,9)+7
al=[chr(ord('a') + i) for i in range(26)]
direction=[[1,0],[0,1],[-1,0],[0,-1]]

n=int(input())
a=list(map(int,input().split()))
pc="pairwise coprime"
sc="setwise coprime"
nc="not coprime"
a.sort()
tmp=a[0]

for i in range(n):
    tmp=math.gcd(tmp,a[i])
if tmp!=1:
    print(nc)
    exit()

dic=defaultdict(int)
for i in range(n):dic[a[i]]+=1

ans=0
for i in range(a[-1]):
    now=i+1
    cnt=0
    # print(i)
    while now<=a[-1]:
        cnt+=dic[a[i]]
        now+=i+1
    if cnt>1:
        ans=i+1

if ans!=1:
    print(sc)
else:
    print(pc)
# print(ans)

Fixed code:
import bisect, copy, heapq, math, sys
from collections import *
from functools import lru_cache
from itertools import accumulate, combinations, permutations, product
def input():
    return sys.stdin.readline()[:-1]
def ruiseki(lst):
    return [0]+list(accumulate(lst))
def celi(a,b):
    return -(-a//b)
sys.setrecursionlimit(5000000)
mod=pow(10,9)+7
al=[chr(ord('a') + i) for i in range(26)]
direction=[[1,0],[0,1],[-1,0],[0,-1]]

n=int(input())
a=list(map(int,input().split()))
pc="pairwise coprime"
sc="setwise coprime"
nc="not coprime"
a.sort()
tmp=a[0]

for i in range(n):
    tmp=math.gcd(tmp,a[i])
if tmp!=1:
    print(nc)
    exit()

dic=defaultdict(int)
for i in range(n):dic[a[i]]+=1

ans=0
for i in range(a[-1]):
    now=i+1
    cnt=0
    # print(i)
    while now<=a[-1]:
        cnt+=dic[now]
        now+=i+1
    if cnt>1:
        ans=i+1

if ans!=1:
    print(sc)
else:
    print(pc)
# print(ans)
Buggy code:
import sys
n=int(input())
A=[int(i) for i in input().split()]

N=10**6
spf = [i for i in range(N+1)]

for i in range(2,N):
    if i**2>N:
        break
    if spf[i] == i:
        for j in range(i**2,N+1,i):
            if spf[j] == j:
                spf[j] = i

def get(n):
    ps = set()
    while n != 1:
        ps.add(spf[n])
        n //= spf[n]
    return ps

f1=True
f2=True

n0 = list(get(A[0]))
K=set(n0)
J=set(n0)

for a in A[1:]:
    res = get(a)
    #print(K,J,res)
    
    if len(K & res) != 0:
        f1 = False
        
    if len(res) != 0:
        K &= res
        
    if len(J & res) !=0:
        f2 = False
        
    if len(res) != 0:
        J |= res
        
#print(K,J,res)        
        
if 1 in A:
    f1 = True

    
if f1:
    if f2:
        print("pairwise coprime")
    else:
        print("setwise coprime")
else:
    print("not coprime")

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

N=10**6
spf = [i for i in range(N+1)]

for i in range(2,N):
    if i**2>N:
        break
    if spf[i] == i:
        for j in range(i**2,N+1,i):
            if spf[j] == j:
                spf[j] = i

def get(n):
    ps = set()
    while n != 1:
        ps.add(spf[n])
        n //= spf[n]
    return ps

#f1=True
f2=True

n0 = list(get(A[0]))
K=set(n0)
J=set(n0)

for a in A[1:]:
    res = get(a)
    #print(K,J,res)
    
    if len(res) != 0:
        K &= res
        
    if len(J & res) !=0:
        f2 = False
        
    if len(res) != 0:
        J |= res
        
#print(K,J,res)        
        
if (1 in A) or len(K) == 0:
    f1 = True
else:
    f1 = False
    
if f1:
    if f2:
        print("pairwise coprime")
    else:
        print("setwise coprime")
else:
    print("not coprime")
Buggy code:
N = int(input())
A = list(map(int, input().split()))

B = [0 for i in range(max(A)+1)]

for i in range(2, len(B)):
  if B[i] != -1:
    continue
  for j in range(i, len(B), i):
    B[j] = i

def func(X):
  buf = set()
  while X>1:
    x = B[X]
    buf.add(x)
    while X%x==0:
      X = X//x
  return buf

set1 = func(A[0])
set2 = set(set1)
totallen = len(set1)
for a in A[1:]:
  set3 = func(a)
  totallen += len(set3)
  set1.union(set3)
  set2.intersection(set3)
if len(set2)==0:
  print("not coprime")
elif len(set1)==totallen:
  print("pairwise coprime")
else:
  print("setwise coprime")

Fixed code:
N = int(input())
A = list(map(int, input().split()))
 
B = [0 for i in range(max(A)+1)]
 
for i in range(2, len(B)):
  if B[i] != 0:
    continue
  for j in range(i, len(B), i):
    B[j] = i

def func(X):
  buf = set()
  while X>1:
    x = B[X]
    buf.add(x)
    while X%x==0:
      X = X//x
  #print(buf)
  return buf
 
set1 = func(A[0])
set2 = func(A[0])
totallen = len(set1)
for a in A[1:]:
  set3 = func(a)
  totallen += len(set3)
  #print(a, set1, set2)
  set1 |= set3
  set2 &= set3
  #print(set1, set2, set3)
#print(totallen, set1, set2)
if len(set2)!=0:
  print("not coprime")
elif len(set1)==totallen:
  print("pairwise coprime")
else:
  print("setwise coprime")
Buggy code:
from collections import defaultdict
import math

def gcd(a, b):
    if a < b:
        return gcd(b, a)
    while b > 0:
        a, b = b, a % b
    return a

def sieve_of_eratosthenes(n):
    sieve = list(range(n+1))
    m = int(math.sqrt(n))
    for i in range(2, m + 1):
        if sieve[i] < i:
            continue
        for j in range(i * i, n + 1, i):
            if sieve[j] == j:
                sieve[j] = i
    return sieve

def factorize_by_sieve(x, sieve):
    factor = defaultdict(int)
    while sieve[x] != x:
        factor[sieve[x]] += 1
        x //= sieve[x]
    factor[x] += 1
    return factor

n = int(input())
a_list = list(map(int, input().split()))
a_list.sort()

sieve = sieve_of_eratosthenes(a_list[-1])
pairwise = True
setwise = True
primes = set()
x = a_list[0]
for a in a_list:
    x = gcd(x, a)
    if pairwise and a != 1:
        factor = factorize_by_sieve(a, sieve).keys()
        pairwise = primes.isdisjoint(factor):
        primes |= factor

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




Fixed code:
from collections import defaultdict
import math

def gcd(a, b):
    if a < b:
        return gcd(b, a)
    while b > 0:
        a, b = b, a % b
    return a

def sieve_of_eratosthenes(n):
    sieve = list(range(n+1))
    m = int(math.sqrt(n))
    for i in range(2, m + 1):
        if sieve[i] < i:
            continue
        for j in range(i * i, n + 1, i):
            if sieve[j] == j:
                sieve[j] = i
    return sieve

def factorize_by_sieve(x, sieve):
    factor = defaultdict(int)
    while sieve[x] != x:
        factor[sieve[x]] += 1
        x //= sieve[x]
    factor[x] += 1
    return factor

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

sieve = sieve_of_eratosthenes(max(a_list))
pairwise = True
setwise = True
primes = set()
x = a_list[0]
for a in a_list:
    x = gcd(x, a)
    if pairwise and a != 1:
        factor = set(factorize_by_sieve(a, sieve).keys())
        pairwise = primes.isdisjoint(factor)
        primes |= factor

if pairwise:
    print("pairwise coprime")
elif x == 1:
    print("setwise coprime")
else:
    print("not coprime")
Buggy code:
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 set(arr)

import math
N=int(input())
A=list(map(int,input().split()))
ans=['pairwise coprime','setwise coprime','not coprime']
P=[0]*(10**6+1)
k=0
s=set()
for a in A:
    tmp=factorization(a)
    if tmp&s==set():
        s|=tmp
    else:
        k=-1
        break
if k==-1:
    g=1
    for a in A:
        g=math.gcd(g,a)
    if g==1:
        k=1
    else:
        k=2
print(ans[k])

Fixed code:
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 set(arr)

import math
N=int(input())
A=list(map(int,input().split()))
ans=['pairwise coprime','setwise coprime','not coprime']
k=0
s=factorization(A[0])
for a in A[1:]:
    tmp=factorization(a)-{1}
    if s&tmp==set():
        s|=tmp
    else:
        k=-1
        break
if k==-1:
    g=A[0]
    for a in A[1:]:
        g=math.gcd(g,a)
    if g==1:
        k=1
    else:
        k=2
print(ans[k])
Buggy code:
from math import gcd
from functools import reduce

def make_prime_table(n):
    sieve = list(range(n + 1))
    sieve[0] = -1
    sieve[1] = -1
    for i in range(4, n + 1, 2):
        sieve[i] = 2
    for i in range(3, int(n ** 0.5) + 1, 2):
        if sieve[i] != i:
            continue
        for j in range(i * i, n + 1, i * 2):
            if sieve[j] == j:
                sieve[j] = i
    return sieve


def prime_factorize(n):
    result = []
    while n != 1:
        p = prime_table[n]
        e = 0
        while n % p == 0:
            n //= p
            e += 1
        result.append((p, e))
    return result


def f():
    s = set()
    for i in range(N - 1, -1. -1):
        t = prime_factorize(A[i])
        for p, _ in t:
            if p in s:
                return False
            s.add(p)
    return True


N, *A = map(int, open(0).read().split())

prime_table = make_prime_table(10 ** 6)
if f():
    print('pairwise coprime')
elif reduce(gcd, A) == 1:
    print('setwise coprime')
else:
    print('not coprime')


Fixed code:
from math import gcd
from functools import reduce

def make_prime_table(n):
    sieve = list(range(n + 1))
    sieve[0] = -1
    sieve[1] = -1
    for i in range(4, n + 1, 2):
        sieve[i] = 2
    for i in range(3, int(n ** 0.5) + 1, 2):
        if sieve[i] != i:
            continue
        for j in range(i * i, n + 1, i * 2):
            if sieve[j] == j:
                sieve[j] = i
    return sieve


def prime_factorize(n):
    result = []
    while n != 1:
        p = prime_table[n]
        e = 0
        while n % p == 0:
            n //= p
            e += 1
        result.append((p, e))
    return result


def f():
    s = set()
    for i in range(N - 1, -1, -1):
        t = prime_factorize(A[i])
        for p, _ in t:
            if p in s:
                return False
            s.add(p)
    return True


N, *A = map(int, open(0).read().split())

prime_table = make_prime_table(10 ** 6)
if f():
    print('pairwise coprime')
elif reduce(gcd, A) == 1:
    print('setwise coprime')
else:
    print('not coprime')
Buggy code:
N=int(input())
A=list(map(int,input().split()) )
import math

se = A[0]
for i in range(1,N):
    se = math.gcd(se,A[i])
set_wise = se==1

NMAX = 10**6+2
divisors = [i for i in range(NMAX+1)]
p=2
while p*p <=NMAX:
    if divisors[p]==p:
        for r in range(2*p,NMAX+1,p):
            if divisors[r]==r:
                divisors[r]=p
    p+=1
    
from collections import defaultdict
def soinsu_osak(to_devide):
    d = defaultdict(int)
    while to_devide>1:
        d[divisors[to_devide]]+=1
        to_devide //= divisors[to_devide]
    return list(d.keys())

been=[0]*NMAX
f=False
for aa in A:
    soinsu = soinsu_osak(aa)
    for s in soinsu:
        if been[s]==0:
            been[s]=1
        else:
            pair_wise=False
            f=True
            break
    if f:
        break

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

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

se = A[0]
for i in range(1,N):
    se = math.gcd(se,A[i])
set_wise = se==1

NMAX = 10**6+2
divisors = [i for i in range(NMAX+1)]
p=2
while p*p <=NMAX:
    if divisors[p]==p:
        for r in range(2*p,NMAX+1,p):
            if divisors[r]==r:
                divisors[r]=p
    p+=1
    
from collections import defaultdict
def soinsu_osak(to_devide):
    d = defaultdict(int)
    while to_devide>1:
        d[divisors[to_devide]]+=1
        to_devide //= divisors[to_devide]
    return list(d.keys())

been=[0]*NMAX
pair_wise=True
f=False
for aa in A:
    soinsu = soinsu_osak(aa)
    for s in soinsu:
        if been[s]==0:
            been[s]=1
        else:
            pair_wise=False
            f=True
            break
    if f:
        break

if pair_wise:
    print("pairwise coprime")
elif set_wise:
    print("setwise coprime")
else:
    print("not coprime")
Buggy code:
n = int(input())
a = list(map(int,input().split()))
r = max(a)+1
s = []
t = [0]*r
for i in range(r):
    s.append([])
for i in range(2,r):
    for j in range(1,-(-r//i)):
        s[i*j].append(i)
for i in range(n):
    for j in range(len(s[a[i]])):
        t[s[a[i]][j]] += 1
print(t)
if(max(t) == n):
    print('not coprime')
elif(max(t) <= 1):
    print('pairwise coprime')
else:
    print('setwise coprime')

Fixed code:
n = int(input())
a = list(map(int,input().split()))
r = max(a)+1
s = []
t = [0]*r
for i in range(r):
    s.append([])
for i in range(2,r):
    if(s[i] == []):
        for j in range(1,-(-r//i)):
            s[i*j].append(i)
for i in range(n):
    for j in range(len(s[a[i]])):
        t[s[a[i]][j]] += 1
if(max(t) == n):
    print('not coprime')
elif(max(t) <= 1):
    print('pairwise coprime')
else:
    print('setwise coprime')
Buggy code:
import math
n = int(input())
a = list(map(int, input().split()))
#

sosu = [1 for _ in range(10**6+1)]
sosu[0] = 0
sosu[1] = 1
i = 2
while i < len(sosu):
    j = i*2
    if sosu[i] == 0:
        i += 1
        continue
    while j < len(sosu):
        sosu[j] = 0
        j += i
    i += 1
sosus = []
for i in range(2, len(sosu)):
    if sosu[i]:
        sosus.append(i)

sosuset = set()
flag = 0
GCD = a[0]
for i in range(n-1, -1, -1):
    J = 0
    j = sosus[J]
    while j*j <= a[i]:
        if a[i]%j == 0 and j in sosuset:
            flag = 1
            break
        while a[i]%j == 0:
            a[i]//=j
            sosuset.add(j)
        J += 1
        j = sosus[J]
    if a[i] != 1:
        sosuset.add(a[i])
    GCD = math.gcd(GCD, a[i])

if GCD == 1 and flag == 0:
    print("pairwise coprime")
elif GCD == 1 and flag == 1:
    print("setwise coprime")
else:
    print("not coprime")


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

sosu = [1 for _ in range(10**6+1)]
sosu[0] = 0
sosu[1] = 1
i = 2
while i < len(sosu):
    j = i*2
    if sosu[i] == 0:
        i += 1
        continue
    while j < len(sosu):
        sosu[j] = 0
        j += i
    i += 1

sosus = []
for i in range(2, len(sosu)):
    if sosu[i]:
        sosus.append(i)

sosuset = set()
flag = 0
GCD = a[0]
for i in range(n-1, -1, -1):
    J = 0
    j = sosus[J]
    GCD = math.gcd(GCD, a[i])

    while j*j <= a[i]:
        if a[i]%j == 0 and j in sosuset:
            flag = 1
            break
        while a[i]%j == 0:
            a[i]//=j
            sosuset.add(j)
        J += 1
        j = sosus[J]
    if a[i] in sosuset:
        flag = 1
    if a[i] != 1:
        sosuset.add(a[i])


if GCD == 1 and flag == 0:
    print("pairwise coprime")
elif GCD == 1 and flag == 1:
    print("setwise coprime")
else:
    print("not coprime")