def davenPort3(listValues):
print('davenPort 3')
x = int(listValues[0])
y = int(listValues[1])
z = int(listValues[2])
if x in [2, 3, 4, 6]:
if int(x) == int(y):
return compute_constant(listValues)
elif ((x == 3) & (x < int(y)) & (y == int(z)) &
(bltin_gcd(int(y / 3), 6) == 1)):
return compute_constant(listValues)
elif (x * (y**2) - (2 * y) - x - 2) <= z:
return compute_constant(listValues)
elif ((bltin_gcd(x, y) == 1) & (bltin_gcd(y, z) == 1)):
values = []
prod = x * y * z
values.append(prod)
return davenPort1(values)
return errorMessage()
elif (x == y == z):
list = decompose_number(x)
if all(val == list[0] for val in list):
return compute_constant(listValues)
#if all(val == list[0] for val in list) & (int(list[0]) == 2) & (len(list)%5 == 0):
# return compute_constant(lisValues)
return errorMessage()
def primRoots(modulo):
required_set = {num for num in range(1, modulo) if bltin_gcd(num, modulo)}
return [
g for g in range(1, modulo) if required_set ==
{pow(g, powers, modulo)
for powers in range(1, modulo)}
]
def calculate_k(order):
rand = 0
while not bltin_gcd(rand, int(order)) == 1:
rand = randint(1, order - 1)
return rand
def davenPort2(listValues):
x = int(listValues[0])
y = int(listValues[1])
if (checkListIsValid(listValues)):
return compute_constant(listValues)
elif (bltin_gcd(x, y) == 1):
return x * y
return errorMessage()
def main_process():
num = 0
limit = 12000
for d in range(2, limit + 1):
for n in range(d // 3, d // 2 + 1):
if (d > 2 * n) and (d < 3 * n) and bltin_gcd(n, d) == 1:
num += 1
print(colored('mycount=', 'red'), num)
def numbers_are_co_prime(number1, number2):
result = bltin_gcd(number1, number2)
if result == 1:
print("{} and {} are co-prime".format(number1, number2))
return True
else:
print(
"{} and {} are not co-prime and can both be divided by {}".format(
number1, number2, result))
return False
def __init__(self, a, b, mstr):
from math import gcd as bltin_gcd
super(T52, self).__init__()
self.a = int(a)
self.b = int(b)
self.mstr = mstr
self.m = len(mstr)
assert (len(set(mstr)) == self.m), "alphabet has repeated symbols"
assert (bltin_gcd(a, self.m) == 1), "{} and {} are not coprime".format(
self.a, self.m)
def primRoots(_inprime):
required_set = {
num
for num in range(1, _inprime) if bltin_gcd(num, _inprime)
}
return [
g for g in range(1, _inprime) if required_set ==
{pow(g, powers, _inprime)
for powers in range(1, _inprime)}
]
def generate_keys(self, p, q):
n = p * q
totient = (p-1)*(q-1)
e = 2
while(bltin_gcd(e, totient) != 1):
e += 1
print("totient = {} e = {}".format(totient, e))
d = modinv(e, totient)
print("d = ", d)
return (e, n), (d, n)
def __init__(self):
self.sharedPrime = sympy.randprime(1, 100)
required_set = {
num
for num in range(1, self.sharedPrime)
if bltin_gcd(num, self.sharedPrime)
}
self.sharedBase = random.choice([
g for g in range(1, self.sharedPrime) if required_set == {
pow(g, powers, self.sharedPrime)
for powers in range(1, self.sharedPrime)
}
]) % self.sharedPrime
self.secretKey = None
self.encodedMessage = None
def solve():
"""
this function considers 10 random values for m and n and returns the solutions for all the values
between (1 and max(m))
"""
count = 0
while count <= 10:
m_choice = np.random.choice(list_m)
n_choice = np.random.choice(list_n)
# m should be be equal to n
if m_choice != n_choice:
if bltin_gcd(m_choice, n_choice) == 1:
count = count + 1
for i in range(1, m_choice + 1):
print(m_choice, n_choice, i)
puzzle = WaterJug(initial_state, m_choice, n_choice, i)
ans = iterative_deepening_search(puzzle)
print(ans.path())
def _coprime2(a, b):
return bltin_gcd(a, b) == 1
def coprime2(a, b):
if a == 1 or b == 1:
return False
return bltin_gcd(a, b) == 1
def isCoprime(a, b):
return bltin_gcd(a, b) == 1
def co1(a, b):
return bltin_gcd(a, b) != 1
def are_relatively_prime(self, a, b):
if bltin_gcd(a, b) == 1:
return True
return False
from itertools import permutations
from math import gcd as bltin_gcd
# Write your code here
N = input()
String_special = '47474747474747474744444444444'
st1 = len(N)-len(String_special)
if st1>0:
for i in range(st1):
String_special=String_special+'47'
s2 = sorted([int(''.join(p)) for p in set(permutations(String_special,len(N)))])
SpecialList=[]
for i in s2:
if i <= int(N):
SpecialList.append(i)
for i in range(1,len(N)):
s = sorted([int(''.join(p)) for p in set(permutations(String_special,i))])
SpecialList = SpecialList+s
result=[]
print(SpecialList)
for i in range(len(SpecialList)):
for j in range(i,len(SpecialList)):
a=SpecialList[i]
b=SpecialList[j]
if bltin_gcd(a, b) == 1 and ((a,b) or(b,a)) not in result :
result.append((SpecialList[i], SpecialList[j]))
print(len(result))
def coprime(a, b):
"""Returns True if a is coprime to b, otherwise False"""
return bltin_gcd(a, b) == 1
def check_solvability(self, state, m, n):
""" Checks if m and n are co-prime"""
return bltin_gcd(m, n) == 1
def is_coprime(self, a, b):
return bltin_gcd(a, b) == 1
from math import gcd as bltin_gcd
import random
primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]
for t in range(int(input())):
n = int(input())
a = list(map(int, input().split()[:n]))
c = 0
if (bltin_gcd(a[0], a[n - 1]) != 1):
if (a[0] not in primes and bltin_gcd(a[0], a[n - 1]) != 1):
ind = random.randint(0, 14)
a[0] = primes[ind]
c += 1
elif (a[n - 1] not in primes and bltin_gcd(a[0], a[n - 1]) != 1):
ind = random.randint(0, 14)
a[n - 1] = primes[ind]
c += 1
for i in range(1, n):
if (bltin_gcd(a[i - 1], a[i]) != 1):
if (a[i - 1] not in primes and bltin_gcd(a[i - 1], a[i]) != 1):
ind = random.randint(0, 14)
a[i - 1] = primes[ind]
c += 1
elif (a[i] not in primes and bltin_gcd(a[i - 1], a[i]) != 1):
ind = random.randint(0, 14)
a[i] = primes[ind]
c += 1
print(c)
for i in a:
print(i, end=' ')
print()
def _coprime2(a, b):
return bltin_gcd(a, b) == 1
def checkcoprime(p, q):
return bltin_gcd(p, q) == 1
def coprime2(a, b): # chech relative prime or not
return bltin_gcd(a, b) == 1
def coprime(a: int, b: int) -> bool:
return bltin_gcd(a, b) == 1
def coprime(a, b):
"""Function that checks if a and b are coprime"""
return bltin_gcd(a, b) == 1
def coprime(a, b): return bltin_gcd(a, b) == 1
def co_prime(num, n_or_num_of_coprimes):
return bltin_gcd(num, n_or_num_of_coprimes) == 1
def check_coprimality(a, b):
return bltin_gcd(a, b) == 1
from math import gcd as bltin_gcd
#import random
#primes=[2,3,5,7,11,13,17,19,23,29,31,37,41,43,47]
for t in range(int(input())):
n = int(input())
a = list(map(int, input().split()[:n]))
flag = 0
i = 1
while ((i < n) and (bltin_gcd(a[0], a[i]) == 1)):
i += 1
if (i == n):
flag = 0
else:
flag = 1
if (a[0] == 47):
a[i] = 43
else:
a[i] = 47
print(flag)
for k in a:
print(k, end=' ')
print()
'''if(bltin_gcd(a[0],a[n-1])!=1):
if(a[0] not in primes and bltin_gcd(a[0],a[n-1])!=1):
ind=random.randint(0,14)
a[0]=primes[ind]
c+=1
elif(a[n-1] not in primes and bltin_gcd(a[0],a[n-1])!=1):
ind=random.randint(0,14)
a[n-1]=primes[ind]
