Buggy python submission (verdict: Runtime Error):
from copy import deepcopy
def factor(N):
    ans = []
    for i in range(1,int(np.sqrt(N))+1):
        if N%i == 0:
            ans.append(i)
            if N//i != i:
                ans.append(i)
    return ans

def check(K,N):
    while N>=K:
        if N%K == 0:
            N = N//K
        else:
            N = N%K
    if N == 1:
        return True
    else:
        return False

N = int(input())
ans = len(factor(N-1)[1:])
for K in factor(N)[1:]:
    if check(K,N):
        ans += 1

print(ans)   


Fixed submission:
def primelist(n):
    is_prime = [True] * (n + 1)
    is_prime[0] = False
    is_prime[1] = False
    for i in range(2, int(n**0.5) + 1):
        if not is_prime[i]:
            continue
        for j in range(i * 2, n + 1, i):
            is_prime[j] = False
    return [i for i in range(n + 1) if is_prime[i]]

def factorization(n):
    plist = primelist(int(n**0.5))
    factor = []
    for p in plist:
        k = 0
        while n%p==0:
            k+=1
            n//=p
        if k>0:
            factor.append((p,k))
        if n==1:
            break
    if n!=1:
        factor.append((n,1))

    return factor

def primelist(n):
    is_prime = [True] * (n + 1)
    is_prime[0] = False
    is_prime[1] = False
    for i in range(2, int(n**0.5) + 1):
        if not is_prime[i]:
            continue
        for j in range(i * 2, n + 1, i):
            is_prime[j] = False
    return [i for i in range(n + 1) if is_prime[i]]

def factorization(n):
    plist = primelist(int(n**0.5))
    factor = []
    for p in plist:
        k = 0
        while n%p==0:
            k+=1
            n//=p
        if k>0:
            factor.append((p,k))
        if n==1:
            break
    if n!=1:
        factor.append((n,1))

    return factor

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

    # divisors.sort()
    return divisors


def main():
    n = int(input())
    f1 = divisors(n)
    f2 = factorization(n-1)
        
    s = 1
    for f_i in f2:
        s *=(f_i[1]+1)

    for d in f1[1:]:
        t = test(n,d)
        if t==1:
            s+=1

    print(s-1)
    

def test(n,k):

    while n>=k:
        if n%k==0:
            n//=k
        else:
            n%=k
    return n



if __name__ == "__main__":
    main()

Buggy python submission (verdict: Runtime Error):
from copy import deepcopy
import numpy as np
def factor(N):
    ans = []
    for i in range(1,int(np.sqrt(N))+1):
        if N%i == 0:
            ans.append(i)
            if N//i != i:
                ans.append(i)
    return ans

def check(K,N):
    while N>=K:
        if N%K == 0:
            N = N//K
        else:
            N = N%K
    if N%K == 1:
        return True
    else:
        return False

N = int(input())
ans = len(factor(N-1)[1:])
for K in factor(N)[1:]:
    if check(K,N):
        ans += 1

print(ans)   


Fixed submission:
def primelist(n):
    is_prime = [True] * (n + 1)
    is_prime[0] = False
    is_prime[1] = False
    for i in range(2, int(n**0.5) + 1):
        if not is_prime[i]:
            continue
        for j in range(i * 2, n + 1, i):
            is_prime[j] = False
    return [i for i in range(n + 1) if is_prime[i]]

def factorization(n):
    plist = primelist(int(n**0.5))
    factor = []
    for p in plist:
        k = 0
        while n%p==0:
            k+=1
            n//=p
        if k>0:
            factor.append((p,k))
        if n==1:
            break
    if n!=1:
        factor.append((n,1))

    return factor

def primelist(n):
    is_prime = [True] * (n + 1)
    is_prime[0] = False
    is_prime[1] = False
    for i in range(2, int(n**0.5) + 1):
        if not is_prime[i]:
            continue
        for j in range(i * 2, n + 1, i):
            is_prime[j] = False
    return [i for i in range(n + 1) if is_prime[i]]

def factorization(n):
    plist = primelist(int(n**0.5))
    factor = []
    for p in plist:
        k = 0
        while n%p==0:
            k+=1
            n//=p
        if k>0:
            factor.append((p,k))
        if n==1:
            break
    if n!=1:
        factor.append((n,1))

    return factor

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

    # divisors.sort()
    return divisors


def main():
    n = int(input())
    f1 = divisors(n)
    f2 = factorization(n-1)
        
    s = 1
    for f_i in f2:
        s *=(f_i[1]+1)

    for d in f1[1:]:
        t = test(n,d)
        if t==1:
            s+=1

    print(s-1)
    

def test(n,k):

    while n>=k:
        if n%k==0:
            n//=k
        else:
            n%=k
    return n



if __name__ == "__main__":
    main()