print('hello, world')

import copy
begining = [False,False,False,False,False,None,True,True,True,True,True]
#False = black True = white
its = [0]
def swap(layout, step):
    layoutCopy = copy.deepcopy(layout)
    layoutCopy[(step[0]+step[1])], layoutCopy[step[1]] = layoutCopy[step[1]], layoutCopy[(step[0]+step[1])]
    return layoutCopy
def isSolved(layout):
    for i in range(len(layout)):
        if(layout[i] == False):
            return (i >= (len(layout)/2))
def recurse(layout, its, steps = []):
    if isSolved(layout):
        its[0] += 1
        print(layout,list(x[0] for x in steps))
        return
    step = None
    for i in range(len(layout)):
        if(layout[i] == None):
            if(i >= 1): #If the empty space could have something to the left
                if(layout[i - 1] == False):
                    step = [-1,i]
                    recurse(swap(layout,step), its, (steps+[step]))
                if(i > 1): #If the empty space could have something 2 to the left
                    if(layout[i - 2] == False):
                        step = [-2,i]
                        recurse(swap(layout,step), its, (steps+[step]))
            if(i < (len(layout)-1)): #If the empty space could have something to the right
                if(layout[i + 1] == True):
                    step = [1,i]
                    recurse(swap(layout,step), its, (steps+[step]))
                if(i < (len(layout)-2)): #If the empty space could have something to the right
                    if(layout[i + 2] == True):
                        step = [2,i]
                        recurse(swap(layout,step), its, (steps+[step]))
    its[0] += 1
    #return None
recurse(begining,its,[])
print(its[0])

# Given a number n, print all primes smaller than or equal to n. It is also given that n is a small number.
# For example, if n is 10, the output should be “2, 3, 5, 7”. If n is 20, the output should be “2, 3, 5, 7, 11, 13, 17, 19”.


# Python program to print all primes smaller than or equal to
# n using Sieve of Eratosthenes

def SieveOfEratosthenes(n):
	
	# Create a boolean array "prime[0..n]" and initialize
	# all entries it as true. A value in prime[i] will
	# finally be false if i is Not a prime, else true.
	prime = [True for i in range(n + 1)]
	p = 2
	while (p * p <= n):
		
		# If prime[p] is not changed, then it is a prime
		if (prime[p] == True):
			
			# Update all multiples of p
			for i in range(p * 2, n + 1, p):
				prime[i] = False
		p += 1
	prime[0]= False
	prime[1]= False
	# Print all prime numbers
	for p in range(n + 1):
		if prime[p]:
			print (p)

# driver program
if __name__=='__main__':
    n = 30
    print("Following are the prime numbers smaller")
    print("than or equal to ", n)
    print("than or equal to ", n)
    SieveOfEratosthenes(n)

def byte_size(s):
  return len(s.encode('utf-8'))
  
byte_size('😀') # 4
byte_size('Hello World') # 11

class ProposalParser:
    """A class to parse IKE and ESP proposal strings into human-readable formats.

    This class supports parsing of IKE and ESP proposals, extracting encryption, hash, PRF (for IKE),
    and Diffie-Hellman (DH) group information. It also handles the concatenation of these components
    into a structured format, indicating whether Perfect Forward Secrecy (PFS) is enabled for ESP proposals.
    The parser uses predefined mappings for DH groups, encryption algorithms, hash functions, and Pseudo-Random Functions (PRFs).
    It can process a list of proposals and return a formatted string summarizing the cryptographic parameters.
    Attributes:

        dh_mapping (dict): A mapping of Diffie-Hellman groups to their corresponding identifiers

        enc_mapping (dict): A mapping of encryption algorithms to their corresponding identifiers

        hash_mapping (dict): A mapping of hash functions to their corresponding identifiers

        prf_mapping (dict): A mapping of Pseudo-Random Functions to their corresponding identifiers

    Methods:
        parse_ike_proposal(proposal): Parses a single IKE or ESP proposal string into a structured dictionary with encryption, hash, PRF, and DH group information.

        process_proposals(proposal_list): Processes a comma-separated list of IKE or ESP proposals, concatenating encryption, hash, PRF (for IKE), and DH group values, and indicating whether PFS is enabled for ESP proposals.

    """
    
    def __init__(self):
        """Initialize the parser with mappings for DH groups, encryption, hash, and PRF."""
        self.dh_mapping = {
            'MODP_768': '1',
            'MODP_1024': '2',
            'MODP_1536': '5',
            'MODP_2048': '14',
            'MODP_3072': '15',
            'MODP_4096': '16',
            'MODP_6144': '17',
            'MODP_8192': '18',
            'ECP_256': '19',
            'ECP_384': '20',
            'ECP_521': '21',
            'ECP_192': '25',
            'ECP_224': '26',
            'MODP_1024_160': '22',
            'MODP_2048_224': '23',
            'MODP_2048_256': '24',
            'FFDHE_2048': '256',
            'FFDHE_3072': '257',
            'FFDHE_4096': '258',
            'FFDHE_6144': '259',
            'FFDHE_8192': '260',
            'ECP_224_BP': '27',
            'ECP_256_BP': '28',
            'ECP_384_BP': '29',
            'ECP_512_BP': '30',
            'CURVE_25519': '31',
            'CURVE_448': '32',
        }
        
        self.enc_mapping = {
            'AES_CBC_128': 'AES128',
            'AES_CBC_192': 'AES192',
            'AES_CBC_256': 'AES256',
            'AES_GCM_16_128': 'AES128-GCM-16',
            'AES_GCM_16_192': 'AES192-GCM-16',
            'AES_GCM_16_256': 'AES256-GCM-16',
            'AES_GCM_8_128': 'AES128-GCM-8',
            'AES_GCM_8_256': 'AES256-GCM-8',
            'AES_GCM_12_128': 'AES128-GCM-12',
            'AES_GCM_12_256': 'AES256-GCM-12',
            'AES_CCM_16_128': 'AES128-CCM-16',
            'AES_CCM_16_256': 'AES256-CCM-16',
            'AES_CTR_128': 'AES128-CTR',
            'AES_CTR_192': 'AES192-CTR',
            'AES_CTR_256': 'AES256-CTR',
            '3DES_CBC': '3DES',
            'DES_CBC': 'DES',
            'CAMELLIA_CBC_128': 'CAMELLIA128',
            'CAMELLIA_CBC_256': 'CAMELLIA256',
            'CHACHA20_POLY1305': 'CHACHA20-POLY1305',
            'BLOWFISH_CBC': 'BLOWFISH',
            'CAST5_CBC': 'CAST5'
        }
        
        self.hash_mapping = {
            'HMAC_MD5': 'MD5',
            'HMAC_MD5_96': 'MD5',
            'HMAC_SHA1': 'SHA1',
            'HMAC_SHA1_96': 'SHA1',
            'HMAC_SHA2_256': 'SHA2-256',
            'HMAC_SHA2_256_128': 'SHA2-256',
            'HMAC_SHA2_384': 'SHA2-384',
            'HMAC_SHA2_384_192': 'SHA2-384',
            'HMAC_SHA2_512': 'SHA2-512',
            'HMAC_SHA2_512_256': 'SHA2-512',
            'HMAC_SHA3_224': 'SHA3-224',
            'HMAC_SHA3_256': 'SHA3-256',
            'HMAC_SHA3_384': 'SHA3-384',
            'HMAC_SHA3_512': 'SHA3-512',
            'AES_GMAC_128': 'GMAC-128',
            'AES_GMAC_192': 'GMAC-192',
            'AES_GMAC_256': 'GMAC-256',
            'POLY1305': 'POLY1305'
        }
        
        self.prf_mapping = {
            'PRF_HMAC_MD5': 'MD5',
            'PRF_HMAC_SHA1': 'SHA1',
            'PRF_HMAC_SHA2_256': 'SHA2-256',
            'PRF_HMAC_SHA2_384': 'SHA2-384',
            'PRF_HMAC_SHA2_512': 'SHA2-512',
            'PRF_AES128_CMAC': 'AES128-CMAC',
            'PRF_AES128_XCBC': 'AES128-XCBC',
            'PRF_HMAC_SHA3_224': 'SHA3-224',
            'PRF_HMAC_SHA3_256': 'SHA3-256',
            'PRF_HMAC_SHA3_384': 'SHA3-384',
            'PRF_HMAC_SHA3_512': 'SHA3-512'
        }

    def parse_ike_proposal(self, proposal):
        """
        Parse an IKE or ESP proposal string into a structured format.

        Args:
            proposal (str): The proposal string, e.g., "IKE:AES_CBC_256/HMAC_SHA2_256/PRF_HMAC_SHA2_256/MODP_2048"
            
        Returns:
            dict: A dictionary with keys 'encryption', 'hash', 'prf', and 'dh_group'
        """

        # Split the proposal into components based on '/'
        components = proposal.split('/')
        
        result = {
            'encryption': [],
            'hash': [],
            'prf': [],
            'dh_group': []
        }
        
        
        is_ike = proposal.startswith('IKE:')
        is_esp = proposal.startswith('ESP:')
        

        # Remove IKE or ESP prefix if present for easier parsing later
        if is_ike or is_esp:
            components[0] = components[0].replace('IKE:', '').replace('ESP:', '')
        

        
        # Determine the current section based on the first component
        # Determine the current section based on the first component
        enc_components = []
        hash_components = []
        prf_components = []
        dh_components = []
        unknown_components = []  # To track unrecognized components

        for component in components:
            categorized = False

            # Encryption components
            if (component in self.enc_mapping or 
                any(s in component for s in ['AES_CBC', 'AES_GCM', 'AES_CTR', 'CHACHA20', 
                                            'BLOWFISH', 'CAST5', 'DES', '3DES', 'CAMELLIA'])):
                enc_components.append(component)
                categorized = True

            # Hash components
            if (component in self.hash_mapping or 
                any(s in component for s in [ 'HMAC_MD5', 'POLY1305', 'AES_GMAC'])):
                hash_components.append(component)
                categorized = True
            else:
                hash_components.append("None")

            # PRF components (only if is_ike is True)
            if is_ike and 'PRF_' in component:
                prf_components.append(component)
                categorized = True

            # Diffie-Hellman components
            if (component in self.dh_mapping or 
                any(s in component for s in ['MODP', 'ECP', 'FFDHE', 'CURVE'])):
                dh_components.append(component)
                categorized = True

            # Skip irrelevant components
            if component == 'NO_EXT_SEQ':
                continue

            # Log unrecognized components
            if not categorized:
                unknown_components.append(component)

        # Optional: Log or handle unknown components
        if unknown_components:
            print(f"Warning: Unrecognized components: {unknown_components}")
        

        # Map encryption components
        for enc in enc_components:
            mapped_enc = self.enc_mapping.get(enc, 'Unknown')
            if mapped_enc != 'Unknown' and mapped_enc not in result['encryption']:
                result['encryption'].append(mapped_enc)
        
        # Map hash components (skip for AEAD ciphers like AES-GCM)
        #if not any(enc.startswith('AES_GCM') or enc.startswith('AES_CCM') or enc == 'CHACHA20_POLY1305' for enc in enc_components):
        for hash_val in hash_components:
            print(hash_components)
            mapped_hash = self.hash_mapping.get(hash_val, 'Unknown')
            if mapped_hash != 'Unknown' and mapped_hash not in result['hash']:
                result['hash'].append(mapped_hash)
            if mapped_hash == 'Unknown':
                result['hash'].append(mapped_hash)

        
        # Map PRF components
        for prf in prf_components:
            mapped_prf = self.prf_mapping.get(prf, 'Unknown')
            if mapped_prf == "Unknown":
                result['prf'].append(mapped_prf)
            if mapped_prf != 'Unknown' and mapped_prf not in result['prf']:
                result['prf'].append(mapped_prf)


        # Map DH group components
        for dh in dh_components:
            mapped_dh = self.dh_mapping.get(dh)
            if mapped_dh != 'None' and mapped_dh not in result['dh_group']:
                result['dh_group'].append(mapped_dh)

        
        # Handle ESP case (no PRF for ESP proposals)
        if is_esp:
            result['prf'] = ['None']
        
        if not result['encryption']:
            result['encryption'] = ['Unknown']

        # if not result['hash']:
        #     result['hash'] = ['Unknown']
        
        print(result['hash'])

        return result

    def process_proposals(self, proposal_list):
        """
        Process a list of IKE or ESP proposals, concatenating encryption, hash, PRF (for IKE only), 
        and DH group values, and indicate whether PFS is enabled for ESP proposals only.
        
        Args:
            proposal_list (str): Comma-separated string of IKE or ESP proposals
        
        Returns:
            str: Formatted string with concatenated encryption, hash, PRF (for IKE), DH groups, and PFS status (for ESP)
        """
        proposal_list = proposal_list.replace(',', ', ')
        proposals = proposal_list.strip().split(', ')

        
        # Collect unique encryption, hash, PRF, and DH groups
        enc_set = set()
        hash_set = set()
        prf_set = set()
        dh_set = set()
        


        # Parse each proposal and update the sets for later sorting and formatting
        for proposal in proposals:
            parsed = self.parse_ike_proposal(proposal.strip())
            print(parsed)
            enc_set.update(parsed['encryption'])
            if parsed['hash'] != ['None']:
                hash_set.update(parsed['hash'])
            else:
                hash_set.update(parsed['hash'])
            if parsed['prf'] != ['None']:
                prf_set.update(parsed['prf'])
            if parsed['dh_group'] != ['None']:
                dh_set.update(parsed['dh_group'])

        
        # Convert sets to sorted lists
        enc_list = sorted(list(enc_set))
        hash_list = sorted(list(hash_set))
        prf_list = sorted(list(prf_set))
        dh_list = sorted(list(dh_set), key=lambda x: int(x))

        
        # Determine PFS status for ESP proposals only
        is_ike = any(proposal.startswith('IKE:') for proposal in proposals)
        pfs_status = "PFS: Enabled" if dh_set and not is_ike else "PFS: None"

        
        # Format output as a single concatenated string
        enc_part = f"Encryption: {', '.join(enc_list)}" if enc_list else "Encryption: None"
        hash_part = f"Hash: {', '.join(hash_list)}"
        dh_part = f"DH Group(s): {', '.join(dh_list)}" if dh_list else "DH Group(s): None"
        prf_part = f"PRF: {', '.join(prf_list)}" if prf_list else "PRF: None"

        
        # Return formatted string based on whether it's an IKE or ESP proposal
        if is_ike:
            return f"{enc_part} {hash_part} {prf_part} {dh_part}"
        else:
            return f"{enc_part} {hash_part} {dh_part} {pfs_status}"
            
# Example usage
if __name__ == "__main__":
    parser = ProposalParser()

    unknown_hash = "IKE:AES_CBC_256/INVALID_HASH/PRF_HMAC_SHA2_256/MODP_2048"
    none_hash = "IKE:AES_CBC_256/PRF_HMAC_SHA2_256/MODP_2048"

    # Outputs Encryption: AES256 Hash: Unknown PRF: SHA2-256 DH Group(s): 14 <-- Correct!
    print(parser.process_proposals(unknown_hash))

    # Outputs Encryption: AES256 Hash: Unknown PRF: SHA2-256 DH Group(s): 14 <-- Incorrect
    print(parser.process_proposals(none_hash))

#Sets
U = {0,1,2,3,4,5,6,7,8,9}
P = {1,2,3,4}
Q = {4,5,6}
R = {3,4,6,8,9}

def set2bits(xs,us) :
    bs=[]
    for x in us :
        if x in xs :
            bs.append(1)
        else:
            bs.append(0)
    assert len(us) == len(bs)
    return bs

def union(set1,set2) :
    finalSet = set()
    bitList1 = set2bits(set1, U)
    bitList2 = set2bits(set2, U)

    for i in range(len(U)) :
        if(bitList1[i] or bitList2[i]) :
            finalSet.add(i)

    return finalSet

def intersection(set1,set2) :
    finalSet = set()
    bitList1 = set2bits(set1, U)
    bitList2 = set2bits(set2, U)

    for i in range(len(U)) :
        if(bitList1[i] and bitList2[i]) :
            finalSet.add(i)

    return finalSet

def compliment(set1) :
    finalSet = set()
    bitList = set2bits(set1, U)

    for i in range(len(U)) :
        if(not bitList[i]) :
            finalSet.add(i)

    return finalSet

def implication(a,b):
    return union(compliment(a), b)

###########################################################################################
######################         Problems 1-6         #######################################
###########################################################################################

#p \/ (q /\ r) = (p \/ q) /\ (p \/ r)
def prob1():
    return union(P, intersection(Q,R)) == intersection(union(P,Q), union(P,R))

#p /\ (q \/ r) = (p /\ q) \/ (p /\ r)
def prob2():
    return intersection(P, union(Q,R)) == union(intersection(P,Q), intersection(P,R))

#~(p /\ q) = ~p \/ ~q
def prob3():
    return compliment(intersection(P,R)) == union(compliment(P), compliment(R))

#~(p \/ q) = ~p /\ ~q
def prob4():
    return compliment(union(P,Q)) == intersection(compliment(P), compliment(Q))

#(p=>q) = (~q => ~p)
def prob5():
    return implication(P,Q) == implication(compliment(Q), compliment(P))

#(p => q) /\ (q => r)  =>  (p => r)
def prob6():
    return implication(intersection(implication(P,Q), implication(Q,R)), implication(P,R))


print("Problem 1: ", prob1())
print("Problem 2: ", prob2())
print("Problem 3: ", prob3())
print("Problem 4: ", prob4())
print("Problem 5: ", prob5())
print("Problem 6: ", prob6())

'''
Problem 1:  True
Problem 2:  True
Problem 3:  True
Problem 4:  True
Problem 5:  True
Problem 6:  {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
'''