class TrieNode:
    def __init__(self):
        self.children = {}
        self.is_end_of_word = False


class Trie:
    def __init__(self):
        self.root = TrieNode()

    def insert(self, word):
        node = self.root
        for char in word:
            if char not in node.children:
                node.children[char] = TrieNode()
            node = node.children[char]
        node.is_end_of_word = True

    def search(self, word):
        node = self.root
        for char in word:
            if char not in node.children:
                return False
            node = node.children[char]
        return node.is_end_of_word

    def starts_with_prefix(self, prefix):
        node = self.root
        for char in prefix:
            if char not in node.children:
                return False
            node = node.children[char]
        return True


class CrypticStateMachine:
    def __init__(self):
        self.trie = Trie()

    def encrypt(self, message, shift):
        """
        Encrypts the message using Caesar cipher with the given shift.
        """
        encrypted_message = ""
        for char in message:
            if char.isalpha():
                ascii_offset = ord('a') if char.islower() else ord('A')
                encrypted_char = chr((ord(char) - ascii_offset + shift) % 26 + ascii_offset)
                encrypted_message += encrypted_char
                self.trie.insert(encrypted_char)
            else:
                encrypted_message += char
        return encrypted_message

    def decrypt(self, encrypted_message, shift):
        """
        Decrypts the encrypted message using Caesar cipher with the given shift.
        """
        decrypted_message = ""
        for char in encrypted_message:
            if char.isalpha():
                ascii_offset = ord('a') if char.islower() else ord('A')
                decrypted_message += chr((ord(char) - ascii_offset - shift) % 26 + ascii_offset)
            else:
                decrypted_message += char
        return decrypted_message

    def all_encryptions(self, message):
        """
        Generates all possible encrypted messages for the given input message.
        """
        for shift in range(26):
            yield self.encrypt(message, shift)

    def search_encrypted_message(self, prefix):
        """
        Searches for encrypted messages starting with the given prefix.
        """
        return self.trie.starts_with_prefix(prefix)


# Usage
cryptic_state_machine = CrypticStateMachine()
message = "I never said she stole my money"
all_encrypted_messages = list(cryptic_state_machine.all_encryptions(message))
for i, encrypted_message in enumerate(all_encrypted_messages):
    print(f"Shift {i}: {encrypted_message}")

# Example search for encrypted messages starting with a prefix
print(cryptic_state_machine.search_encrypted_message("J of"))  # True
print(cryptic_state_machine.search_encrypted_message("X il"))  # False