SKULLTAG_FREQS = [
        0.14473691, 0.01147017, 0.00167522, 0.03831121, 0.00356579, 0.03811315,
        0.00178254, 0.00199644, 0.00183511, 0.00225716, 0.00211240, 0.00308829,
        0.00172852, 0.00186608, 0.00215921, 0.00168891, 0.00168603, 0.00218586,
        0.00284414, 0.00161833, 0.00196043, 0.00151029, 0.00173932, 0.00218370,
        0.00934121, 0.00220530, 0.00381211, 0.00185456, 0.00194675, 0.00161977,
        0.00186680, 0.00182071, 0.06421956, 0.00537786, 0.00514019, 0.00487155,
        0.00493925, 0.00503143, 0.00514019, 0.00453520, 0.00454241, 0.00485642,
        0.00422407, 0.00593387, 0.00458130, 0.00343687, 0.00342823, 0.00531592,
        0.00324890, 0.00333388, 0.00308613, 0.00293776, 0.00258918, 0.00259278,
        0.00377105, 0.00267488, 0.00227516, 0.00415997, 0.00248763, 0.00301555,
        0.00220962, 0.00206990, 0.00270369, 0.00231694, 0.00273826, 0.00450928,
        0.00384380, 0.00504728, 0.00221251, 0.00376961, 0.00232990, 0.00312574,
        0.00291688, 0.00280236, 0.00252436, 0.00229461, 0.00294353, 0.00241201,
        0.00366590, 0.00199860, 0.00257838, 0.00225860, 0.00260646, 0.00187256,
        0.00266552, 0.00242641, 0.00219450, 0.00192082, 0.00182071, 0.02185930,
        0.00157439, 0.00164353, 0.00161401, 0.00187544, 0.00186248, 0.03338637,
        0.00186968, 0.00172132, 0.00148509, 0.00177749, 0.00144620, 0.00192442,
        0.00169683, 0.00209439, 0.00209439, 0.00259062, 0.00194531, 0.00182359,
        0.00159096, 0.00145196, 0.00128199, 0.00158376, 0.00171412, 0.00243433,
        0.00345704, 0.00156359, 0.00145700, 0.00157007, 0.00232342, 0.00154198,
        0.00140730, 0.00288807, 0.00152830, 0.00151246, 0.00250203, 0.00224420,
        0.00161761, 0.00714383, 0.08188576, 0.00802537, 0.00119484, 0.00123805,
        0.05632671, 0.00305156, 0.00105584, 0.00105368, 0.00099246, 0.00090459,
        0.00109473, 0.00115379, 0.00261223, 0.00105656, 0.00124381, 0.00100326,
        0.00127550, 0.00089739, 0.00162481, 0.00100830, 0.00097229, 0.00078864,
        0.00107240, 0.00084409, 0.00265760, 0.00116891, 0.00073102, 0.00075695,
        0.00093916, 0.00106880, 0.00086786, 0.00185600, 0.00608367, 0.00133600,
        0.00075695, 0.00122077, 0.00566955, 0.00108249, 0.00259638, 0.00077063,
        0.00166586, 0.00090387, 0.00087074, 0.00084914, 0.00130935, 0.00162409,
        0.00085922, 0.00093340, 0.00093844, 0.00087722, 0.00108249, 0.00098598,
        0.00095933, 0.00427593, 0.00496661, 0.00102775, 0.00159312, 0.00118404,
        0.00114947, 0.00104936, 0.00154342, 0.00140082, 0.00115883, 0.00110769,
        0.00161112, 0.00169107, 0.00107816, 0.00142747, 0.00279804, 0.00085922,
        0.00116315, 0.00119484, 0.00128559, 0.00146204, 0.00130215, 0.00101551,
        0.00091756, 0.00161184, 0.00236375, 0.00131872, 0.00214120, 0.00088875,
        0.00138570, 0.00211960, 0.00094060, 0.00088083, 0.00094564, 0.00090243,
        0.00106160, 0.00088659, 0.00114514, 0.00095861, 0.00108753, 0.00124165,
        0.00427016, 0.00159384, 0.00170547, 0.00104431, 0.00091395, 0.00095789,
        0.00134681, 0.00095213, 0.00105944, 0.00094132, 0.00141883, 0.00102127,
        0.00101911, 0.00082105, 0.00158448, 0.00102631, 0.00087938, 0.00139290,
        0.00114658, 0.00095501, 0.00161329, 0.00126542, 0.00113218, 0.00123661,
        0.00101695, 0.00112930, 0.00317976, 0.00085346, 0.00101190, 0.00189849,
        0.00105728, 0.00186824, 0.00092908, 0.00160896,
        ]

class HuffmanObject(object):
    def __init__(self, freqs):
        self.huffman_freqs = freqs
        self.huffman_tree = []
        self.huffman_table = [None] * 256

        self.__build_binary_tree()
        self.__binary_tree_to_lookup_table(self.huffman_tree)

    def __build_binary_tree(self):
        """
        Create the huffman tree from frequency list found in the
        current object.
        """

        # Create starting leaves
        for i in range(256):
            self.huffman_tree.append({
                'frq': self.huffman_freqs[i],
                'asc': i,
            })

        # Pair leaves and branches based on frequency until there is a
        # single root
        for i in range(255):
            lowest_key1 = -1
            lowest_key2 = -1
            lowest_frq1 = 1e30
            lowest_frq2 = 1e30

            # Find two lowest frequencies
            for j in range(256):
                if not self.huffman_tree[j]:
                    continue
                if self.huffman_tree[j]['frq'] < lowest_frq1:
                    lowest_key2 = lowest_key1
                    lowest_frq2 = lowest_frq1
                    lowest_key1 = j
                    lowest_frq1 = self.huffman_tree[j]['frq']
                elif self.huffman_tree[j]['frq'] < lowest_frq2:
                    lowest_key2 = j
                    lowest_frq2 = self.huffman_tree[j]['frq']

            # Join the two together under a new branch
            self.huffman_tree[lowest_key1] = {
                        'frq': lowest_frq1 + lowest_frq2,
                        '0': self.huffman_tree[lowest_key2],
                        '1': self.huffman_tree[lowest_key1],
                        }
            self.huffman_tree[lowest_key2] = None

        # Make the root the list
        self.huffman_tree = self.huffman_tree[lowest_key1]

    def __binary_tree_to_lookup_table(self, branch, binary_path = ''):
        """
        Recursively create the lookup table used to encode a message.
        """

        # Go through a branch finding leaves while tracking the path taken
        if '0' in branch:
            self.__binary_tree_to_lookup_table(branch['0'], binary_path + '0')
            self.__binary_tree_to_lookup_table(branch['1'], binary_path + '1')
        else:
            self.huffman_table[branch['asc']] = binary_path

    def encode(self, data_string):
        """
        Encode a string into a huffman-coded string.
        """

        if type(data_string) is not bytes:
            raise ValueError('Must pass bytes to encode')

        binary_string = ''

        # Match ASCII to entries in the lookup table
        for byte in data_string:
            binary_string += self.huffman_table[byte]

        # Convert binary string into ASCII
        encoded_string = b'';
        for i in range(0, len(binary_string), 8):
            binary = binary_string[i:i+8]
            encoded_string += bytes([int(binary[::-1], 2)])

        # If the huffman-coded string is longer than the original
        # string, return the original string instead.  Putting an
        # ASCII value 0xff where the padding bit should be signals to
        # the decoder that the message is not encoded.
        if len(data_string) <= len(encoded_string):
            return b'\xff' + data_string

        # In the first byte, store the number of padding bits
        padding_value = (8 - (len(binary_string) % 8)) % 8
        encoded_string = bytes([padding_value]) + encoded_string

        return encoded_string

    def decode(self, data_string):
        """
        Decode a huffman-coded string into a string.
        """

        if type(data_string) is not bytes:
            raise ValueError('Must pass bytes to decode')

        # Obtain and remove the number of padding bits stored in the
        # first byte.
        padding_length = data_string[0]
        data_string = data_string[1:]

        # If the padding bit is set to 0xff the message is not encoded.
        if padding_length == 0xff:
            return data_string

        # Convert ascii string into binary string
        binary_string = ''
        for byte in data_string:
            binary_string += '{0:08b}'.format(byte)[::-1]

        # Remove padding bits from the end
        binary_string = binary_string[:len(binary_string) - padding_length]

        # Match binary to entries in the huffman tree
        decoded_string = b'';
        tree_node = self.huffman_tree

        for bit in binary_string:
            if bit in tree_node:
                tree_node = tree_node[bit]
            else:
                decoded_string += bytes([tree_node['asc']])
                tree_node = self.huffman_tree[bit]

        decoded_string += bytes([tree_node['asc']])

        return decoded_string
