Base64 is a standard for encoding binary data using only 64 ASCII characters. The encoding alphabet contains the Latin characters A-Z, a-z and 0-9 (62 characters) and two additional characters depending on the implementation system. Every three original bytes are encoded with four characters (thus increasing the number of bytes by $$$25\%$$$). For the purpose of this task, the additional characters are + and /.

To convert data to base64, the first byte is placed in the most significant eight bits of a 24-bit buffer, the next one in the middle eight, and the third one in the least significant eight bits. If less than three bytes are encoded, then the corresponding buffer bits are set to zero. Then every six bits of the buffer, starting with the most significant ones, are used as indexes of the string ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/ (indexing starts from zero) and its characters, pointed to by the indices, are placed in the output string. If only one or two bytes are encoded, the result is only the first two or three characters of the string, and the output string is padded with two or one = characters. The process is repeated on the remaining input data.

The table shows the result of encoding the Cat string:

Write a program that encodes a sequence of bytes using the base64 standard.