A digital computer has 32-bit instructions. There are a number of different instruction formats, and the number of bits in each format used for opcodes varies depending on the bits needed for other fields. If the first bit of the opcode is 0, then there are three opcode bits. If the first bit of the opcode is 1 and the second bit of the opcode is 0, then there are six opcode bits. If the first bit of the opcode is 1 and the second bit of the opcode is 1, then there are nine opcode bits. How many distinct opcodes are available for this computer?
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