A 16 ×16 square sheet of paper is folded once in half horizontally and once in half vertically to make an 8 × 8 square.  This square is again folded in half twice to make a 4 × 4 square.  This square is folded in half twice to make a 2 × 2 square. This square is folded in half twice to make a 1 × 1 square.  Finally, a scissor is used to make cuts through both diagonals of all the layers of the 1 × 1 square.  How many pieces of paper result?

Let's think step by step and output the final answer within \boxed{}.
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