A jigsaw puzzle contains various kinds of pieces: corners, edges, and interior pieces. The diagram shows an inventory of the various shapes in a certain 40x25 jigsaw puzzle; in other words, the numbers on each piece is the number of those types of pieces in this puzzle. Shapes that are identical up to rotation have been grouped together.

Determine the five missing values. As your answer, submit the product \(a\cdot b\cdot c\cdot d\cdot e\).

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