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The Frobozz Magic Lock Company is in the business of manufacturing push button style combination door locks. A push button door lock consists of a number of push buttons B, (1 ≤ B ≤ 11), labeled “1” through “B”. The lock is opened by pressing the correct sequence of button combinations and then turning the doorknob. If the sequence of presses is correct, the door magically opens.
A combination consists of 1 or more buttons being pressed simultaneously. A sequence consists of a series of combinations. A sequence must have at least one combination. Once a button has been used in a combination, it may not be used again in the same sequence. In addition, it is not necessary to use all the buttons in a sequence. For example, for B = 8:
(1-2-3)(4)(7-8)
is a valid sequence with 3 combinations (1-2-3), (4), and (7-8). Note that buttons 5 and 6 are not used in this sequence.
(1-2-3)(2-4)(5-6)
is not a valid sequence, since button 2 appears in 2 combinations (1-2-3) and (2-4).
The CEO of Frobozz, J. Pierpont Flathead, wants you to write a program that determines the number of valid sequences possible for given values of B. The program must be able to process a list of lock orders (datasets) from customers and generate a report showing the order number, the value of B, and the number of valid sequences possible. This list will always contain at least one dataset, but no more than 100 datasets.
有一个B个按钮的锁，按下一些按钮打开门，有多少开门方式，其中，一些按钮可以选，可以不选，选中的按钮 可以分成一些集合，集合之间无序，是同时按下的。
N个不同的数字，放到一些不同的BOX里面，数字你不必用完，Box的个数也是可变的.比如三个球，你可以只放一个BOX，也可以放二个或者三个，但是四个BOX那就不可能了.每个数字只能放到一个BOX里，问有多少种放法.