题目描述

Consider m natural numbers n_{1}, n_{2}, …, n_{m }with the property n_{1³ }n_{2³ }…³ n_{m}>0. We define a Young table as an arrangement in a table of n_{1}+n_{2}+…+n_{m} natural numbers (bigger than 0 and any two different), so that the i^{th} line has n_{i} elements (1£ i£ m) in ascending order from left to right, and the elements from the same column are in ascending order from bottom to top. An example of Young table for m=4, n_{1}=6, n_{2}=4, n_{3}=4, n_{4}=1 is the following:

Task: Given n_{1}, n_{2}, …, n_{m} { ** ** } **determine the number of Young tables containing the elements ** ** **1, 2, …, n{1}+n_{2}+…+n_{m}.

输入格式

on the first line is: the natural number m; on the second line are: the numbers n_{1}, n_{2}, …, n_{m} separated by a space.

输出格式

contain the number of Young tables that can be built. ** Constraints: ** ** 1<= m<= 20 ** n_{1<=}12

2
3 2

5

提示

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题目来源

Romania2002