Young
Consider m natural numbers n1, n2, ..., nm with the property n1 >= n2 >= ... >= nm > 0.
We define a Young table as an arrangement in a table of n1 + n2 + ... + nm natural numbers (bigger than 0 and any two different), so that the ith line has ni 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, n1 = 6, n2 = 4, n3 = 4, n4 = 1 is the following:
1 2 5 9 10 15
3 6 7 13
4 8 12 14
11
Given n1, n2, ..., nm determine the number of Young tables containing the elements 1, 2, ..., n1+n2+...+nm.
The input has the stucture:
on the first line is: the natural number m (1 <= m <= 20);
on the second line are: the numbers n1, n2, ..., nm separated by a space (n1 <= 12).
The output will contain the number of Young tables that can be built.
2 3 2
5
The five Young tables are:
| 1 | 3 | 5 | 1 | 2 | 3 | 1 | 2 | 4 | ||
| 2 | 4 | 4 | 5 | 3 | 5 | |||||
| 1 | 3 | 4 | 1 | 2 | 5 | |||||
| 2 | 5 | 3 | 4 |
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