1825：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.

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