2551 - Tablouri Young

Consider m natural numbers n1, n2, …, nm with the property n13 n23 …3 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: 12591015 36713 481214 11

Task: Given n1, n2, …, nm determine the number of Young tables containing the elements 1, 2, …, n1+n2+…+nm.

on the first line is: the natural number m; on the second line are: the numbers n1, n2, …, nm separated by a space.

contain the number of Young tables that can be built. Constraints: 1<= m<= 20 n1<=12