Tablouri Young
题目描述
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:
|
1 |
2 |
5 |
9 |
10 |
15 |
|
3 |
6 |
7 |
13 |
||
|
4 |
8 |
12 |
14 |
||
|
11 |
Task:
Given n1, n2, …, nm determine the number of Young tables containing the elements 1, 2, …, n1+n2+…+nm.
输入格式
- on the first line is: the natural number m;
- on the second line are: the numbers n1, n2, …, nm separated by a space.
输出格式
contain the number of Young tables that can be built.
Constraints:
- 1<= m<= 20
- n1<=12
2
3 2
5