2551. Tablouri Young
#2551. 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
样例
样例输入
2
3 2
样例输出
5