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Language:
Young
 Time Limit: 1000MS Memory Limit: 30000K Total Submissions: 706 Accepted: 162

Description

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.

Input

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).

Output

The output will contain the number of Young tables that can be built.

Sample Input

```2
3 2```

Sample Output

`5`

Hint

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

Source

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