Description

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:

**Task:

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

Format

Input

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

Output

contain the number of Young tables that can be built.

Constraints:

1<= m<= 20* n1<=12

Samples

2

3 2

5