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#2551. Tablouri Young

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Description

Consider m natural numbers n1, n2, …, nm with the property n n …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.

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

Sample Input

2

3 2



Sample Output


5

Hint

Source

Romania2002