Rectangle#1478

Rectangle

2 seconds

64 megabytes

Hard

Given a rectangle of size $m \times n$ m \times n, determine the number of ways to split it into two parts such that each part is a connected set of unit cells.

For example, there are six ways to split a $2 \times 2$ 2 \times 2 square in this manner, as shown in the figure below.

Input

The input contains two integers $m$ and $n$ ( $1 \leq m, n \leq 11$ 1 \leq m, n \leq 11).

Output

Print a single number: the number of ways to split the rectangle as described.

Examples

Example 1

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m \times n

2 \times 2

1 \leq m, n \leq 11