Description

Given an $N \times M$ grid, each cell can be colored black or white. All black cells must be connected, all white cells must be connected, and at least one black cell is on the border while at least one white cell is on the border. How many valid colorings are there?

Input Format

The first line contains two positive integers $N, M$.

Output Format

Output a single positive integer representing the answer.

1 2   

2   

2 3

30

Hint

Constraints: For $100 \%$ of the testdata: $1 \le N \le 7$, $1 \le M \le 8$.

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