G. Grid Gradient
time limit per test
3 seconds
memory limit per test
1024 megabytes
input
standard input
output
standard output

Mr. Nežmah has received a grid with $$$n$$$ rows and $$$m$$$ columns as a birthday present. He wants to fill it up with numbers from 1 to 4, and as he is obsessed with gradients, he wants the absolute difference between numbers written in cells sharing a side to be exactly one.

As he is even more obsessed with counting stuff, help him find the number of such grids modulo 998 244 353!

Input

The first line contains integers $$$n$$$ and $$$m$$$ $$$(1 \leq n, m \leq 24)$$$.

Output

In a single line, output the number of such grids modulo 998 244 353.

Examples
Input
1 2
Output
6
Input
3 2
Output
34
Input
7 10
Output
657297226
Note

In the first example, there are exactly six ways to fill up such a grid. They are the following: $$$(1, 2), (2, 1), (2, 3), (3, 2), (3, 4), (4, 3)$$$.