Grid Magic

Brandon Greg Jr. the number theorist and combinatorist is working on prime numbers in grids. An $n$ by $m$ grid of digits ($0$ to $9$) is called a superprime grid if every non-empty prefix of every row and column (including the full rows and columns) are primes when concatenated.

For example, the following is a superprime grid:

$2$

$3$

$3$

$3$

$1$

$1$

$3$

$1$

$7$

This is because $2$, $23$, $233$, $3$, $31$, $311$, and $317$ are all prime.

Brandon wants to count the number of $n$ by $m$ superprime grids.

Input

The only line of input contains two space-separated numbers $n$ and $m$ ($1\le n, m\le 8$).

Output

Output the number of $n$ by $m$ superprime grids.

Sample Input 1 Sample Output 1
1 1
4
Sample Input 2 Sample Output 2
3 2
5