Problem Statement

Let $X = 10^{100}$. Inaba has $N$ checker pieces on the number line, where the $i$-th checker piece is at coordinate $X^{i}$ for all $1 \leq i \leq N$.

Every second, Inaba chooses two checker pieces, $A$ and $B$, and move $A$ to the symmetric point of its current position with respect to $B$. After that, $B$ is removed. (It is possible that $A$ and $B$ occupy the same position, and it is also possible for $A$ to occupy the same position as another checker piece after the move).

After $N - 1$ seconds, only one checker piece will remain. Find the number of distinct possible positions of that checker piece, modulo $10^{9} + 7$.

Constraints

• $1 \leq N \leq 50$
• $N$ is an integer.

Input

Input is given from Standard Input in the following format:

N

Output

Print the number of distinct possible positions of the final checker piece, modulo $10^{9} + 7$.