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.

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.

Constraints

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

Sample Input 1

3

Sample Output 1

12

There are 3 checker pieces, positioned at 10^{100}, 10^{200}, 10^{300} respectively. Call them A, B, C respectively.
Here are two (of the 12) possible sequence of moves :

• Let A jump over B in the first second, and let A jump over C in the second second. The final position of A is $2 \times 10^{300} - 2 \times 10^{200} + 10^{100}$.

• Let C jump over A in the first second, and let B jump over C in the second second. The final position of B is -$2 \times 10^{300} - 10^{200} + 4 \times 10^{100}$.

There are a total of $3 \times 2 \times 2 = 12$ possible sequence of moves, and the final piece are in different positions in all of them.

Sample Input 2

4

Sample Output 2

84

Sample Input 3

22

Sample Output 3

487772376

Remember to output your answer modulo 10^{9} + 7.

见题面 Input 部分

见题面 Output 部分