题目描述
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.
Examples
Input
3
Output
12
Input
4
Output
84
Input
22
Output
487772376
输入格式
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输出格式
见题面