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
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int mod=1000000007;
int n,C[51][51],dp[51][101];
int main()
{
	for(int i=0;i<=50;++i)
	{
		C[i][0]=1;
		for(int j=1;j<=i;++j)(C[i][j]=C[i-1][j-1]+C[i-1][j])>=mod?C[i][j]-=mod:0;
	}
	scanf("%d",&n);
	dp[1][n]=n,dp[1][n-1]=n;
	for(int i=1;i<n;++i)
		for(int j=-n;j<=n;++j)
			if(dp[i][j+n])
				for(int k=max(1,abs(j));k<=n-i;++k)//num of 2^i
					if(!(j+k&1))
						for(int l=0;l<=k;++l)//negative
						{
							int t=(k-2*l+j)>>1;
							if(t>=-n&&t<=n)dp[i+k][t+n]=(dp[i+k][t+n]+1ll*C[n-i][k]*C[k][l]%mod*dp[i][j+n])%mod;
						}
	printf("%d",dp[n][n]);
	return 0;
}