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 <iostream>
using namespace std;
#define ref(i,x,y)for(int i=x;i<=y;++i)
const int mod=1e9+7;
int n,c[51][51],f[51][51][51],g[51][51][51];
int main(){
	cin>>n;
	ref(i,0,n)c[i][0]=1;
	ref(i,1,n)ref(j,1,i)c[i][j]=(c[i-1][j]+c[i-1][j-1])%mod;
	ref(i,0,n-1)f[1][i-i/2][i/2]=n;
	ref(i,1,n){
		if(i>1)ref(i1,0,n-1)ref(i2,0,n-1-i1){
			f[i][i1][i2]=g[i][i1][i2];
			if(i1&&i2)(f[i][i1][i2]+=f[i][i1-1][i2-1])%mod;
		}
		ref(i1,0,n-1)ref(i2,0,n-1-i1)if(f[i][i1][i2]){
			ref(I,0,i1+i2){
				int s=1LL*c[n-i][I]*c[n-i-I][i1+i2-I]%mod*f[i][i1][i2]%mod;
				int op=max(0,I-i2),ed=min(I,i1);
				(g[i+i1+i2][i1-ed][I-ed]+=s)%=mod;
			}
		}
	}
	cout<<f[n][0][0]<<endl;
}