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 <bits/stdc++.h>
#define pb push_back
#define cmin(a,b) (a>b?a=b:a)
#define cmax(a,b) (a<b?a=b:a)
#define mem(a,k) memset(a,k,sizeof(a))
#define lop(i,s,t) for(int i=s;i<(t);++i)
#define rep(i,s,t) for(int i=s;i<=(t);++i)
#define dec(i,s,t) for(int i=s;i>=(t);--i)
#define fore(i,v) for(int i=g[v],d=es[i].d;i;i=es[i].nxt,d=es[i].d)
using namespace std;
 
#define Pr(f,...) printf(f,##__VA_ARGS__),fflush(stdout)
 
typedef long long ll;
 
const int N=105,P=1e9+7;

int add(int x,int y){ x+=y; return x>=P?x-P:x; }
int mul(int x,int y){ return 1ll*x*y%P; }
void upd(int &x,int y){ x=add(x,y); }

int n=50,f[N][N],C[N][N],ans;

int main(int argc,char *argv[]){
#ifdef CURIOUSCAT
	freopen("dat.in","r",stdin);
	freopen("my.out","w",stdout);
#endif
	scanf("%d",&n); 
	C[0][0]=1;
	rep(i,1,n){
		C[i][0]=1;
		rep(j,1,i)C[i][j]=add(C[i-1][j-1],C[i-1][j]);
	}
	f[1][0+n]=n,f[1][-1+n]=n;
	rep(i,1,n-1)rep(j,-n,n)if(f[i][j+n])rep(a,0,n-i)rep(b,0,n-a-i){
		if((!a&&!b)||(j+a-b)%2!=0||j<-a-b||j>a+b||(j&1)!=((a+b)&1))continue;
		upd(f[i+a+b][(j+a-b)/2+n],mul(f[i][j+n],mul(C[a+b][a],C[n-i][a+b])));
	}
	printf("%d\n",f[n][0+n]); 
}