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>
using namespace std;
#define ref(i,x,y)for(int i=x;i<=y;++i)
const int N=101;
const int mod=1e9+7;
int n,c[N][N],dp[N][N][N],f[N][N];
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,1,n)dp[1][i>>1][(i-1)>>1]=n;
	ref(i,1,n){
		ref(ss,1,n-i){
			memset(f,0,sizeof f);
			int ii=i+ss;
			ref(s0,0,ss){int s1=ss-s0;
				if(!dp[i][s0][s1])continue;
				ref(I,0,ss){
					int s=1LL*c[n-i][I]*c[n-i-I][ss-I]%mod*dp[i][s0][s1]%mod;
					int lo=max(0,I-s1),ma=min(I,s0);
					if(lo>ma)continue;
					(f[s0-ma][I-ma]+=s)%=mod;
				}
			}
			ref(s0,1,n)ref(s1,1,n-s0)
				(f[s0][s1]+=f[s0-1][s1-1])%=mod;
			ref(s0,0,n)ref(s1,0,n-s0)
				(dp[ii][s0][s1]+=f[s0][s1])%=mod;
		}
	}
	cout<<dp[n][0][0]<<endl;
}