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 cs const
#define pb push_back
using namespace std;
cs int Mod = 1e9 + 7;
int add(int a, int b){ return a + b >= Mod ? a + b - Mod : a + b; }
int dec(int a, int b){ return a - b < 0 ? a - b + Mod : a - b; }
int mul(int a, int b){ return 1ll * a * b % Mod; }
void Add(int &a, int b){ a = add(a,b); }
void Mul(int &a, int b){ a = mul(a,b); }
void Dec(int &a, int b){ a = dec(a,b); }
cs int N = 55;
int n, dp[N][N], C[N][N];
int main(){
	#ifdef FSYolanda
	freopen("1.in","r",stdin);
	#endif
	scanf("%d",&n);
	for(int i=0; i<=n; i++) C[i][0]=1;
	for(int i=1; i<=n; i++)
	for(int j=1; j<=i; j++) C[i][j]=add(C[i-1][j-1],C[i-1][j]);
	dp[1][0]=dp[1][1]=n; 
	for(int i=1; i<n; i++)
	for(int j=0,coe; j<=i; j++) if(coe=dp[i][j]) 
 	for(int k=max(j,1); k<=n-i; k++) {
		if((k+j)&1) continue; 
		int t=(k+j)>>1; for(int x=0; x<=k; x++) 
		Add(dp[i+k][abs(t-x)],mul(coe,mul(C[n-i][k],C[k][x])));
	} cout<<dp[n][0]; return 0;
}