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;

using ll=int64_t;
#define int ll

#define FOR(i,a,b) for(int i=int(a);i<int(b);i++)
#define REP(i,b) FOR(i,0,b)
#define MP make_pair
#define PB push_back
#define ALL(x) x.begin(),x.end()
#ifdef MAROON_LOCAL
#define cerr (cerr<<"-- line "<<__LINE__<<" -- ")
#else
class CerrDummy{}cerrDummy;
template<class T>
CerrDummy& operator<<(CerrDummy&cd,const T&){
	return cd;
}
using charTDummy=char;
using traitsDummy=char_traits<charTDummy>;
CerrDummy& operator<<(CerrDummy&cd,basic_ostream<charTDummy,traitsDummy>&(basic_ostream<charTDummy,traitsDummy>&)){
	return cd;
}
#define cerr cerrDummy
#endif
#define REACH cerr<<"reached"<<endl
#define DMP(x) cerr<<#x<<":"<<x<<endl
#define ZERO(x) memset(x,0,sizeof(x))
#define ONE(x) memset(x,-1,sizeof(x))

using pi=pair<int,int>;
using vi=vector<int>;
using ld=long double;

template<class T,class U>
ostream& operator<<(ostream& os,const pair<T,U>& p){
	os<<"("<<p.first<<","<<p.second<<")";
	return os;
}

template<class T>
ostream& operator <<(ostream& os,const vector<T>& v){
	os<<"[";
	REP(i,(int)v.size()){
		if(i)os<<",";
		os<<v[i];
	}
	os<<"]";
	return os;
}

ll read(){
	ll i;
	scanf("%" SCNd64,&i);
	return i;
}

void printSpace(){
	printf(" ");
}

void printEoln(){
	printf("\n");
}

void print(ll x,int suc=1){
	printf("%" PRId64,x);
	if(suc==1)
		printEoln();
	if(suc==2)
		printSpace();
}

string readString(){
	static char buf[3341000];
	scanf("%s",buf);
	return string(buf);
}

char* readCharArray(){
	static char buf[3341000];
	static int bufUsed=0;
	char* ret=buf+bufUsed;
	scanf("%s",ret);
	bufUsed+=strlen(ret)+1;
	return ret;
}

template<class T,class U>
void chmax(T& a,U b){
	if(a<b)
		a=b;
}

template<class T,class U>
void chmin(T& a,U b){
	if(b<a)
		a=b;
}

template<class T>
T Sq(const T& t){
	return t*t;
}

#define CAPITAL
void Yes(bool ex=true){
	#ifdef CAPITAL
	cout<<"YES"<<endl;
	#else
	cout<<"Yes"<<endl;
	#endif
	if(ex)exit(0);
}
void No(bool ex=true){
	#ifdef CAPITAL
	cout<<"NO"<<endl;
	#else
	cout<<"No"<<endl;
	#endif
	if(ex)exit(0);
}

const ll infLL=LLONG_MAX/3;

#ifdef int
const int inf=infLL;
#else
const int inf=INT_MAX/2-100;
#endif

const int mod=1000000007;
template<class T,class U>
void add(T& a,U b){
	a=((ll)a+b)%mod;
}

template<class T,class U>
void sub(T& a,U b){
	a=((ll)a-b%mod+mod)%mod;
}

template<class T,class U>
void mult(T& a,U b){
	a=((ll)a*b)%mod;
}

ll modPow(ll a,ll p){
	ll s=1;
	while(p){
		if(p&1)mult(s,a);
		mult(a,a);
		p>>=1;
	}
	return s;
}

ll modInv(ll a){
	return modPow(a,mod-2);
}

const int Vmax=1000010;
int fact[Vmax],factInv[Vmax];
void InitFact(){
	fact[0]=1;
	FOR(i,1,Vmax){
		fact[i]=fact[i-1];
		mult(fact[i],i);
	}
	factInv[Vmax-1]=modInv(fact[Vmax-1]);
	for(int i=Vmax-2;i>=0;i--){
		factInv[i]=factInv[i+1];
		mult(factInv[i],i+1);
	}
}
int Choose(int n,int k){
	return ll(fact[n])*factInv[n-k]%mod*factInv[k]%mod;
}
int Binom(int a,int b){
	return ll(fact[a+b])*factInv[a]%mod*factInv[b]%mod;
}

const int Nmax=51;
int dp[2][Nmax][Nmax][Nmax];

int Solve(int n){
	ZERO(dp);
	int cur=0,ans=0;
	dp[cur][1][1][0]=fact[n];
	REP(_,n){
		REP(a,n+1)REP(b,n+1){
			int z=dp[cur][n][a][b];
			mult(z,factInv[a]);
			mult(z,factInv[b]);
			add(ans,z);
		}
		int nx=cur^1;
		ZERO(dp[nx]);
		REP(s,n+1)REP(a,n+1)REP(b,n+1)if(dp[cur][s][a][b])REP(c,n+1)REP(d,n+1){
			if(c+d==0)continue;
			if(s+c+d>n)continue;
			int w=c-d;
			if(-b<=w&&w<=a){
				int z=dp[cur][s][a][b];
				mult(z,factInv[a-w]);
				mult(z,factInv[b+w]);
				add(dp[nx][s+c+d][c][d],z);
			}
		}
		cur=nx;
	}
	return ans;
}

signed main(){
	InitFact();
	int n=read();
	print(Solve(n));
}
