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 <map>
#include <set>
#include <ctime>
#include <queue>
#include <stack>
#include <cmath>
#include <vector>
#include <bitset>
#include <cstdio>
#include <cctype>
#include <string>
#include <numeric>
#include <cstring>
#include <cassert>
#include <climits>
#include <cstdlib>
#include <iostream>
#include <algorithm>
#include <functional>
using namespace std ;
#define rep(i, a, b) for (register int i = (a); i <= (b); ++i)
#define per(i, a, b) for (register int i = (a); i >= (b); --i)
#define loop(it, v) for (auto it = v.begin(); it != v.end(); it++)
#define cont(i, x) for (register int i = head[x]; i; i = edge[i].nex)
#define clr(a) memset(a, 0, sizeof(a))
#define ass(a, cnt) memset(a, cnt, sizeof(a))
#define cop(a, b) memcpy(a, b, sizeof(a))
#define lowbit(x) (x & -x)
#define all(x) x.begin(), x.end()
#define SC(t, x) static_cast <t> (x)
#define ub upper_bound
#define lb lower_bound
#define pqueue priority_queue
#define mp make_pair
#define pb push_back
#define pof pop_front
#define pob pop_back
#define fi first
#define se second
#define y1 y1_
#define Pi acos(-1.0)
#define iv inline void
#define enter putchar('\n')
#define siz(x) ((int)x.size())
#define file(x) freopen(x".in", "r", stdin),freopen(x".out", "w", stdout)
typedef double db ;
typedef long long ll ;
typedef unsigned long long ull ;
typedef pair <int, int> pii ;
typedef vector <int> vi ;
typedef vector <pii> vii ;
typedef queue <int> qi ;
typedef queue <pii> qii ;
typedef set <int> si ;
typedef map <int, int> mii ;
typedef map <string, int> msi ;
const int maxn = 1e6 + 100 ;
const int inf = 0x3f3f3f3f ;
const int iinf = 1 << 30 ;
const ll linf = 2e18 ;
const ll mod = 1e9 + 7 ;
const double eps = 1e-5 ;

ll n;

ll c[55][55], f[55][55];

signed main()
{
	scanf("%lld", &n);
	c[0][0] = 1;
	rep(i, 1, n)
	{
		c[i][0] = 1;
		rep(j, 1, i) c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % mod;
	}
	f[1][0] = n, f[1][1] = n;
	rep(i, 1, n - 1) rep(j, 0, i) rep(k, max(j, 1), n - i)
	{
		if((k - j) & 1) continue;
		rep(x, 0, k) (f[i + k][abs(x - (k - j) / 2)] += c[n - i][k] * c[k][x] % mod * f[i][j] % mod) %= mod;
	}
	printf("%lld\n", f[n][0]);
	return 0;
}