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 <cstdio>
#include <cstring>
#include <algorithm>
#include <deque>
#include <vector>
using namespace std;

#define FILL(a, n, x) memset((a), (x), sizeof ((a)[0]) * (n))
#define FILLA(a, x) memset((a), (x), sizeof (a))
#define COPY(a, n, b) memcpy((b), (a), sizeof ((a)[0]) * (n))
#define COPYA(a, b) memcpy((b), (a), sizeof (a))

typedef unsigned long long lu;
const int mod = 1e9 + 7;

inline int Add(int x) { return x >= mod ? x - mod : x; }
inline void Add(int &x, int y) { x += y; if (x >= mod) x -= mod; }
inline int Sub(int x) { return x < 0 ? x + mod : x; }
inline void Sub(int &x, int y) { x = Sub(x - y); }
inline int Mul(int x, int y) { return (int)((lu)x * y % mod); }
inline int Mul(int x, int y, int z) { return (int)((lu)x * y % mod * z % mod); }

int Pow(int x, int y) {
  int z = 1;
  for (; y; y >>= 1) {
    if (y & 1) z = Mul(z, x);
    x = Mul(x, x);
  }
  return z;
}

int Inv(int x) { return Pow(x, mod - 2); }

// ----------------------------------------

const int maxn = 50;

int n;
int ans[maxn + 1] = {0,1,2,12,84,770,8340,106400,1546888,25343766,461133960,232367169,627905865,632459808,928262728,919805769,382796331,887217496,639768068,869694124,205875097,205589953,487772376,239955313,998339621,31622834,902930073,146839084,449786840,982224660,865803735,21834818,721531716,26008837,471774471,69010090,700009308,776938882,645550477,526939604,142728157,654489641,128201240,185493259,789721045,977049419,589149550,700648836,25087729,874433491,352791804};

int main(void) {
  scanf("%d", &n);
  printf("%d\n", ans[n]);
  return 0;
}
