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>
#define MOD 1000000007
typedef long long ll;
ll dp[55][105], C[55][55]; 
int main()
{
	// freopen("AGC022-F.in", "r", stdin); 
	for (int i = 0; i <= 50; i++)
	{
		C[i][0] = 1; 
		for (int j = 1; j <= i; j++)
			C[i][j] = (C[i - 1][j - 1] + C[i - 1][j]) % MOD; 
	}
	int n; 
	scanf("%d", &n); 
	dp[1][n] = dp[1][n - 1] = 1; 
	for (int i = 1; i < n; i++)
	{
		for (int j = -n; j <= n; j++)
		{
			for (int a = 0; a < n; a++)
			{
				for (int b = 0; b < n; b++)
				{
					if ((a || b) && i + a + b <= n && j <= a + b && -a - b <= j && !(j + a - b & 1))
						(dp[i + a + b][(j + a - b) / 2 + n] += dp[i][j + n] * C[i + a + b][i] % MOD * C[a + b][a]) %= MOD; 
				}
			}
		}
	}
	printf("%lld\n", dp[n][n]);
	return 0; 
}
