Problem:
 Score : 1600 points    Problem Statement 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 .        Sample Input 1 3      Sample Output 1 12  There are 3 checker pieces, positioned at 10^{100}, 10^{200}, 10^{300} respectively. Call them A, B, C respectively.  Here are two (of the 12 ) possible sequence of moves :    Let A jump over B in the first second, and let A jump over C in the second second. The final position of A is 2 \times 10^{300} - 2 \times 10^{200} + 10^{100} .    Let C jump over A in the first second, and let B jump over C in the second second. The final position of B is -2 \times 10^{300} - 10^{200} + 4 \times 10^{100} .    There are a total of 3 \times 2 \times 2 = 12 possible sequence of moves, and the final piece are in different positions in all of them.       Sample Input 2 4      Sample Output 2 84       Sample Input 3 22      Sample Output 3 487772376  Remember to output your answer modulo 10^{9} + 7 .

Solution (Python):
print[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][input()]