Consider the binary representation of integers to define the points in {0,1}^n
Example: n=3 , S = {0,3,5,6} = {(0,0,0) , (0,1,1) , (1,0,1) , (1,1,0)}

For n = 3 the a(3) = 2 solutions:
S = {0,3,5,6}
S = {1,2,4,7}

For n = 4 the a(4) = 16 solutions:
S = {0,3,5,9,14}
S = {0,3,6,10,13}
S = {0,5,6,11,12}
S = {0,7,9,10,12}
S = {0,7,11,13,14}
S = {1,2,4,8,15}
S = {1,2,7,11,12}
S = {1,4,7,10,13}
S = {1,6,8,11,13}
S = {1,6,10,12,15}
S = {2,4,7,9,14}
S = {2,5,8,11,14}
S = {2,5,9,12,15}
S = {3,4,8,13,14}
S = {3,4,9,10,15}
S = {3,5,6,8,15}

For n = 5 the a(5) = 352 solutions:
S = {0,3,5,9,17,30}
S = {0,3,5,14,22,25}
S = {0,3,6,10,18,29}
S = {0,3,6,13,21,26}
S = {0,3,9,14,21,26}
S = {0,3,10,13,22,25}
S = {0,3,13,17,22,26}
S = {0,3,13,21,25,30}
S = {0,3,14,18,21,25}
S = {0,3,14,22,26,29}
S = {0,5,6,11,19,28}
S = {0,5,6,12,20,27}
S = {0,5,9,14,19,28}
S = {0,5,11,12,22,25}
S = {0,5,11,17,22,28}
S = {0,5,11,19,25,30}
S = {0,5,14,19,20,25}
S = {0,5,14,22,27,28}
S = {0,6,10,13,19,28}
S = {0,6,11,12,21,26}
S = {0,6,11,18,21,28}
S = {0,6,11,19,26,29}
S = {0,6,13,19,20,26}
S = {0,6,13,21,27,28}
S = {0,7,9,10,19,28}
S = {0,7,9,12,21,26}
S = {0,7,9,17,26,28}
S = {0,7,9,19,21,30}
S = {0,7,10,12,22,25}
S = {0,7,10,18,25,28}
S = {0,7,10,19,22,29}
S = {0,7,11,13,17,30}
S = {0,7,11,14,18,29}
S = {0,7,11,17,18,28}
S = {0,7,11,19,29,30}
S = {0,7,12,20,25,26}
S = {0,7,12,21,22,27}
S = {0,7,13,14,20,27}
S = {0,7,13,17,20,26}
S = {0,7,13,21,27,30}
S = {0,7,14,18,20,25}
S = {0,7,14,22,27,29}
S = {0,9,10,12,23,24}
S = {0,9,14,19,21,24}
S = {0,9,14,23,26,28}
S = {0,10,13,19,22,24}
S = {0,10,13,23,25,28}
S = {0,11,12,21,22,24}
S = {0,11,12,23,25,26}
S = {0,11,13,14,23,24}
S = {0,11,13,17,22,24}
S = {0,11,13,23,25,30}
S = {0,11,14,18,21,24}
S = {0,11,14,23,26,29}
S = {0,13,14,19,20,24}
S = {0,13,14,23,27,28}
S = {0,15,17,18,20,24}
S = {0,15,17,22,26,28}
S = {0,15,18,21,25,28}
S = {0,15,19,20,25,26}
S = {0,15,19,21,22,24}
S = {0,15,19,21,25,30}
S = {0,15,19,22,26,29}
S = {0,15,21,22,27,28}
S = {0,15,23,25,26,28}
S = {0,15,23,27,29,30}
S = {1,2,4,8,16,31}
S = {1,2,4,15,23,24}
S = {1,2,7,11,19,28}
S = {1,2,7,12,20,27}
S = {1,2,8,15,20,27}
S = {1,2,11,12,23,24}
S = {1,2,12,16,23,27}
S = {1,2,12,20,24,31}
S = {1,2,15,19,20,24}
S = {1,2,15,23,27,28}
S = {1,4,7,10,18,29}
S = {1,4,7,13,21,26}
S = {1,4,8,15,18,29}
S = {1,4,10,13,23,24}
S = {1,4,10,16,23,29}
S = {1,4,10,18,24,31}
S = {1,4,15,18,21,24}
S = {1,4,15,23,26,29}
S = {1,6,8,11,18,29}
S = {1,6,8,13,20,27}
S = {1,6,8,16,27,29}
S = {1,6,8,18,20,31}
S = {1,6,10,12,16,31}
S = {1,6,10,15,19,28}
S = {1,6,10,16,19,29}
S = {1,6,10,18,28,31}
S = {1,6,11,13,23,24}
S = {1,6,11,18,23,28}
S = {1,6,11,19,24,29}
S = {1,6,12,15,21,26}
S = {1,6,12,16,21,27}
S = {1,6,12,20,26,31}
S = {1,6,13,20,23,26}
S = {1,6,13,21,24,27}
S = {1,6,15,19,21,24}
S = {1,6,15,23,26,28}
S = {1,7,10,13,20,27}
S = {1,7,10,18,27,28}
S = {1,7,10,19,20,29}
S = {1,7,11,12,18,29}
S = {1,7,12,18,21,27}
S = {1,7,12,20,26,29}
S = {1,8,11,13,22,25}
S = {1,8,15,18,20,25}
S = {1,8,15,22,27,29}
S = {1,10,12,15,22,25}
S = {1,10,12,16,23,25}
S = {1,10,12,22,24,31}
S = {1,10,13,20,23,25}
S = {1,10,13,22,24,27}
S = {1,10,15,19,20,25}
S = {1,10,15,22,27,28}
S = {1,11,12,18,23,25}
S = {1,11,12,22,24,29}
S = {1,12,15,18,21,25}
S = {1,12,15,22,26,29}
S = {1,14,16,19,21,25}
S = {1,14,16,23,27,29}
S = {1,14,18,20,23,25}
S = {1,14,18,20,24,31}
S = {1,14,18,21,24,27}
S = {1,14,18,23,27,28}
S = {1,14,19,20,24,29}
S = {1,14,20,23,26,29}
S = {1,14,22,24,27,29}
S = {1,14,22,26,28,31}
S = {2,4,7,9,17,30}
S = {2,4,7,14,22,25}
S = {2,4,8,15,17,30}
S = {2,4,9,14,23,24}
S = {2,4,9,16,23,30}
S = {2,4,9,17,24,31}
S = {2,4,15,17,22,24}
S = {2,4,15,23,25,30}
S = {2,5,8,11,17,30}
S = {2,5,8,14,20,27}
S = {2,5,8,16,27,30}
S = {2,5,8,17,20,31}
S = {2,5,9,12,16,31}
S = {2,5,9,15,19,28}
S = {2,5,9,16,19,30}
S = {2,5,9,17,28,31}
S = {2,5,11,14,23,24}
S = {2,5,11,17,23,28}
S = {2,5,11,19,24,30}
S = {2,5,12,15,22,25}
S = {2,5,12,16,22,27}
S = {2,5,12,20,25,31}
S = {2,5,14,20,23,25}
S = {2,5,14,22,24,27}
S = {2,5,15,19,22,24}
S = {2,5,15,23,25,28}
S = {2,7,9,14,20,27}
S = {2,7,9,17,27,28}
S = {2,7,9,19,20,30}
S = {2,7,11,12,17,30}
S = {2,7,12,17,22,27}
S = {2,7,12,20,25,30}
S = {2,8,11,14,21,26}
S = {2,8,15,17,20,26}
S = {2,8,15,21,27,30}
S = {2,9,12,15,21,26}
S = {2,9,12,16,23,26}
S = {2,9,12,21,24,31}
S = {2,9,14,20,23,26}
S = {2,9,14,21,24,27}
S = {2,9,15,19,20,26}
S = {2,9,15,21,27,28}
S = {2,11,12,17,23,26}
S = {2,11,12,21,24,30}
S = {2,12,15,17,22,26}
S = {2,12,15,21,25,30}
S = {2,13,16,19,22,26}
S = {2,13,16,23,27,30}
S = {2,13,17,20,23,26}
S = {2,13,17,20,24,31}
S = {2,13,17,22,24,27}
S = {2,13,17,23,27,28}
S = {2,13,19,20,24,30}
S = {2,13,20,23,25,30}
S = {2,13,21,24,27,30}
S = {2,13,21,25,28,31}
S = {3,4,8,13,17,30}
S = {3,4,8,14,18,29}
S = {3,4,8,16,29,30}
S = {3,4,8,17,18,31}
S = {3,4,9,10,16,31}
S = {3,4,9,15,21,26}
S = {3,4,9,16,21,30}
S = {3,4,9,17,26,31}
S = {3,4,10,15,22,25}
S = {3,4,10,16,22,29}
S = {3,4,10,18,25,31}
S = {3,4,13,14,23,24}
S = {3,4,13,17,23,26}
S = {3,4,13,21,24,30}
S = {3,4,14,18,23,25}
S = {3,4,14,22,24,29}
S = {3,4,15,21,22,24}
S = {3,4,15,23,25,26}
S = {3,5,6,8,16,31}
S = {3,5,6,15,23,24}
S = {3,5,8,15,22,25}
S = {3,5,8,16,25,30}
S = {3,5,8,17,22,31}
S = {3,5,9,14,16,31}
S = {3,5,14,16,23,25}
S = {3,5,14,22,24,31}
S = {3,6,8,15,21,26}
S = {3,6,8,16,26,29}
S = {3,6,8,18,21,31}
S = {3,6,10,13,16,31}
S = {3,6,13,16,23,26}
S = {3,6,13,21,24,31}
S = {3,8,13,14,20,27}
S = {3,8,13,17,22,27}
S = {3,8,13,20,25,30}
S = {3,8,14,18,21,27}
S = {3,8,14,20,26,29}
S = {3,8,15,20,25,26}
S = {3,8,15,21,22,27}
S = {3,9,10,15,20,27}
S = {3,9,14,16,21,27}
S = {3,9,14,20,26,31}
S = {3,10,13,16,22,27}
S = {3,10,13,20,25,31}
S = {3,12,16,21,22,27}
S = {3,12,16,21,25,30}
S = {3,12,16,22,26,29}
S = {3,12,16,23,25,26}
S = {3,12,17,18,23,27}
S = {3,12,17,22,26,31}
S = {3,12,18,21,25,31}
S = {3,12,20,24,29,30}
S = {3,12,20,25,26,31}
S = {3,12,21,22,24,31}
S = {3,13,14,16,23,27}
S = {3,13,14,20,24,31}
S = {4,7,9,14,18,29}
S = {4,7,9,17,26,29}
S = {4,7,9,18,21,30}
S = {4,7,10,13,17,30}
S = {4,7,10,17,22,29}
S = {4,7,10,18,25,30}
S = {4,8,13,14,19,28}
S = {4,8,15,17,18,28}
S = {4,8,15,19,29,30}
S = {4,9,10,15,19,28}
S = {4,9,10,16,23,28}
S = {4,9,10,19,24,31}
S = {4,9,14,18,23,28}
S = {4,9,14,19,24,29}
S = {4,9,15,18,21,28}
S = {4,9,15,19,26,29}
S = {4,10,13,17,23,28}
S = {4,10,13,19,24,30}
S = {4,10,15,17,22,28}
S = {4,10,15,19,25,30}
S = {4,11,16,21,22,28}
S = {4,11,16,23,29,30}
S = {4,11,17,18,23,28}
S = {4,11,17,18,24,31}
S = {4,11,17,22,24,29}
S = {4,11,17,23,26,29}
S = {4,11,18,21,24,30}
S = {4,11,18,23,25,30}
S = {4,11,19,24,29,30}
S = {4,11,19,25,26,31}
S = {5,6,8,15,19,28}
S = {5,6,8,16,27,28}
S = {5,6,8,19,20,31}
S = {5,6,11,12,16,31}
S = {5,6,11,16,23,28}
S = {5,6,11,19,24,31}
S = {5,8,11,14,18,29}
S = {5,8,11,17,22,29}
S = {5,8,11,18,25,30}
S = {5,8,14,18,27,28}
S = {5,8,14,19,20,29}
S = {5,8,15,18,25,28}
S = {5,8,15,19,22,29}
S = {5,9,12,15,18,29}
S = {5,9,14,16,19,29}
S = {5,9,14,18,28,31}
S = {5,10,16,19,22,29}
S = {5,10,16,19,25,30}
S = {5,10,16,22,27,28}
S = {5,10,16,23,25,28}
S = {5,10,17,20,23,29}
S = {5,10,17,22,28,31}
S = {5,10,18,24,27,30}
S = {5,10,18,25,28,31}
S = {5,10,19,20,25,31}
S = {5,10,19,22,24,31}
S = {5,11,12,16,22,29}
S = {5,11,12,18,25,31}
S = {5,11,14,16,23,29}
S = {5,11,14,18,24,31}
S = {6,8,11,13,17,30}
S = {6,8,11,17,26,29}
S = {6,8,11,18,21,30}
S = {6,8,13,17,27,28}
S = {6,8,13,19,20,30}
S = {6,8,15,17,26,28}
S = {6,8,15,19,21,30}
S = {6,9,16,19,21,30}
S = {6,9,16,19,26,29}
S = {6,9,16,21,27,28}
S = {6,9,16,23,26,28}
S = {6,9,17,24,27,29}
S = {6,9,17,26,28,31}
S = {6,9,18,20,23,30}
S = {6,9,18,21,28,31}
S = {6,9,19,20,26,31}
S = {6,9,19,21,24,31}
S = {6,10,12,15,17,30}
S = {6,10,13,16,19,30}
S = {6,10,13,17,28,31}
S = {6,11,12,16,21,30}
S = {6,11,12,17,26,31}
S = {6,11,13,16,23,30}
S = {6,11,13,17,24,31}
S = {7,8,16,25,26,28}
S = {7,8,16,27,29,30}
S = {7,8,17,18,20,31}
S = {7,8,17,18,27,28}
S = {7,8,17,20,26,29}
S = {7,8,17,22,27,29}
S = {7,8,18,20,25,30}
S = {7,8,18,21,27,30}
S = {7,8,19,20,29,30}
S = {7,8,19,21,22,31}
S = {7,9,10,12,16,31}
S = {7,9,10,16,27,28}
S = {7,9,10,19,20,31}
S = {7,9,12,16,26,29}
S = {7,9,12,18,21,31}
S = {7,9,14,16,27,29}
S = {7,9,14,18,20,31}
S = {7,10,12,16,25,30}
S = {7,10,12,17,22,31}
S = {7,10,13,16,27,30}
S = {7,10,13,17,20,31}
S = {7,11,12,16,29,30}
S = {7,11,12,17,18,31}
S = {7,11,13,14,16,31}

For n = 6 the a(6) = 240 solutions:
S = {0,7,25,30,42,45,51,52}
S = {0,7,25,30,43,44,50,53}
S = {0,7,26,29,41,46,51,52}
S = {0,7,26,29,43,44,49,54}
S = {0,7,27,28,41,46,50,53}
S = {0,7,27,28,42,45,49,54}
S = {0,11,21,30,38,45,51,56}
S = {0,11,21,30,39,44,50,57}
S = {0,11,22,29,37,46,51,56}
S = {0,11,22,29,39,44,49,58}
S = {0,11,23,28,37,46,50,57}
S = {0,11,23,28,38,45,49,58}
S = {0,13,19,30,38,43,53,56}
S = {0,13,19,30,39,42,52,57}
S = {0,13,22,27,35,46,53,56}
S = {0,13,22,27,39,42,49,60}
S = {0,13,23,26,35,46,52,57}
S = {0,13,23,26,38,43,49,60}
S = {0,14,19,29,37,43,54,56}
S = {0,14,19,29,39,41,52,58}
S = {0,14,21,27,35,45,54,56}
S = {0,14,21,27,39,41,50,60}
S = {0,14,23,25,35,45,52,58}
S = {0,14,23,25,37,43,50,60}
S = {0,15,19,28,37,42,54,57}
S = {0,15,19,28,38,41,53,58}
S = {0,15,21,26,35,44,54,57}
S = {0,15,21,26,38,41,51,60}
S = {0,15,22,25,35,44,53,58}
S = {0,15,22,25,37,42,51,60}
S = {1,6,24,31,42,45,51,52}
S = {1,6,24,31,43,44,50,53}
S = {1,6,26,29,40,47,51,52}
S = {1,6,26,29,43,44,48,55}
S = {1,6,27,28,40,47,50,53}
S = {1,6,27,28,42,45,48,55}
S = {1,10,20,31,38,45,51,56}
S = {1,10,20,31,39,44,50,57}
S = {1,10,22,29,36,47,51,56}
S = {1,10,22,29,39,44,48,59}
S = {1,10,23,28,36,47,50,57}
S = {1,10,23,28,38,45,48,59}
S = {1,12,18,31,38,43,53,56}
S = {1,12,18,31,39,42,52,57}
S = {1,12,22,27,34,47,53,56}
S = {1,12,22,27,39,42,48,61}
S = {1,12,23,26,34,47,52,57}
S = {1,12,23,26,38,43,48,61}
S = {1,14,18,29,36,43,55,56}
S = {1,14,18,29,39,40,52,59}
S = {1,14,20,27,34,45,55,56}
S = {1,14,20,27,39,40,50,61}
S = {1,14,23,24,34,45,52,59}
S = {1,14,23,24,36,43,50,61}
S = {1,15,18,28,36,42,55,57}
S = {1,15,18,28,38,40,53,59}
S = {1,15,20,26,34,44,55,57}
S = {1,15,20,26,38,40,51,61}
S = {1,15,22,24,34,44,53,59}
S = {1,15,22,24,36,42,51,61}
S = {2,5,24,31,41,46,51,52}
S = {2,5,24,31,43,44,49,54}
S = {2,5,25,30,40,47,51,52}
S = {2,5,25,30,43,44,48,55}
S = {2,5,27,28,40,47,49,54}
S = {2,5,27,28,41,46,48,55}
S = {2,9,20,31,37,46,51,56}
S = {2,9,20,31,39,44,49,58}
S = {2,9,21,30,36,47,51,56}
S = {2,9,21,30,39,44,48,59}
S = {2,9,23,28,36,47,49,58}
S = {2,9,23,28,37,46,48,59}
S = {2,12,17,31,37,43,54,56}
S = {2,12,17,31,39,41,52,58}
S = {2,12,21,27,33,47,54,56}
S = {2,12,21,27,39,41,48,62}
S = {2,12,23,25,33,47,52,58}
S = {2,12,23,25,37,43,48,62}
S = {2,13,17,30,36,43,55,56}
S = {2,13,17,30,39,40,52,59}
S = {2,13,20,27,33,46,55,56}
S = {2,13,20,27,39,40,49,62}
S = {2,13,23,24,33,46,52,59}
S = {2,13,23,24,36,43,49,62}
S = {2,15,17,28,36,41,55,58}
S = {2,15,17,28,37,40,54,59}
S = {2,15,20,25,33,44,55,58}
S = {2,15,20,25,37,40,51,62}
S = {2,15,21,24,33,44,54,59}
S = {2,15,21,24,36,41,51,62}
S = {3,4,24,31,41,46,50,53}
S = {3,4,24,31,42,45,49,54}
S = {3,4,25,30,40,47,50,53}
S = {3,4,25,30,42,45,48,55}
S = {3,4,26,29,40,47,49,54}
S = {3,4,26,29,41,46,48,55}
S = {3,8,20,31,37,46,50,57}
S = {3,8,20,31,38,45,49,58}
S = {3,8,21,30,36,47,50,57}
S = {3,8,21,30,38,45,48,59}
S = {3,8,22,29,36,47,49,58}
S = {3,8,22,29,37,46,48,59}
S = {3,12,16,31,37,42,54,57}
S = {3,12,16,31,38,41,53,58}
S = {3,12,21,26,32,47,54,57}
S = {3,12,21,26,38,41,48,63}
S = {3,12,22,25,32,47,53,58}
S = {3,12,22,25,37,42,48,63}
S = {3,13,16,30,36,42,55,57}
S = {3,13,16,30,38,40,53,59}
S = {3,13,20,26,32,46,55,57}
S = {3,13,20,26,38,40,49,63}
S = {3,13,22,24,32,46,53,59}
S = {3,13,22,24,36,42,49,63}
S = {3,14,16,29,36,41,55,58}
S = {3,14,16,29,37,40,54,59}
S = {3,14,20,25,32,45,55,58}
S = {3,14,20,25,37,40,50,63}
S = {3,14,21,24,32,45,54,59}
S = {3,14,21,24,36,41,50,63}
S = {4,9,18,31,35,46,53,56}
S = {4,9,18,31,39,42,49,60}
S = {4,9,19,30,34,47,53,56}
S = {4,9,19,30,39,42,48,61}
S = {4,9,23,26,34,47,49,60}
S = {4,9,23,26,35,46,48,61}
S = {4,10,17,31,35,45,54,56}
S = {4,10,17,31,39,41,50,60}
S = {4,10,19,29,33,47,54,56}
S = {4,10,19,29,39,41,48,62}
S = {4,10,23,25,33,47,50,60}
S = {4,10,23,25,35,45,48,62}
S = {4,11,17,30,34,45,55,56}
S = {4,11,17,30,39,40,50,61}
S = {4,11,18,29,33,46,55,56}
S = {4,11,18,29,39,40,49,62}
S = {4,11,23,24,33,46,50,61}
S = {4,11,23,24,34,45,49,62}
S = {4,15,17,26,34,41,55,60}
S = {4,15,17,26,35,40,54,61}
S = {4,15,18,25,33,42,55,60}
S = {4,15,18,25,35,40,53,62}
S = {4,15,19,24,33,42,54,61}
S = {4,15,19,24,34,41,53,62}
S = {5,8,18,31,35,46,52,57}
S = {5,8,18,31,38,43,49,60}
S = {5,8,19,30,34,47,52,57}
S = {5,8,19,30,38,43,48,61}
S = {5,8,22,27,34,47,49,60}
S = {5,8,22,27,35,46,48,61}
S = {5,10,16,31,35,44,54,57}
S = {5,10,16,31,38,41,51,60}
S = {5,10,19,28,32,47,54,57}
S = {5,10,19,28,38,41,48,63}
S = {5,10,22,25,32,47,51,60}
S = {5,10,22,25,35,44,48,63}
S = {5,11,16,30,34,44,55,57}
S = {5,11,16,30,38,40,51,61}
S = {5,11,18,28,32,46,55,57}
S = {5,11,18,28,38,40,49,63}
S = {5,11,22,24,32,46,51,61}
S = {5,11,22,24,34,44,49,63}
S = {5,14,16,27,34,41,55,60}
S = {5,14,16,27,35,40,54,61}
S = {5,14,18,25,32,43,55,60}
S = {5,14,18,25,35,40,52,63}
S = {5,14,19,24,32,43,54,61}
S = {5,14,19,24,34,41,52,63}
S = {6,8,17,31,35,45,52,58}
S = {6,8,17,31,37,43,50,60}
S = {6,8,19,29,33,47,52,58}
S = {6,8,19,29,37,43,48,62}
S = {6,8,21,27,33,47,50,60}
S = {6,8,21,27,35,45,48,62}
S = {6,9,16,31,35,44,53,58}
S = {6,9,16,31,37,42,51,60}
S = {6,9,19,28,32,47,53,58}
S = {6,9,19,28,37,42,48,63}
S = {6,9,21,26,32,47,51,60}
S = {6,9,21,26,35,44,48,63}
S = {6,11,16,29,33,44,55,58}
S = {6,11,16,29,37,40,51,62}
S = {6,11,17,28,32,45,55,58}
S = {6,11,17,28,37,40,50,63}
S = {6,11,21,24,32,45,51,62}
S = {6,11,21,24,33,44,50,63}
S = {6,13,16,27,33,42,55,60}
S = {6,13,16,27,35,40,53,62}
S = {6,13,17,26,32,43,55,60}
S = {6,13,17,26,35,40,52,63}
S = {6,13,19,24,32,43,53,62}
S = {6,13,19,24,33,42,52,63}
S = {7,8,17,30,34,45,52,59}
S = {7,8,17,30,36,43,50,61}
S = {7,8,18,29,33,46,52,59}
S = {7,8,18,29,36,43,49,62}
S = {7,8,20,27,33,46,50,61}
S = {7,8,20,27,34,45,49,62}
S = {7,9,16,30,34,44,53,59}
S = {7,9,16,30,36,42,51,61}
S = {7,9,18,28,32,46,53,59}
S = {7,9,18,28,36,42,49,63}
S = {7,9,20,26,32,46,51,61}
S = {7,9,20,26,34,44,49,63}
S = {7,10,16,29,33,44,54,59}
S = {7,10,16,29,36,41,51,62}
S = {7,10,17,28,32,45,54,59}
S = {7,10,17,28,36,41,50,63}
S = {7,10,20,25,32,45,51,62}
S = {7,10,20,25,33,44,50,63}
S = {7,12,16,27,33,42,54,61}
S = {7,12,16,27,34,41,53,62}
S = {7,12,17,26,32,43,54,61}
S = {7,12,17,26,34,41,52,63}
S = {7,12,18,25,32,43,53,62}
S = {7,12,18,25,33,42,52,63}
S = {8,15,17,22,34,37,59,60}
S = {8,15,17,22,35,36,58,61}
S = {8,15,18,21,33,38,59,60}
S = {8,15,18,21,35,36,57,62}
S = {8,15,19,20,33,38,58,61}
S = {8,15,19,20,34,37,57,62}
S = {9,14,16,23,34,37,59,60}
S = {9,14,16,23,35,36,58,61}
S = {9,14,18,21,32,39,59,60}
S = {9,14,18,21,35,36,56,63}
S = {9,14,19,20,32,39,58,61}
S = {9,14,19,20,34,37,56,63}
S = {10,13,16,23,33,38,59,60}
S = {10,13,16,23,35,36,57,62}
S = {10,13,17,22,32,39,59,60}
S = {10,13,17,22,35,36,56,63}
S = {10,13,19,20,32,39,57,62}
S = {10,13,19,20,33,38,56,63}
S = {11,12,16,23,33,38,58,61}
S = {11,12,16,23,34,37,57,62}
S = {11,12,17,22,32,39,58,61}
S = {11,12,17,22,34,37,56,63}
S = {11,12,18,21,32,39,57,62}
S = {11,12,18,21,33,38,56,63}