import math

heights=[0,1,3,6,10,15,21,28,36,45,55,66,78,91,105,120]

def build_row(rlst, k, tri):
  row = []
  for parent in rlst:
    if parent == rlst[0]:
      lc = parent - k
      if (lc in rlst) or (lc in row):
        return []
      rc = k
    else:
      if row == []:
        rc = k
        lc = parent - k
      else:
        lc = row[-1]
        rc = parent - lc
    if (lc in tri) or (rc in tri) or (lc < 1) or (rc < 1):
      return []
    if (rc in rlst) or (rc in row) or (rc == lc):
      continue
    if parent == rlst[0]:
      row.append(lc)
    row.append(rc)
  if len(row) == len(rlst) + 1:
    return row
  else:
    return []  

def get_rows(lst,tri):
  if len(lst) == 1:
    tri = lst
  ct = lst[0]
  if len(lst) == 1:
    if lst[0] % 2 == 0:
      ct = int(lst[0] / 2)
    else:
      ct = int((lst[0] / 2) + 1)
  for k in range(ct):
    if len(lst)+1 == heights.index(len(tri)):
      a = -1*heights.index(len(tri))
      tri = tri[:a]
    row = build_row(lst, k, tri)
    if row != []:
      tri = tri + row
      get_rows(row,tri)
    else:
      if tri not in triangles[tri[0]-1]:
        if triangles[tri[0]-1] != []:
          if len(triangles[tri[0]-1][-1]) == 1:
            if len(lst) > 1:
             del(triangles[tri[0]-1][-1])
        if len(triangles[tri[0]-1]) > 2:
          if triangles[tri[0]-1][-1][:len(tri)] ==  tri[:heights.index(len(tri))]:
            if len(tri[:heights.index(len(tri))]) > 2:
              del(triangles[tri[0]-1][-1])
          if triangles[tri[0]-1][-1] == tri[:len(triangles[tri[0]-1][-1])]:
            del(triangles[tri[0]-1][-1])
          if tri == triangles[tri[0]-1][-1][:len(tri)]:
            continue       
        triangles[tri[0]-1].append(tri)

seq = []
tri = []
triangles = []
for m in range(1,17):
  triangles.append([])
  get_rows([m],tri)
  seq.append(len(triangles[m-1]))
print(seq)
for m in range(len(triangles)):
  for t in triangles[m]:
   print(t)