diff --git a/.DS_Store b/.DS_Store
new file mode 100644
index 0000000..a0fe261
Binary files /dev/null and b/.DS_Store differ
diff --git a/6_18_2024_catalan/__pycache__/catalan.cpython-312.pyc b/6_18_2024_catalan/__pycache__/catalan.cpython-312.pyc
new file mode 100644
index 0000000..0533210
Binary files /dev/null and b/6_18_2024_catalan/__pycache__/catalan.cpython-312.pyc differ
diff --git a/6_18_2024_catalan/catalan.py b/6_18_2024_catalan/catalan.py
index 8946549..1dce92c 100644
--- a/6_18_2024_catalan/catalan.py
+++ b/6_18_2024_catalan/catalan.py
@@ -2,6 +2,7 @@
 
 def parenthesizations(n):
   """
+
   Returns a set of all possible parenthesizations of length n.
 
   Parameters:
@@ -17,9 +18,25 @@ def parenthesizations(n):
   if n == 0:
     return {""}
   else:
-    # TODO
-    pass
+    output = set()
+    parenthesizations_helper("", n, n, output)
+    return output
 
+"""
+res - result string
+open - number of open parenthesis
+close - number of close parenthesis
+output - output set
+"""
+def parenthesizations_helper(res, open, close, output):
+  if open == 0 and close == 0:
+    output.add(res)
+  else:
+    if open > 0:
+      parenthesizations_helper(res + "(", open - 1, close, output)
+    if close != open:
+      parenthesizations_helper(res + ")", open, close - 1, output)             
+      
 def product_orders(n):
   """
   Returns a set of all possible ways to multiply of n elements.
@@ -41,8 +58,23 @@ def product_orders(n):
   elif n == 2:
     return {"?*?"}
   else:
-    # TODO
-    pass
+    output = set()
+    return product_orders_helper(n, n)
+    
+
+def product_orders_helper(n, overall_length):
+  if n == 1:
+    return {"?"}
+  output = set()
+  for i in range(1, n):
+    for j in product_orders_helper(i, overall_length):
+      for k in product_orders_helper(n - i, overall_length):
+        new_string = j + "*" + k
+        if new_string[0] == "?" or new_string[len(new_string) - 1] == "?":
+          if n < overall_length:
+            new_string = "(" + new_string + ")"
+        output.add(new_string)
+  return output
 
 def permutations_avoiding_231(n):
   """
@@ -58,11 +90,32 @@ def permutations_avoiding_231(n):
   >>> permutations_avoiding_231(4)
   {(1, 2, 3, 4), (1, 2, 4, 3), (1, 3, 2, 4), (1, 4, 2, 3), (1, 4, 3, 2), (2, 1, 3, 4), (2, 1, 4, 3), (3, 1, 2, 4), (3, 2, 1, 4), (4, 1, 2, 3), (4, 1, 3, 2), (4, 2, 1, 3), (4, 3, 1, 2), (4, 3, 2, 1)}
   """
+  
   if n < 3:
     return set(itertools.permutations(range(1, n+1)))
   else:
-    # TODO
-    pass
+    perms = itertools.permutations(range(1, n+1))
+    output = set()
+    found = False
+    for perm in perms:
+      found = False
+      for i in range(n - 2):
+        first = perm[i]
+        for j in range(i + 1, n - 1):
+          second = perm[j]
+          for k in range(j + 1, n):
+            third = perm[k]
+            if second > first and first > third:
+              found = True
+              break
+          if found:
+            break
+        if found:
+          break
+      if not found:
+        output.add(perm)
+    return output     
+    
 
 def triangulations(n):
   """
@@ -84,5 +137,23 @@ def triangulations(n):
   elif n == 3:
     return {tuple()}
   else:
-    pass
-    # TODO
\ No newline at end of file
+    vertices = list(range(n - 1))
+    output = set()
+    for i in range (n - 2):
+      output = output.union(triangulation_helper(i, vertices))
+    return output
+
+
+def triangulation_helper(start, vertices):
+  length = len(vertices)
+  vertices = sorted(vertices)
+  output = set()
+  if len(vertices) == 3:
+    return {((vertices[(start) % length], vertices[(start + 1) % length]), (vertices[start % length], vertices[(start + 2) % length]))}
+  else:
+    triangle = ((vertices[(start) % length], vertices[(start + 1) % length]), (vertices[start % length], vertices[(start + 2) % length]))
+    del vertices[(start + 1) % length]
+    output.add(triangle)
+    return output.union(triangulation_helper(start, vertices))
+  
+    
\ No newline at end of file
diff --git a/6_18_2024_catalan/main.ipynb b/6_18_2024_catalan/main.ipynb
index eab3ee3..baa58e0 100644
--- a/6_18_2024_catalan/main.ipynb
+++ b/6_18_2024_catalan/main.ipynb
@@ -10,7 +10,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 1,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -37,7 +37,9 @@
    "outputs": [],
    "source": [
     "for n in range(1, 11):\n",
-    "  pass"
+    "  x = catalan.parenthesizations(n)\n",
+    "  print(x)\n",
+    "  print(len(x))"
    ]
   },
   {
@@ -51,12 +53,41 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 2,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "{'?*?'}\n",
+      "1\n",
+      "{'(?*?)*?', '?*(?*?)'}\n",
+      "2\n",
+      "{'(?*(?*?))*?', '?*(?*(?*?))', '(?*?)*(?*?)', '((?*?)*?)*?', '?*((?*?)*?)'}\n",
+      "5\n",
+      "{'((?*(?*?))*?)*?', '(?*(?*(?*?)))*?', '?*((?*(?*?))*?)', '(((?*?)*?)*?)*?', '(?*?)*(?*?)*?', '?*(((?*?)*?)*?)', '(?*?)*((?*?)*?)', '?*(?*(?*(?*?)))', '?*(?*((?*?)*?))', '?*(?*?)*(?*?)', '(?*?)*(?*(?*?))', '(?*(?*?))*(?*?)', '(?*((?*?)*?))*?', '((?*?)*?)*(?*?)'}\n",
+      "14\n",
+      "{'(?*(?*?))*(?*?)*?', '(((?*?)*?)*?)*(?*?)', '?*(?*?)*((?*?)*?)', '((?*?)*?)*(?*(?*?))', '(?*(?*(?*?)))*(?*?)', '?*((((?*?)*?)*?)*?)', '(?*?)*(?*((?*?)*?))', '((?*((?*?)*?))*?)*?', '((?*(?*(?*?)))*?)*?', '?*(?*(?*((?*?)*?)))', '?*(?*(?*?)*(?*?))', '?*(?*(((?*?)*?)*?))', '(?*(?*?))*((?*?)*?)', '((?*?)*?)*((?*?)*?)', '(?*(?*((?*?)*?)))*?', '(?*((?*?)*?))*(?*?)', '((?*(?*?))*?)*(?*?)', '(?*?)*((?*?)*?)*?', '(?*(((?*?)*?)*?))*?', '?*((?*?)*(?*?)*?)', '(((?*(?*?))*?)*?)*?', '((?*?)*?)*(?*?)*?', '?*(?*(?*?))*(?*?)', '?*(?*(?*(?*(?*?))))', '(?*?)*(?*(?*(?*?)))', '(?*?)*((?*(?*?))*?)', '(?*(?*?)*(?*?))*?', '(?*(?*(?*(?*?))))*?', '((((?*?)*?)*?)*?)*?', '?*((?*?)*?)*(?*?)', '?*(?*((?*(?*?))*?))', '?*(?*?)*(?*(?*?))', '(?*?)*(?*?)*(?*?)', '?*(((?*(?*?))*?)*?)', '?*((?*(?*(?*?)))*?)', '(?*(?*?))*(?*(?*?))', '((?*?)*(?*?)*?)*?', '(?*?)*(((?*?)*?)*?)', '?*((?*((?*?)*?))*?)', '(?*((?*(?*?))*?))*?', '(?*?)*(?*(?*?))*?'}\n",
+      "41\n",
+      "{'?*(?*?)*(((?*?)*?)*?)', '((?*(?*(?*(?*?))))*?)*?', '?*(?*(?*(?*?))*(?*?))', '((?*?)*?)*(?*(?*(?*?)))', '(?*(?*(?*?)))*(?*(?*?))', '(?*?)*(?*(((?*?)*?)*?))', '?*(?*((?*?)*?))*(?*?)', '(?*?)*(?*((?*(?*?))*?))', '((((?*(?*?))*?)*?)*?)*?', '(?*((?*?)*?))*(?*(?*?))', '(?*?)*((?*?)*(?*?)*?)', '(?*(?*(?*?)*(?*?)))*?', '(?*(?*?)*(?*(?*?)))*?', '((?*(?*?))*?)*(?*?)*?', '(?*?)*(?*?)*(?*?)*?', '(?*(?*(?*?)))*(?*?)*?', '((?*(?*?)*(?*?))*?)*?', '?*(((?*?)*?)*(?*?)*?)', '((((?*?)*?)*?)*?)*(?*?)', '(?*?)*(?*?)*((?*?)*?)', '?*(((?*?)*(?*?)*?)*?)', '?*((?*(?*?))*?)*(?*?)', '?*((?*?)*(?*(?*?))*?)', '?*(?*((?*(?*(?*?)))*?))', '(?*?)*((?*((?*?)*?))*?)', '(?*?)*(?*(?*(?*(?*?))))', '(((?*((?*?)*?))*?)*?)*?', '?*(((?*((?*?)*?))*?)*?)', '(?*(?*?))*((?*(?*?))*?)', '((?*(?*?))*?)*((?*?)*?)', '(?*?)*(?*(?*(?*?)))*?', '(?*(?*(?*(?*(?*?)))))*?', '?*(?*(?*?))*(?*(?*?))', '((?*(?*(?*?)))*?)*(?*?)', '(?*(((?*?)*?)*?))*(?*?)', '(?*(?*?))*((?*?)*?)*?', '?*(?*(?*(((?*?)*?)*?)))', '?*(?*?)*(?*(?*(?*?)))', '(?*?)*((?*?)*?)*(?*?)', '(?*((?*?)*?)*(?*?))*?', '(?*((?*?)*?))*(?*?)*?', '(?*(?*((?*(?*?))*?)))*?', '(?*(?*(?*?))*(?*?))*?', '(((?*(?*?))*?)*?)*(?*?)', '?*((?*?)*?)*(?*(?*?))', '?*((?*?)*((?*?)*?)*?)', '((?*?)*(?*(?*?))*?)*?', '?*((((?*(?*?))*?)*?)*?)', '((?*?)*?)*((?*?)*?)*?', '?*(?*(?*?)*((?*?)*?))', '((?*((?*?)*?))*?)*(?*?)', '?*(?*(?*(?*(?*(?*?)))))', '?*((?*((?*(?*?))*?))*?)', '((?*(?*?))*?)*(?*(?*?))', '(((?*?)*?)*?)*((?*?)*?)', '((?*?)*(?*?)*?)*(?*?)', '(?*?)*((?*(?*(?*?)))*?)', '(?*?)*(?*?)*(?*(?*?))', '(?*(?*?)*((?*?)*?))*?', '?*(((?*(?*(?*?)))*?)*?)', '(?*(?*?))*(?*?)*(?*?)', '?*((?*(((?*?)*?)*?))*?)', '?*(?*(((?*(?*?))*?)*?))', '(((?*?)*?)*(?*?)*?)*?', '?*(?*?)*((?*(?*?))*?)', '(?*((?*?)*(?*?)*?))*?', '(?*?)*((?*(?*?))*?)*?', '(?*(?*?))*(?*(?*?))*?', '(?*?)*(?*(?*?))*(?*?)', '(((?*?)*?)*?)*(?*(?*?))', '(?*((?*((?*?)*?))*?))*?', '((?*?)*((?*?)*?)*?)*?', '?*((?*(?*((?*?)*?)))*?)', '(?*(?*?))*(?*((?*?)*?))', '(?*((?*(?*?))*?))*(?*?)', '(?*?)*(?*(?*?)*(?*?))', '(?*?)*((((?*?)*?)*?)*?)', '?*(?*((((?*?)*?)*?)*?))', '?*(?*(?*(?*?)))*(?*?)', '((?*(((?*?)*?)*?))*?)*?', '?*(((?*?)*?)*?)*(?*?)', '?*((?*(?*?))*(?*?)*?)', '(?*(?*(((?*?)*?)*?)))*?', '(((?*(?*(?*?)))*?)*?)*?', '?*(?*?)*(?*?)*(?*?)', '?*(((((?*?)*?)*?)*?)*?)', '?*(?*(?*?))*((?*?)*?)', '(?*?)*(?*((?*?)*?))*?', '(?*(?*((?*?)*?)))*(?*?)', '(?*(?*?))*(?*(?*(?*?)))', '(((((?*?)*?)*?)*?)*?)*?', '(((?*?)*(?*?)*?)*?)*?', '(?*((((?*?)*?)*?)*?))*?', '((?*?)*?)*(?*?)*(?*?)', '?*(?*(?*(?*?)*(?*?)))', '?*((?*?)*?)*((?*?)*?)', '((?*?)*?)*(((?*?)*?)*?)', '?*(?*?)*(?*((?*?)*?))', '((?*(?*?))*(?*?)*?)*?', '(?*(?*(?*(?*?))))*(?*?)', '(((?*?)*?)*?)*(?*?)*?', '(?*(?*?)*(?*?))*(?*?)', '?*(?*(?*((?*(?*?))*?)))', '?*((?*(?*(?*(?*?))))*?)', '(?*?)*(((?*(?*?))*?)*?)', '(?*?)*(((?*?)*?)*?)*?', '?*(?*(?*(?*((?*?)*?))))', '(?*(?*?))*(((?*?)*?)*?)', '?*(?*(?*?)*(?*(?*?)))', '(?*(?*(?*?)))*((?*?)*?)', '(?*((?*(?*(?*?)))*?))*?', '((?*?)*?)*((?*(?*?))*?)', '(?*((?*?)*?))*((?*?)*?)', '(?*(?*(?*((?*?)*?))))*?', '(?*?)*(?*(?*((?*?)*?)))', '?*(?*((?*?)*?)*(?*?))', '((?*?)*?)*(?*(?*?))*?', '((?*(?*((?*?)*?)))*?)*?', '((?*((?*(?*?))*?))*?)*?', '?*(?*((?*((?*?)*?))*?))', '(?*(((?*(?*?))*?)*?))*?', '?*(?*((?*?)*(?*?)*?))', '?*((?*(?*?)*(?*?))*?)', '((?*?)*?)*(?*((?*?)*?))'}\n",
+      "124\n",
+      "{'((((?*?)*(?*?)*?)*?)*?)*?', '(?*(?*(?*?)*(?*(?*?))))*?', '(?*(?*?))*(?*(?*?)*(?*?))', '?*((?*(?*(?*?)))*?)*(?*?)', '(?*?)*((?*?)*?)*((?*?)*?)', '?*(?*(?*?))*((?*(?*?))*?)', '((((?*(?*?))*?)*?)*?)*(?*?)', '?*(?*((?*(?*?))*?))*(?*?)', '(?*?)*(((?*(?*?))*?)*?)*?', '((?*?)*(?*?)*?)*(?*?)*?', '(?*?)*(?*((?*((?*?)*?))*?))', '(?*?)*((?*?)*((?*?)*?)*?)', '(((?*(?*?))*?)*?)*(?*(?*?))', '((?*(?*(?*?))*(?*?))*?)*?', '((?*?)*?)*(?*?)*(?*(?*?))', '(?*?)*((?*(((?*?)*?)*?))*?)', '?*(?*(?*(?*(?*?)*(?*?))))', '(?*?)*((?*(?*(?*(?*?))))*?)', '(?*((?*?)*?)*(?*(?*?)))*?', '((?*(?*?))*?)*(((?*?)*?)*?)', '?*((?*(((?*(?*?))*?)*?))*?)', '?*((?*(?*(((?*?)*?)*?)))*?)', '(?*(?*(?*?)))*(?*(?*?))*?', '((?*?)*((?*(?*?))*?)*?)*?', '((?*((?*(?*(?*?)))*?))*?)*?', '(?*?)*(((?*((?*?)*?))*?)*?)', '?*((?*((?*?)*?))*(?*?)*?)', '((?*?)*?)*(?*?)*(?*?)*?', '(?*(?*(?*?)))*(?*((?*?)*?))', '(?*(?*?))*(?*?)*(?*?)*?', '(?*((?*((?*(?*?))*?))*?))*?', '(?*?)*(?*((?*?)*(?*?)*?))', '((?*?)*?)*((((?*?)*?)*?)*?)', 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'?*(?*(?*(?*?)))*((?*(?*?))*(?*?)*?)'}\n",
+      "12822\n"
+     ]
+    }
+   ],
    "source": [
     "for n in range(2, 12):\n",
-    "  pass"
+    "  x = catalan.product_orders(n)\n",
+    "  print(x)\n",
+    "  print(len(x))"
    ]
   },
   {
@@ -70,12 +101,39 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 2,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "{(1,)}\n",
+      "1\n",
+      "{(1, 2), (2, 1)}\n",
+      "2\n",
+      "{(1, 3, 2), (1, 2, 3), (2, 1, 3), (3, 2, 1), (3, 1, 2)}\n",
+      "5\n",
+      "{(1, 4, 2, 3), (4, 2, 1, 3), (2, 1, 3, 4), (1, 3, 2, 4), (4, 3, 1, 2), (1, 2, 3, 4), (1, 2, 4, 3), (3, 1, 2, 4), (2, 1, 4, 3), (4, 1, 2, 3), (4, 3, 2, 1), (1, 4, 3, 2), (3, 2, 1, 4), (4, 1, 3, 2)}\n",
+      "14\n",
+      "{(1, 5, 4, 2, 3), (5, 4, 1, 3, 2), (5, 1, 2, 4, 3), (1, 5, 2, 3, 4), (2, 1, 5, 3, 4), (5, 1, 2, 3, 4), (5, 3, 1, 2, 4), (2, 1, 4, 3, 5), (1, 5, 3, 2, 4), (5, 4, 1, 2, 3), (5, 4, 2, 1, 3), (5, 4, 3, 2, 1), (1, 2, 3, 5, 4), (5, 1, 4, 3, 2), (1, 2, 3, 4, 5), (5, 3, 2, 1, 4), (1, 4, 3, 2, 5), (4, 3, 1, 2, 5), (5, 1, 4, 2, 3), (2, 1, 3, 5, 4), (5, 2, 1, 4, 3), (4, 1, 2, 3, 5), (2, 1, 3, 4, 5), (5, 1, 3, 2, 4), (1, 3, 2, 4, 5), (1, 3, 2, 5, 4), (4, 3, 2, 1, 5), (3, 1, 2, 5, 4), (4, 1, 3, 2, 5), (5, 4, 3, 1, 2), (1, 2, 4, 3, 5), (3, 1, 2, 4, 5), (1, 4, 2, 3, 5), (1, 5, 2, 4, 3), (1, 5, 4, 3, 2), (2, 1, 5, 4, 3), (3, 2, 1, 4, 5), (3, 2, 1, 5, 4), (4, 2, 1, 3, 5), (5, 2, 1, 3, 4), (1, 2, 5, 3, 4), (1, 2, 5, 4, 3)}\n",
+      "42\n",
+      "{(1, 3, 2, 6, 4, 5), (1, 3, 2, 6, 5, 4), (5, 4, 1, 3, 2, 6), (6, 5, 3, 2, 1, 4), (1, 4, 3, 2, 6, 5), (1, 5, 4, 2, 3, 6), (6, 1, 2, 3, 5, 4), (2, 1, 5, 3, 4, 6), (1, 5, 4, 3, 2, 6), (6, 5, 1, 4, 3, 2), (6, 2, 1, 3, 5, 4), (6, 5, 1, 3, 2, 4), (6, 5, 4, 1, 3, 2), (1, 5, 2, 4, 3, 6), (1, 2, 6, 5, 3, 4), (6, 1, 4, 3, 2, 5), (6, 5, 2, 1, 4, 3), (1, 5, 3, 2, 4, 6), (1, 3, 2, 4, 6, 5), (6, 5, 4, 1, 2, 3), (1, 2, 4, 3, 6, 5), (5, 4, 3, 1, 2, 6), (6, 1, 5, 3, 2, 4), (4, 1, 2, 3, 5, 6), (1, 3, 2, 4, 5, 6), (2, 1, 6, 5, 4, 3), (3, 2, 1, 6, 5, 4), (4, 1, 2, 3, 6, 5), (1, 2, 3, 4, 6, 5), (3, 1, 2, 6, 4, 5), (6, 2, 1, 5, 4, 3), (6, 5, 3, 1, 2, 4), (1, 2, 3, 4, 5, 6), (1, 6, 5, 4, 3, 2), (4, 2, 1, 3, 6, 5), (6, 2, 1, 5, 3, 4), (1, 6, 3, 2, 5, 4), (5, 1, 4, 2, 3, 6), (6, 1, 3, 2, 5, 4), (1, 5, 2, 3, 4, 6), (2, 1, 3, 6, 5, 4), (6, 5, 4, 2, 1, 3), (6, 1, 3, 2, 4, 5), (6, 5, 4, 3, 2, 1), (1, 2, 6, 5, 4, 3), (4, 1, 3, 2, 6, 5), (1, 2, 3, 6, 4, 5), (1, 6, 4, 2, 3, 5), (2, 1, 3, 6, 4, 5), (6, 1, 5, 2, 4, 3), (6, 2, 1, 3, 4, 5), (6, 1, 2, 3, 4, 5), (1, 6, 2, 5, 3, 4), (6, 1, 4, 2, 3, 5), (1, 6, 2, 5, 4, 3), (4, 1, 3, 2, 5, 6), (5, 1, 2, 3, 4, 6), (4, 3, 1, 2, 6, 5), (3, 1, 2, 5, 4, 6), (2, 1, 6, 5, 3, 4), (3, 2, 1, 6, 4, 5), (6, 4, 3, 1, 2, 5), (1, 6, 2, 3, 4, 5), (1, 6, 2, 3, 5, 4), (2, 1, 3, 4, 5, 6), (2, 1, 3, 4, 6, 5), (4, 3, 1, 2, 5, 6), (5, 2, 1, 3, 4, 6), (6, 1, 5, 4, 3, 2), (5, 4, 1, 2, 3, 6), (1, 2, 6, 3, 4, 5), (6, 4, 1, 3, 2, 5), (5, 4, 3, 2, 1, 6), (6, 1, 2, 4, 3, 5), (6, 1, 5, 4, 2, 3), (1, 3, 2, 5, 4, 6), (6, 3, 1, 2, 5, 4), (5, 1, 2, 4, 3, 6), (3, 2, 1, 4, 6, 5), (6, 3, 1, 2, 4, 5), (1, 6, 3, 2, 4, 5), (6, 5, 4, 3, 1, 2), (3, 2, 1, 4, 5, 6), (1, 6, 5, 2, 4, 3), (1, 2, 5, 3, 4, 6), (3, 1, 2, 4, 6, 5), (5, 3, 2, 1, 4, 6), (5, 2, 1, 4, 3, 6), (6, 4, 2, 1, 3, 5), (1, 6, 5, 2, 3, 4), (5, 1, 3, 2, 4, 6), (6, 4, 1, 2, 3, 5), (6, 5, 1, 2, 4, 3), (1, 6, 4, 3, 2, 5), (6, 5, 1, 2, 3, 4), (2, 1, 4, 3, 5, 6), (2, 1, 6, 4, 3, 5), (5, 1, 4, 3, 2, 6), (1, 2, 6, 4, 3, 5), (1, 6, 5, 4, 2, 3), (4, 2, 1, 3, 5, 6), (1, 2, 3, 6, 5, 4), (6, 3, 2, 1, 4, 5), (1, 4, 3, 2, 5, 6), (6, 3, 2, 1, 5, 4), (5, 4, 2, 1, 3, 6), (2, 1, 3, 5, 4, 6), (6, 5, 1, 4, 2, 3), (2, 1, 5, 4, 3, 6), (1, 6, 2, 4, 3, 5), (6, 2, 1, 4, 3, 5), (6, 1, 5, 2, 3, 4), (6, 5, 2, 1, 3, 4), (3, 1, 2, 6, 5, 4), (5, 3, 1, 2, 4, 6), (6, 4, 3, 2, 1, 5), (1, 2, 4, 3, 5, 6), (2, 1, 6, 3, 5, 4), (3, 1, 2, 4, 5, 6), (3, 2, 1, 5, 4, 6), (1, 2, 6, 3, 5, 4), (6, 1, 2, 5, 4, 3), (1, 2, 5, 4, 3, 6), (4, 3, 2, 1, 5, 6), (2, 1, 4, 3, 6, 5), (4, 3, 2, 1, 6, 5), (2, 1, 6, 3, 4, 5), (1, 2, 3, 5, 4, 6), (1, 4, 2, 3, 5, 6), (1, 4, 2, 3, 6, 5), (6, 1, 2, 5, 3, 4), (1, 6, 5, 3, 2, 4)}\n",
+      "132\n",
+      "{(5, 2, 1, 4, 3, 6, 7), (2, 1, 7, 3, 4, 5, 6), (1, 2, 3, 7, 5, 4, 6), (1, 7, 2, 6, 3, 5, 4), (1, 2, 6, 5, 4, 3, 7), (4, 1, 3, 2, 5, 6, 7), (1, 2, 7, 4, 3, 5, 6), (3, 2, 1, 4, 5, 7, 6), (1, 6, 3, 2, 4, 5, 7), (7, 2, 1, 6, 4, 3, 5), (2, 1, 6, 5, 4, 3, 7), (1, 7, 6, 5, 2, 4, 3), (1, 2, 4, 3, 5, 7, 6), (1, 2, 4, 3, 7, 5, 6), (6, 5, 1, 3, 2, 4, 7), (7, 4, 3, 2, 1, 5, 6), (1, 2, 3, 7, 6, 4, 5), (1, 2, 5, 4, 3, 6, 7), (5, 4, 1, 3, 2, 6, 7), (7, 5, 1, 2, 3, 4, 6), (4, 3, 2, 1, 7, 5, 6), (6, 3, 1, 2, 4, 5, 7), (5, 4, 3, 2, 1, 6, 7), (1, 4, 3, 2, 7, 5, 6), (1, 7, 2, 5, 4, 3, 6), (2, 1, 3, 7, 6, 5, 4), (6, 4, 1, 2, 3, 5, 7), (2, 1, 7, 4, 3, 5, 6), (1, 3, 2, 6, 4, 5, 7), (7, 6, 5, 4, 2, 1, 3), (6, 5, 1, 2, 4, 3, 7), (2, 1, 4, 3, 5, 6, 7), (7, 5, 1, 4, 3, 2, 6), (3, 1, 2, 4, 5, 7, 6), (7, 1, 3, 2, 5, 4, 6), (2, 1, 4, 3, 6, 5, 7), (7, 1, 3, 2, 6, 5, 4), (7, 1, 5, 2, 3, 4, 6), (3, 1, 2, 7, 6, 4, 5), (2, 1, 4, 3, 7, 6, 5), (5, 4, 1, 2, 3, 7, 6), (7, 6, 1, 5, 2, 4, 3), (7, 6, 3, 1, 2, 4, 5), 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+      "429\n",
+      "{(8, 7, 5, 2, 1, 3, 4, 6), (1, 4, 2, 3, 8, 7, 6, 5), (8, 1, 7, 6, 2, 5, 3, 4), (8, 1, 3, 2, 4, 7, 6, 5), (7, 1, 2, 6, 5, 4, 3, 8), (8, 1, 2, 7, 6, 3, 5, 4), (8, 7, 1, 5, 3, 2, 4, 6), (2, 1, 7, 6, 4, 3, 5, 8), (7, 3, 2, 1, 5, 4, 6, 8), (5, 1, 4, 2, 3, 6, 8, 7), (7, 6, 1, 2, 3, 5, 4, 8), (6, 4, 3, 1, 2, 5, 8, 7), (7, 1, 5, 2, 4, 3, 6, 8), (8, 1, 4, 3, 2, 6, 5, 7), (8, 7, 1, 2, 3, 4, 5, 6), (1, 7, 2, 4, 3, 5, 6, 8), (1, 8, 7, 6, 4, 3, 2, 5), (7, 6, 4, 3, 2, 1, 5, 8), (2, 1, 7, 3, 4, 5, 6, 8), (2, 1, 7, 4, 3, 6, 5, 8), (8, 7, 4, 2, 1, 3, 5, 6), (7, 6, 5, 1, 4, 3, 2, 8), (8, 2, 1, 3, 7, 6, 5, 4), (1, 2, 4, 3, 8, 7, 5, 6), (1, 7, 6, 3, 2, 5, 4, 8), (8, 1, 6, 3, 2, 4, 5, 7), (8, 7, 2, 1, 6, 4, 3, 5), (1, 2, 8, 3, 7, 5, 4, 6), (4, 1, 2, 3, 6, 5, 8, 7), (1, 8, 2, 4, 3, 5, 7, 6), (5, 4, 1, 3, 2, 8, 7, 6), (8, 2, 1, 6, 5, 3, 4, 7), (2, 1, 8, 4, 3, 7, 6, 5), (7, 3, 2, 1, 4, 5, 6, 8), (5, 1, 2, 3, 4, 6, 8, 7), (3, 1, 2, 8, 4, 5, 6, 7), (1, 4, 3, 2, 5, 6, 7, 8), (8, 3, 1, 2, 4, 6, 5, 7), (8, 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4, 7, 8), (2, 1, 9, 8, 7, 3, 5, 4, 6), (6, 5, 3, 1, 2, 4, 9, 8, 7), (7, 6, 5, 1, 4, 2, 3, 9, 8), (3, 1, 2, 9, 4, 7, 6, 5, 8), (1, 2, 9, 4, 3, 7, 6, 5, 8), (5, 4, 1, 2, 3, 8, 7, 6, 9), (9, 7, 4, 2, 1, 3, 6, 5, 8), (9, 8, 1, 5, 3, 2, 4, 7, 6), (7, 6, 2, 1, 5, 4, 3, 9, 8), (1, 9, 2, 8, 7, 5, 4, 3, 6), (1, 2, 4, 3, 5, 6, 7, 8, 9), (9, 4, 2, 1, 3, 7, 6, 5, 8), (9, 5, 4, 3, 2, 1, 7, 6, 8), (1, 5, 4, 3, 2, 6, 9, 8, 7), (9, 1, 8, 2, 3, 4, 5, 6, 7), (1, 8, 2, 5, 3, 4, 6, 7, 9), (8, 1, 2, 3, 7, 6, 4, 5, 9), (5, 2, 1, 3, 4, 9, 6, 7, 8), (8, 2, 1, 7, 5, 3, 4, 6, 9), (8, 1, 2, 7, 5, 3, 4, 6, 9), (7, 4, 3, 1, 2, 6, 5, 9, 8), (9, 1, 8, 7, 2, 3, 4, 6, 5), (5, 3, 2, 1, 4, 9, 6, 8, 7), (9, 4, 3, 1, 2, 8, 5, 7, 6), (9, 8, 7, 2, 1, 3, 4, 5, 6), (1, 4, 3, 2, 9, 6, 5, 7, 8), (1, 2, 3, 9, 5, 4, 6, 7, 8), (9, 4, 1, 3, 2, 7, 5, 6, 8), (5, 3, 2, 1, 4, 6, 7, 8, 9), (9, 5, 4, 3, 1, 2, 6, 8, 7), (1, 9, 2, 6, 3, 4, 5, 7, 8), (2, 1, 9, 8, 7, 3, 6, 5, 4), (2, 1, 3, 4, 5, 7, 6, 9, 8), (4, 3, 2, 1, 6, 5, 8, 7, 9), (2, 1, 3, 6, 4, 5, 7, 9, 8), (4, 1, 2, 3, 9, 5, 8, 6, 7), (8, 1, 7, 2, 6, 5, 3, 4, 9), (5, 1, 4, 3, 2, 8, 6, 7, 9), (8, 5, 4, 3, 2, 1, 6, 7, 9), (9, 2, 1, 3, 4, 8, 7, 6, 5), (9, 2, 1, 8, 7, 6, 4, 3, 5), (1, 9, 7, 6, 2, 5, 3, 4, 8), (9, 5, 1, 2, 4, 3, 6, 7, 8), (2, 1, 9, 8, 7, 5, 3, 4, 6), (1, 2, 9, 5, 4, 3, 8, 7, 6), (3, 2, 1, 4, 6, 5, 7, 8, 9), (1, 4, 3, 2, 5, 6, 9, 8, 7), (1, 9, 7, 5, 4, 2, 3, 6, 8), (8, 7, 4, 3, 2, 1, 5, 6, 9), (1, 2, 8, 5, 4, 3, 6, 7, 9), (9, 2, 1, 8, 6, 3, 4, 5, 7), (9, 4, 3, 2, 1, 5, 7, 6, 8), (9, 8, 6, 5, 1, 3, 2, 4, 7), (6, 4, 3, 2, 1, 5, 8, 7, 9), (3, 2, 1, 9, 8, 6, 4, 5, 7), (9, 1, 8, 2, 7, 5, 4, 3, 6), (5, 4, 1, 3, 2, 9, 7, 6, 8), (9, 1, 8, 5, 3, 2, 4, 7, 6), (1, 9, 2, 3, 4, 8, 7, 5, 6), (9, 5, 2, 1, 4, 3, 8, 6, 7), (1, 2, 3, 6, 5, 4, 9, 7, 8), (1, 9, 8, 4, 2, 3, 5, 7, 6), (4, 1, 2, 3, 7, 6, 5, 8, 9), (1, 2, 4, 3, 6, 5, 9, 7, 8), (1, 2, 9, 8, 7, 3, 6, 5, 4), (9, 8, 7, 5, 1, 3, 2, 4, 6), (1, 9, 2, 5, 3, 4, 8, 7, 6), (9, 8, 7, 1, 2, 3, 6, 4, 5), (8, 1, 7, 6, 2, 5, 3, 4, 9), (1, 2, 6, 3, 5, 4, 7, 8, 9), (9, 1, 7, 2, 6, 3, 4, 5, 8), (9, 1, 8, 4, 3, 2, 5, 6, 7), (9, 6, 1, 2, 4, 3, 5, 7, 8), (2, 1, 3, 4, 7, 5, 6, 8, 9), (3, 2, 1, 8, 7, 5, 4, 6, 9), (9, 7, 1, 4, 2, 3, 6, 5, 8), (9, 8, 7, 1, 6, 4, 2, 3, 5), (8, 7, 6, 4, 1, 3, 2, 5, 9), (1, 9, 2, 4, 3, 5, 6, 7, 8), (9, 7, 6, 1, 4, 3, 2, 5, 8), (2, 1, 3, 4, 9, 8, 5, 6, 7), (2, 1, 7, 6, 3, 4, 5, 9, 8), (9, 2, 1, 3, 8, 4, 7, 5, 6), (9, 1, 2, 3, 6, 5, 4, 7, 8), (9, 8, 1, 4, 3, 2, 5, 7, 6), (9, 8, 3, 2, 1, 7, 5, 4, 6), (1, 2, 3, 5, 4, 9, 6, 8, 7), (8, 7, 1, 2, 3, 4, 5, 6, 9), (8, 1, 2, 5, 3, 4, 7, 6, 9), (9, 6, 5, 2, 1, 3, 4, 7, 8), (2, 1, 4, 3, 5, 9, 6, 8, 7), (9, 8, 1, 2, 5, 4, 3, 7, 6), (9, 8, 7, 1, 6, 2, 3, 5, 4), (2, 1, 3, 6, 5, 4, 9, 7, 8), (9, 7, 6, 1, 2, 3, 4, 5, 8), (9, 8, 1, 6, 5, 3, 2, 4, 7), (1, 2, 5, 3, 4, 6, 7, 9, 8), (1, 9, 8, 7, 5, 4, 2, 3, 6), (2, 1, 9, 3, 4, 7, 6, 5, 8), (9, 8, 1, 2, 6, 5, 3, 4, 7), (1, 8, 7, 2, 6, 4, 3, 5, 9), (6, 1, 3, 2, 4, 5, 9, 7, 8), (1, 2, 8, 3, 4, 7, 6, 5, 9), (4, 3, 2, 1, 8, 5, 7, 6, 9), (6, 5, 2, 1, 4, 3, 8, 7, 9), (9, 8, 7, 1, 2, 6, 5, 3, 4), (1, 9, 2, 8, 6, 4, 3, 5, 7), (3, 2, 1, 9, 4, 5, 7, 6, 8), (1, 9, 8, 6, 5, 3, 2, 4, 7), (8, 7, 2, 1, 6, 3, 4, 5, 9), (6, 2, 1, 3, 5, 4, 7, 8, 9), (9, 7, 2, 1, 4, 3, 5, 6, 8), (9, 7, 3, 1, 2, 4, 6, 5, 8), (9, 7, 6, 2, 1, 3, 4, 5, 8), (6, 2, 1, 5, 4, 3, 9, 7, 8), (9, 8, 7, 6, 3, 2, 1, 4, 5), (9, 8, 7, 6, 1, 5, 2, 3, 4), (8, 6, 4, 1, 3, 2, 5, 7, 9), (9, 6, 1, 5, 2, 4, 3, 7, 8), (2, 1, 3, 8, 4, 5, 6, 7, 9), (9, 8, 3, 2, 1, 4, 7, 5, 6), (9, 8, 7, 2, 1, 4, 3, 5, 6), (7, 5, 4, 3, 1, 2, 6, 9, 8), (1, 8, 4, 3, 2, 5, 7, 6, 9), (4, 3, 2, 1, 5, 9, 6, 7, 8), (6, 2, 1, 3, 5, 4, 9, 8, 7), (1, 7, 2, 5, 4, 3, 6, 9, 8), (1, 7, 6, 2, 3, 4, 5, 8, 9), (1, 5, 3, 2, 4, 8, 6, 7, 9), (2, 1, 3, 7, 6, 4, 5, 9, 8), (3, 2, 1, 9, 4, 8, 5, 7, 6), (9, 1, 8, 2, 3, 6, 5, 4, 7), (2, 1, 9, 8, 5, 4, 3, 7, 6), (9, 2, 1, 8, 7, 3, 4, 6, 5), (8, 5, 4, 1, 3, 2, 6, 7, 9), (1, 9, 2, 4, 3, 8, 7, 6, 5), (7, 1, 5, 4, 3, 2, 6, 8, 9), (9, 1, 8, 2, 3, 7, 5, 4, 6), (9, 7, 6, 2, 1, 3, 5, 4, 8), (9, 1, 8, 7, 2, 6, 3, 5, 4), (9, 8, 2, 1, 7, 3, 6, 4, 5), (8, 7, 6, 3, 2, 1, 4, 5, 9), (9, 1, 7, 5, 2, 4, 3, 6, 8), (1, 8, 7, 2, 3, 6, 5, 4, 9), (6, 1, 2, 5, 4, 3, 9, 8, 7), (8, 7, 6, 2, 1, 5, 4, 3, 9), (1, 2, 6, 4, 3, 5, 8, 7, 9), (9, 8, 2, 1, 7, 4, 3, 6, 5), (2, 1, 3, 4, 6, 5, 7, 8, 9), (5, 4, 1, 2, 3, 9, 7, 6, 8), (1, 9, 8, 7, 6, 3, 2, 5, 4), (1, 2, 4, 3, 7, 6, 5, 9, 8), (6, 5, 1, 3, 2, 4, 8, 7, 9), (1, 4, 2, 3, 8, 7, 6, 5, 9), (4, 1, 2, 3, 5, 6, 9, 8, 7), (8, 1, 7, 6, 5, 2, 4, 3, 9), (8, 7, 6, 4, 3, 1, 2, 5, 9), (9, 4, 1, 2, 3, 6, 5, 8, 7), (6, 1, 5, 2, 4, 3, 9, 7, 8), (7, 3, 2, 1, 4, 6, 5, 9, 8), (9, 1, 7, 2, 6, 4, 3, 5, 8), (7, 2, 1, 5, 4, 3, 6, 8, 9), (2, 1, 4, 3, 5, 9, 8, 6, 7), (5, 1, 4, 2, 3, 6, 7, 9, 8), (1, 5, 4, 2, 3, 9, 6, 7, 8), (1, 4, 3, 2, 5, 7, 6, 8, 9), (4, 3, 2, 1, 9, 6, 5, 7, 8), (9, 5, 3, 2, 1, 4, 6, 8, 7), (4, 1, 3, 2, 9, 8, 6, 5, 7), (8, 6, 2, 1, 4, 3, 5, 7, 9), (9, 3, 1, 2, 8, 5, 4, 7, 6), (9, 8, 1, 3, 2, 4, 7, 5, 6), (9, 1, 2, 6, 5, 4, 3, 8, 7), (9, 7, 6, 2, 1, 5, 3, 4, 8), (1, 2, 9, 6, 5, 4, 3, 7, 8), (9, 6, 1, 5, 4, 2, 3, 7, 8), (1, 3, 2, 4, 9, 8, 5, 7, 6), (1, 9, 8, 7, 6, 5, 2, 3, 4), (1, 5, 4, 2, 3, 7, 6, 9, 8), (9, 1, 7, 3, 2, 4, 6, 5, 8), (1, 9, 2, 8, 7, 6, 3, 4, 5), (1, 7, 6, 5, 3, 2, 4, 9, 8), (1, 9, 7, 6, 4, 2, 3, 5, 8), (9, 8, 1, 2, 7, 5, 4, 3, 6), (8, 7, 1, 2, 5, 4, 3, 6, 9), (1, 4, 2, 3, 7, 6, 5, 9, 8), (9, 1, 3, 2, 4, 5, 8, 7, 6), (1, 9, 2, 4, 3, 7, 6, 5, 8), (1, 6, 2, 4, 3, 5, 9, 8, 7), (8, 7, 1, 6, 2, 5, 4, 3, 9), (1, 2, 3, 9, 8, 7, 6, 4, 5), (5, 3, 1, 2, 4, 8, 7, 6, 9), (8, 7, 4, 1, 3, 2, 6, 5, 9), (1, 2, 4, 3, 7, 5, 6, 9, 8), (9, 1, 2, 3, 8, 4, 7, 5, 6), (1, 2, 5, 3, 4, 7, 6, 8, 9), (1, 4, 2, 3, 6, 5, 7, 8, 9), (1, 9, 2, 6, 5, 3, 4, 7, 8), (9, 3, 2, 1, 4, 8, 6, 5, 7), (2, 1, 9, 3, 8, 4, 5, 7, 6), (9, 6, 5, 1, 2, 3, 4, 8, 7), (1, 9, 8, 4, 3, 2, 5, 7, 6), (1, 2, 4, 3, 9, 5, 6, 8, 7), (9, 4, 3, 2, 1, 8, 7, 5, 6), (4, 1, 3, 2, 9, 6, 5, 8, 7), (1, 8, 7, 3, 2, 5, 4, 6, 9), (8, 1, 2, 7, 3, 4, 5, 6, 9), (9, 1, 2, 3, 8, 7, 4, 6, 5), (9, 2, 1, 8, 3, 7, 6, 5, 4), (9, 7, 6, 4, 1, 3, 2, 5, 8), (9, 3, 1, 2, 6, 5, 4, 8, 7), (9, 7, 6, 4, 3, 1, 2, 5, 8), (1, 9, 5, 2, 3, 4, 7, 6, 8), (2, 1, 7, 3, 6, 4, 5, 9, 8), (5, 1, 4, 2, 3, 9, 7, 6, 8), (1, 3, 2, 5, 4, 7, 6, 9, 8), (9, 1, 8, 2, 7, 6, 3, 4, 5), (1, 3, 2, 6, 5, 4, 7, 9, 8), (9, 6, 2, 1, 4, 3, 5, 8, 7), (1, 9, 8, 2, 3, 4, 7, 5, 6), (1, 9, 8, 7, 2, 4, 3, 6, 5), (9, 4, 2, 1, 3, 7, 5, 6, 8), (9, 7, 4, 2, 1, 3, 5, 6, 8), (9, 6, 5, 4, 1, 3, 2, 8, 7), (8, 1, 3, 2, 6, 4, 5, 7, 9), (9, 2, 1, 3, 6, 4, 5, 8, 7), (2, 1, 9, 6, 4, 3, 5, 7, 8), (1, 9, 7, 6, 3, 2, 5, 4, 8), (9, 1, 8, 6, 5, 4, 2, 3, 7), (2, 1, 3, 4, 8, 7, 5, 6, 9), (9, 2, 1, 4, 3, 7, 6, 5, 8), (2, 1, 3, 9, 5, 4, 6, 7, 8), (9, 3, 2, 1, 5, 4, 6, 8, 7), (5, 4, 3, 1, 2, 9, 8, 7, 6), (1, 2, 4, 3, 9, 8, 5, 7, 6), (1, 8, 2, 7, 6, 4, 3, 5, 9), (2, 1, 7, 6, 5, 3, 4, 9, 8), (3, 1, 2, 9, 6, 5, 4, 7, 8), (4, 2, 1, 3, 8, 6, 5, 7, 9), (6, 1, 2, 3, 4, 5, 7, 9, 8), (8, 1, 3, 2, 7, 6, 5, 4, 9), (8, 7, 1, 6, 3, 2, 5, 4, 9), (9, 2, 1, 6, 5, 3, 4, 7, 8), (9, 1, 6, 5, 2, 3, 4, 8, 7), (9, 4, 1, 2, 3, 5, 6, 8, 7), (9, 7, 1, 6, 3, 2, 4, 5, 8), (9, 7, 2, 1, 3, 4, 6, 5, 8), (9, 8, 1, 2, 3, 4, 6, 5, 7), (1, 2, 9, 3, 4, 8, 7, 6, 5), (1, 3, 2, 7, 6, 5, 4, 8, 9), (2, 1, 5, 4, 3, 9, 6, 7, 8), (3, 2, 1, 8, 4, 7, 5, 6, 9), (2, 1, 8, 7, 6, 4, 3, 5, 9), (5, 2, 1, 4, 3, 9, 8, 6, 7), (1, 8, 2, 3, 7, 6, 5, 4, 9), (8, 7, 1, 5, 4, 2, 3, 6, 9), (1, 9, 2, 3, 8, 7, 5, 4, 6), (9, 8, 7, 6, 5, 3, 1, 2, 4), (1, 2, 9, 3, 4, 6, 5, 8, 7), (9, 8, 1, 7, 6, 3, 2, 4, 5), (9, 5, 4, 3, 2, 1, 6, 8, 7), (1, 2, 3, 4, 6, 5, 8, 7, 9), (1, 3, 2, 9, 7, 4, 6, 5, 8), (1, 8, 5, 4, 2, 3, 7, 6, 9), (7, 4, 2, 1, 3, 6, 5, 8, 9), (1, 2, 9, 6, 5, 3, 4, 7, 8), (1, 2, 3, 9, 8, 6, 5, 4, 7), (1, 2, 5, 4, 3, 6, 9, 7, 8), (3, 2, 1, 4, 9, 5, 6, 8, 7), (9, 4, 3, 1, 2, 8, 6, 5, 7), (9, 1, 8, 2, 3, 7, 4, 5, 6), (9, 1, 4, 3, 2, 8, 7, 6, 5), (4, 2, 1, 3, 7, 5, 6, 9, 8), (9, 8, 1, 2, 3, 7, 4, 6, 5), (1, 3, 2, 6, 5, 4, 9, 7, 8), (8, 1, 2, 6, 5, 4, 3, 7, 9), (9, 2, 1, 3, 8, 5, 4, 7, 6), (9, 5, 4, 3, 1, 2, 7, 6, 8), (9, 8, 5, 1, 3, 2, 4, 6, 7), (1, 2, 9, 3, 8, 4, 7, 5, 6), (2, 1, 3, 6, 4, 5, 8, 7, 9), (6, 5, 1, 3, 2, 4, 7, 8, 9), (1, 3, 2, 9, 4, 6, 5, 8, 7), (9, 1, 8, 7, 3, 2, 6, 5, 4), (9, 5, 4, 1, 2, 3, 8, 7, 6), (1, 2, 3, 4, 9, 8, 5, 7, 6), (1, 2, 8, 3, 7, 4, 6, 5, 9), (9, 8, 1, 5, 4, 3, 2, 6, 7), (9, 8, 3, 2, 1, 7, 6, 5, 4), (9, 8, 5, 2, 1, 3, 4, 7, 6), (2, 1, 3, 4, 5, 9, 8, 6, 7), (9, 8, 7, 6, 5, 2, 1, 3, 4), (4, 3, 1, 2, 9, 7, 5, 6, 8), (9, 1, 2, 8, 6, 4, 3, 5, 7), (9, 8, 7, 6, 3, 1, 2, 5, 4), (4, 1, 3, 2, 8, 6, 5, 7, 9), (2, 1, 3, 9, 8, 7, 6, 4, 5), (6, 5, 4, 1, 3, 2, 8, 7, 9), (9, 7, 3, 1, 2, 4, 5, 6, 8), (9, 1, 7, 6, 4, 3, 2, 5, 8), (3, 2, 1, 9, 8, 7, 5, 4, 6), (7, 6, 1, 5, 4, 2, 3, 9, 8), (8, 2, 1, 7, 3, 4, 5, 6, 9), (2, 1, 9, 4, 3, 8, 5, 7, 6), (9, 7, 4, 3, 1, 2, 5, 6, 8), (6, 1, 2, 3, 4, 5, 9, 7, 8), (4, 1, 3, 2, 9, 5, 7, 6, 8), (1, 9, 3, 2, 4, 7, 6, 5, 8)}\n",
+      "4862\n"
+     ]
+    }
+   ],
    "source": [
-    "for n in range(1, 11):\n",
-    "  pass"
+    "for n in range(1, 10):\n",
+    "  x = catalan.permutations_avoiding_231(n)\n",
+    "  print(x)\n",
+    "  print(len(x))"
    ]
   },
   {
@@ -89,18 +147,61 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 2,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "{()}\n",
+      "1\n",
+      "{((0, 1), (0, 2)), ((1, 2), (1, 0))}\n",
+      "2\n",
+      "{((0, 1), (0, 2)), ((1, 2), (1, 3)), ((2, 0), (2, 1)), ((1, 3), (1, 0)), ((0, 2), (0, 3)), ((2, 3), (2, 0))}\n",
+      "6\n",
+      "{((3, 0), (3, 1)), ((1, 2), (1, 3)), ((2, 4), (2, 0)), ((1, 3), (1, 4)), ((2, 0), (2, 1)), ((1, 4), (1, 0)), ((0, 1), (0, 2)), ((0, 3), (0, 4)), ((2, 3), (2, 4)), ((0, 2), (0, 3)), ((3, 4), (3, 0))}\n",
+      "11\n",
+      "{((3, 0), (3, 1)), ((1, 2), (1, 3)), ((0, 4), (0, 5)), ((2, 0), (2, 1)), ((3, 4), (3, 5)), ((2, 3), (2, 4)), ((1, 5), (1, 0)), ((4, 5), (4, 0)), ((1, 4), (1, 5)), ((0, 2), (0, 3)), ((3, 4), (3, 1)), ((1, 3), (1, 4)), ((0, 3), (0, 4)), ((0, 1), (0, 2)), ((4, 0), (4, 1)), ((2, 4), (2, 5)), ((3, 5), (3, 0)), ((2, 5), (2, 0))}\n",
+      "18\n",
+      "{((3, 0), (3, 1)), ((1, 2), (1, 3)), ((3, 5), (3, 6)), ((0, 5), (0, 6)), ((0, 4), (0, 5)), ((2, 0), (2, 1)), ((3, 4), (3, 5)), ((2, 3), (2, 4)), ((5, 1), (5, 3)), ((4, 5), (4, 6)), ((1, 6), (1, 0)), ((1, 5), (1, 6)), ((2, 6), (2, 0)), ((5, 6), (5, 0)), ((1, 4), (1, 5)), ((3, 4), (3, 1)), ((1, 3), (1, 4)), ((2, 5), (2, 6)), ((0, 3), (0, 4)), ((0, 1), (0, 2)), ((4, 6), (4, 0)), ((4, 0), (4, 1)), ((2, 4), (2, 5)), ((3, 6), (3, 0)), ((5, 0), (5, 1)), ((0, 2), (0, 3))}\n",
+      "26\n",
+      "{((1, 2), (1, 3)), ((0, 5), (0, 6)), ((2, 7), (2, 0)), ((0, 4), (0, 5)), ((6, 0), (6, 1)), ((3, 4), (3, 5)), ((2, 3), (2, 4)), ((4, 5), (4, 6)), ((2, 6), (2, 7)), ((5, 6), (5, 7)), ((1, 4), (1, 5)), ((3, 4), (3, 1)), ((2, 5), (2, 6)), ((0, 1), (0, 2)), ((0, 2), (0, 3)), ((3, 0), (3, 1)), ((3, 5), (3, 6)), ((3, 7), (3, 0)), ((6, 7), (6, 0)), ((2, 0), (2, 1)), ((5, 1), (5, 3)), ((1, 6), (1, 7)), ((1, 5), (1, 6)), ((1, 7), (1, 0)), ((4, 6), (4, 7)), ((1, 3), (1, 4)), ((5, 7), (5, 0)), ((0, 3), (0, 4)), ((0, 6), (0, 7)), ((4, 7), (4, 0)), ((5, 6), (5, 1)), ((3, 6), (3, 7)), ((4, 0), (4, 1)), ((2, 4), (2, 5)), ((5, 0), (5, 1)), ((1, 3), (1, 5))}\n",
+      "36\n",
+      "{((1, 2), (1, 3)), ((0, 5), (0, 6)), ((0, 4), (0, 5)), ((6, 0), (6, 1)), ((3, 4), (3, 5)), ((2, 3), (2, 4)), ((4, 8), (4, 0)), ((4, 5), (4, 6)), ((3, 7), (3, 8)), ((2, 6), (2, 7)), ((6, 7), (6, 8)), ((5, 6), (5, 7)), ((7, 1), (7, 3)), ((6, 8), (6, 0)), ((1, 4), (1, 5)), ((2, 8), (2, 0)), ((3, 4), (3, 1)), ((2, 5), (2, 6)), ((0, 1), (0, 2)), ((1, 7), (1, 8)), ((4, 7), (4, 8)), ((0, 2), (0, 3)), ((5, 7), (5, 8)), ((3, 0), (3, 1)), ((3, 8), (3, 0)), ((3, 5), (3, 6)), ((5, 7), (5, 3)), ((0, 7), (0, 8)), ((2, 0), (2, 1)), ((5, 1), (5, 3)), ((1, 6), (1, 7)), ((2, 7), (2, 8)), ((1, 5), (1, 6)), ((7, 0), (7, 1)), ((7, 8), (7, 0)), ((4, 6), (4, 7)), ((1, 3), (1, 4)), ((5, 6), (5, 1)), ((0, 3), (0, 4)), ((0, 6), (0, 7)), ((1, 3), (1, 5)), ((3, 6), (3, 7)), ((4, 0), (4, 1)), ((2, 4), (2, 5)), ((5, 0), (5, 1)), ((5, 8), (5, 0)), ((1, 8), (1, 0))}\n",
+      "47\n",
+      "{((1, 2), (1, 3)), ((3, 9), (3, 0)), ((6, 8), (6, 9)), ((0, 5), (0, 6)), ((2, 8), (2, 9)), ((0, 4), (0, 5)), ((6, 0), (6, 1)), ((3, 4), (3, 5)), ((2, 3), (2, 4)), ((4, 5), (4, 6)), ((3, 7), (3, 8)), ((2, 6), (2, 7)), ((3, 8), (3, 9)), ((6, 7), (6, 8)), ((5, 6), (5, 7)), ((7, 1), (7, 3)), ((7, 9), (7, 0)), ((1, 4), (1, 5)), ((3, 4), (3, 1)), ((2, 5), (2, 6)), ((0, 1), (0, 2)), ((1, 7), (1, 8)), ((4, 7), (4, 8)), ((0, 2), (0, 3)), ((5, 9), (5, 0)), ((8, 9), (8, 0)), ((5, 7), (5, 8)), ((1, 9), (1, 0)), ((3, 0), (3, 1)), ((7, 8), (7, 9)), ((7, 1), (7, 5)), ((3, 5), (3, 6)), ((5, 7), (5, 3)), ((0, 7), (0, 8)), ((0, 8), (0, 9)), ((2, 0), (2, 1)), ((4, 9), (4, 0)), ((5, 1), (5, 3)), ((1, 6), (1, 7)), ((2, 7), (2, 8)), ((1, 5), (1, 6)), ((5, 8), (5, 9)), ((1, 8), (1, 9)), ((7, 0), (7, 1)), ((6, 9), (6, 0)), ((2, 9), (2, 0)), ((4, 6), (4, 7)), ((1, 3), (1, 4)), ((4, 8), (4, 9)), ((0, 3), (0, 4)), ((0, 6), (0, 7)), ((5, 6), (5, 1)), ((3, 6), (3, 7)), ((4, 0), (4, 1)), ((2, 4), (2, 5)), ((7, 8), (7, 1)), ((8, 0), (8, 1)), ((5, 0), (5, 1)), ((1, 3), (1, 5))}\n",
+      "59\n",
+      "{((1, 2), (1, 3)), ((9, 10), (9, 0)), ((9, 1), (9, 3)), ((0, 5), (0, 6)), ((0, 4), (0, 5)), ((6, 0), (6, 1)), ((4, 10), (4, 0)), ((3, 5), (3, 9)), ((5, 6), (5, 7)), ((7, 1), (7, 3)), ((7, 10), (7, 0)), ((3, 10), (3, 0)), ((8, 9), (8, 10)), ((2, 10), (2, 0)), ((4, 7), (4, 8)), ((0, 2), (0, 3)), ((1, 10), (1, 0)), ((5, 7), (5, 8)), ((3, 0), (3, 1)), ((7, 8), (7, 9)), ((7, 1), (7, 5)), ((3, 5), (3, 6)), ((5, 1), (5, 3)), ((1, 6), (1, 7)), ((2, 7), (2, 8)), ((1, 5), (1, 6)), ((5, 8), (5, 9)), ((1, 8), (1, 9)), ((7, 0), (7, 1)), ((4, 8), (4, 9)), ((3, 9), (3, 10)), ((4, 0), (4, 1)), ((7, 8), (7, 1)), ((5, 0), (5, 1)), ((6, 8), (6, 9)), ((2, 8), (2, 9)), ((7, 9), (7, 10)), ((3, 4), (3, 5)), ((2, 3), (2, 4)), ((4, 5), (4, 6)), ((3, 7), (3, 8)), ((2, 6), (2, 7)), ((3, 8), (3, 9)), ((6, 7), (6, 8)), ((9, 0), (9, 1)), ((5, 9), (5, 10)), ((1, 4), (1, 5)), ((3, 4), (3, 1)), ((1, 9), (1, 10)), ((2, 5), (2, 6)), ((0, 1), (0, 2)), ((1, 7), (1, 8)), ((0, 9), (0, 10)), ((5, 7), (5, 3)), ((0, 7), (0, 8)), ((0, 8), (0, 9)), ((5, 7), (5, 9)), ((2, 0), (2, 1)), ((6, 9), (6, 10)), ((8, 10), (8, 0)), ((5, 10), (5, 0)), ((4, 9), (4, 10)), ((4, 6), (4, 7)), ((1, 3), (1, 4)), ((5, 6), (5, 1)), ((0, 3), (0, 4)), ((0, 6), (0, 7)), ((3, 6), (3, 7)), ((6, 10), (6, 0)), ((2, 4), (2, 5)), ((8, 0), (8, 1)), ((1, 3), (1, 5)), ((2, 9), (2, 10))}\n",
+      "73\n"
+     ]
+    }
+   ],
    "source": [
     "for n in range(3, 13):\n",
-    "  pass"
+    "  x = catalan.triangulations(n)\n",
+    "  print(x)\n",
+    "  print(len(x))"
    ]
   }
  ],
  "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
   "language_info": {
-   "name": "python"
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.12.4"
   }
  },
  "nbformat": 4,