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* Copyright (C) 2013 The FindStatCrew <info@findstat.org> *
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------------------------------------------------------------------------
Map identifier: Mp00297
------------------------------------------------------------------------
Map name: ordered tree
------------------------------------------------------------------------
Domain: Parking functions
------------------------------------------------------------------------
Codomain: Ordered trees
------------------------------------------------------------------------
Description: The ordered tree associated with the parking function by Pollak.
Let $(p_1,\dots,p_n)$ be a parking function. Set $c_i = p_{i+1}-p_i \mod (n+1)$ to obtain a Prüfer code, and return the underlying ordered tree rooted at $0$.
------------------------------------------------------------------------
References: [1] (service unreachable) [[MathSciNet:0234843]]
------------------------------------------------------------------------
Code:
def pollak_riordan_to_pruefer(p):
n = len(p)
return [(p[i+1] - p[i]) % (n+1) for i in range(n-1)]
def pruefer_to_tree(c):
c = list(c)
n = len(c)
V = list(range(n+2))
G = Graph([V, []])
for _ in range(n):
i, u = next((i, u) for i, u in enumerate(V) if u not in c)
del V[i]
v = c.pop(0)
G.add_edge(u, v)
G.add_edge(V)
return to_tree(G, 0)
def to_tree(G, r):
if not G:
return LabelledRootedTree([], r)
roots = G[r]
G.delete_vertex(r)
return LabelledRootedTree([to_tree(G.subgraph(G.connected_component_containing_vertex(u)), u)
for u in roots], r)
def mapping(p):
return OrderedTree(pruefer_to_tree(pollak_riordan_to_pruefer(p)))
------------------------------------------------------------------------
Map images:
[1] => [[]]
[1,1] => [[],[]]
[1,2] => [[[]]]
[2,1] => [[[]]]
[1,1,1] => [[],[],[]]
[1,1,2] => [[],[[]]]
[1,2,1] => [[[[]]]]
[2,1,1] => [[],[[]]]
[1,1,3] => [[],[[]]]
[1,3,1] => [[[],[]]]
[3,1,1] => [[],[[]]]
[1,2,2] => [[],[[]]]
[2,1,2] => [[[[]]]]
[2,2,1] => [[],[[]]]
[1,2,3] => [[[],[]]]
[1,3,2] => [[[[]]]]
[2,1,3] => [[[[]]]]
[2,3,1] => [[[[]]]]
[3,1,2] => [[[[]]]]
[3,2,1] => [[[],[]]]
[1,1,1,1] => [[],[],[],[]]
[1,1,1,2] => [[],[],[[]]]
[1,1,2,1] => [[],[[[]]]]
[1,2,1,1] => [[],[[[]]]]
[2,1,1,1] => [[],[],[[]]]
[1,1,1,3] => [[],[],[[]]]
[1,1,3,1] => [[],[[[]]]]
[1,3,1,1] => [[],[[[]]]]
[3,1,1,1] => [[],[],[[]]]
[1,1,1,4] => [[],[],[[]]]
[1,1,4,1] => [[],[[[]]]]
[1,4,1,1] => [[],[[[]]]]
[4,1,1,1] => [[],[],[[]]]
[1,1,2,2] => [[],[],[[]]]
[1,2,1,2] => [[[],[[]]]]
[1,2,2,1] => [[[]],[[]]]
[2,1,1,2] => [[],[[[]]]]
[2,1,2,1] => [[[],[[]]]]
[2,2,1,1] => [[],[],[[]]]
[1,1,2,3] => [[],[[],[]]]
[1,1,3,2] => [[],[[[]]]]
[1,2,1,3] => [[[[[]]]]]
[1,2,3,1] => [[[],[[]]]]
[1,3,1,2] => [[[[[]]]]]
[1,3,2,1] => [[[[],[]]]]
[2,1,1,3] => [[],[[[]]]]
[2,1,3,1] => [[[[[]]]]]
[2,3,1,1] => [[],[[[]]]]
[3,1,1,2] => [[[]],[[]]]
[3,1,2,1] => [[[[[]]]]]
[3,2,1,1] => [[],[[],[]]]
[1,1,2,4] => [[],[[[]]]]
[1,1,4,2] => [[],[[],[]]]
[1,2,1,4] => [[[[[]]]]]
[1,2,4,1] => [[[[],[]]]]
[1,4,1,2] => [[[[[]]]]]
[1,4,2,1] => [[[],[[]]]]
[2,1,1,4] => [[],[[[]]]]
[2,1,4,1] => [[[[[]]]]]
[2,4,1,1] => [[],[[],[]]]
[4,1,1,2] => [[[]],[[]]]
[4,1,2,1] => [[[[[]]]]]
[4,2,1,1] => [[[]],[[]]]
[1,1,3,3] => [[],[],[[]]]
[1,3,1,3] => [[[],[[]]]]
[1,3,3,1] => [[[]],[[]]]
[3,1,1,3] => [[[]],[[]]]
[3,1,3,1] => [[[],[[]]]]
[3,3,1,1] => [[],[],[[]]]
[1,1,3,4] => [[],[[[]]]]
[1,1,4,3] => [[],[[[]]]]
[1,3,1,4] => [[[[],[]]]]
[1,3,4,1] => [[[],[[]]]]
[1,4,1,3] => [[[[],[]]]]
[1,4,3,1] => [[[],[[]]]]
[3,1,1,4] => [[],[[],[]]]
[3,1,4,1] => [[[],[[]]]]
[3,4,1,1] => [[],[[[]]]]
[4,1,1,3] => [[],[[],[]]]
[4,1,3,1] => [[[],[[]]]]
[4,3,1,1] => [[[]],[[]]]
[1,2,2,2] => [[],[],[[]]]
[2,1,2,2] => [[[]],[[]]]
[2,2,1,2] => [[],[[[]]]]
[2,2,2,1] => [[],[],[[]]]
[1,2,2,3] => [[],[[],[]]]
[1,2,3,2] => [[[],[[]]]]
[1,3,2,2] => [[],[[[]]]]
[2,1,2,3] => [[[[],[]]]]
[2,1,3,2] => [[[],[[]]]]
[2,2,1,3] => [[],[[[]]]]
[2,2,3,1] => [[],[[[]]]]
[2,3,1,2] => [[[],[[]]]]
[2,3,2,1] => [[[[],[]]]]
[3,1,2,2] => [[],[[[]]]]
[3,2,1,2] => [[[],[[]]]]
[3,2,2,1] => [[],[[],[]]]
[1,2,2,4] => [[[]],[[]]]
[1,2,4,2] => [[[[[]]]]]
[1,4,2,2] => [[],[[],[]]]
[2,1,2,4] => [[[[[]]]]]
[2,1,4,2] => [[[[],[]]]]
[2,2,1,4] => [[],[[[]]]]
[2,2,4,1] => [[],[[],[]]]
[2,4,1,2] => [[[],[[]]]]
[2,4,2,1] => [[[[[]]]]]
[4,1,2,2] => [[],[[[]]]]
[4,2,1,2] => [[[[[]]]]]
[4,2,2,1] => [[],[[[]]]]
[1,2,3,3] => [[],[[],[]]]
[1,3,2,3] => [[[[[]]]]]
[1,3,3,2] => [[[]],[[]]]
[2,1,3,3] => [[[]],[[]]]
[2,3,1,3] => [[[[[]]]]]
[2,3,3,1] => [[[]],[[]]]
[3,1,2,3] => [[[[],[]]]]
[3,1,3,2] => [[[[[]]]]]
[3,2,1,3] => [[[],[[]]]]
[3,2,3,1] => [[[[[]]]]]
[3,3,1,2] => [[],[[[]]]]
[3,3,2,1] => [[],[[],[]]]
[1,2,3,4] => [[[],[],[]]]
[1,2,4,3] => [[[[[]]]]]
[1,3,2,4] => [[[],[[]]]]
[1,3,4,2] => [[[[[]]]]]
[1,4,2,3] => [[[],[[]]]]
[1,4,3,2] => [[[[],[]]]]
[2,1,3,4] => [[[[[]]]]]
[2,1,4,3] => [[[],[[]]]]
[2,3,1,4] => [[[[],[]]]]
[2,3,4,1] => [[[],[[]]]]
[2,4,1,3] => [[[],[],[]]]
[2,4,3,1] => [[[[[]]]]]
[3,1,2,4] => [[[[[]]]]]
[3,1,4,2] => [[[],[],[]]]
[3,2,1,4] => [[[],[[]]]]
[3,2,4,1] => [[[[],[]]]]
[3,4,1,2] => [[[],[[]]]]
[3,4,2,1] => [[[[[]]]]]
[4,1,2,3] => [[[[],[]]]]
[4,1,3,2] => [[[],[[]]]]
[4,2,1,3] => [[[[[]]]]]
[4,2,3,1] => [[[],[[]]]]
[4,3,1,2] => [[[[[]]]]]
[4,3,2,1] => [[[],[],[]]]
[1,1,1,1,1] => [[],[],[],[],[]]
[1,1,1,1,2] => [[],[],[],[[]]]
[1,1,1,2,1] => [[],[],[[[]]]]
[1,1,2,1,1] => [[],[],[[[]]]]
[1,2,1,1,1] => [[],[],[[[]]]]
[2,1,1,1,1] => [[],[],[],[[]]]
[1,1,1,1,3] => [[],[],[],[[]]]
[1,1,1,3,1] => [[],[],[[[]]]]
[1,1,3,1,1] => [[],[],[[[]]]]
[1,3,1,1,1] => [[],[],[[[]]]]
[3,1,1,1,1] => [[],[],[],[[]]]
[1,1,1,1,4] => [[],[],[],[[]]]
[1,1,1,4,1] => [[],[],[[],[]]]
[1,1,4,1,1] => [[],[],[[],[]]]
[1,4,1,1,1] => [[],[],[[],[]]]
[4,1,1,1,1] => [[],[],[],[[]]]
[1,1,1,1,5] => [[],[],[],[[]]]
[1,1,1,5,1] => [[],[],[[[]]]]
[1,1,5,1,1] => [[],[],[[[]]]]
[1,5,1,1,1] => [[],[[]],[[]]]
[5,1,1,1,1] => [[],[],[],[[]]]
[1,1,1,2,2] => [[],[],[],[[]]]
[1,1,2,1,2] => [[],[[],[[]]]]
[1,1,2,2,1] => [[],[[]],[[]]]
[1,2,1,1,2] => [[],[[],[[]]]]
[1,2,1,2,1] => [[[],[[],[]]]]
[1,2,2,1,1] => [[],[[]],[[]]]
[2,1,1,1,2] => [[],[],[[[]]]]
[2,1,1,2,1] => [[],[[[],[]]]]
[2,1,2,1,1] => [[],[[],[[]]]]
[2,2,1,1,1] => [[],[],[],[[]]]
[1,1,1,2,3] => [[],[],[[],[]]]
[1,1,1,3,2] => [[],[],[[[]]]]
[1,1,2,1,3] => [[],[[[[]]]]]
[1,1,2,3,1] => [[],[[],[[]]]]
[1,1,3,1,2] => [[],[[[[]]]]]
[1,1,3,2,1] => [[],[[[],[]]]]
[1,2,1,1,3] => [[],[[[[]]]]]
[1,2,1,3,1] => [[[[[[]]]]]]
[1,2,3,1,1] => [[],[[[],[]]]]
[1,3,1,1,2] => [[[]],[[[]]]]
[1,3,1,2,1] => [[[[[[]]]]]]
[1,3,2,1,1] => [[],[[],[[]]]]
[2,1,1,1,3] => [[],[],[[[]]]]
[2,1,1,3,1] => [[],[[[[]]]]]
[2,1,3,1,1] => [[[[]]],[[]]]
[2,3,1,1,1] => [[],[],[[[]]]]
[3,1,1,1,2] => [[],[[]],[[]]]
[3,1,1,2,1] => [[],[[[[]]]]]
[3,1,2,1,1] => [[[]],[[[]]]]
[3,2,1,1,1] => [[],[],[[],[]]]
[1,1,1,2,4] => [[],[],[[[]]]]
[1,1,1,4,2] => [[],[],[[[]]]]
[1,1,2,1,4] => [[],[[[[]]]]]
[1,1,2,4,1] => [[],[[[[]]]]]
[1,1,4,1,2] => [[],[[],[[]]]]
[1,1,4,2,1] => [[],[[[[]]]]]
[1,2,1,1,4] => [[],[[[[]]]]]
[1,2,1,4,1] => [[[[[],[]]]]]
[1,2,4,1,1] => [[],[[[[]]]]]
[1,4,1,1,2] => [[[]],[[],[]]]
[1,4,1,2,1] => [[[],[[[]]]]]
[1,4,2,1,1] => [[[]],[[[]]]]
[2,1,1,1,4] => [[],[],[[[]]]]
[2,1,1,4,1] => [[],[[],[[]]]]
[2,1,4,1,1] => [[[]],[[],[]]]
[2,4,1,1,1] => [[],[],[[[]]]]
[4,1,1,1,2] => [[],[[]],[[]]]
[4,1,1,2,1] => [[[[]]],[[]]]
[4,1,2,1,1] => [[],[[[[]]]]]
[4,2,1,1,1] => [[],[[]],[[]]]
[1,1,1,2,5] => [[],[],[[[]]]]
[1,1,1,5,2] => [[],[],[[[]]]]
[1,1,2,1,5] => [[],[[[[]]]]]
[1,1,2,5,1] => [[],[[[[]]]]]
[1,1,5,1,2] => [[],[[[[]]]]]
[1,1,5,2,1] => [[],[[[[]]]]]
[1,2,1,1,5] => [[],[[[[]]]]]
[1,2,1,5,1] => [[[[[[]]]]]]
[1,2,5,1,1] => [[],[[[[]]]]]
[1,5,1,1,2] => [[[]],[[[]]]]
[1,5,1,2,1] => [[[[[[]]]]]]
[1,5,2,1,1] => [[[]],[[[]]]]
[2,1,1,1,5] => [[],[],[[[]]]]
[2,1,1,5,1] => [[],[[[[]]]]]
[2,1,5,1,1] => [[[[]]],[[]]]
[2,5,1,1,1] => [[],[],[[[]]]]
[5,1,1,1,2] => [[],[[]],[[]]]
[5,1,1,2,1] => [[[[]]],[[]]]
[5,1,2,1,1] => [[],[[[[]]]]]
[5,2,1,1,1] => [[],[[]],[[]]]
[1,1,1,3,3] => [[],[],[],[[]]]
[1,1,3,1,3] => [[],[[],[[]]]]
[1,1,3,3,1] => [[],[[]],[[]]]
[1,3,1,1,3] => [[[]],[[],[]]]
[1,3,1,3,1] => [[[],[[],[]]]]
[1,3,3,1,1] => [[],[[]],[[]]]
[3,1,1,1,3] => [[],[[]],[[]]]
[3,1,1,3,1] => [[],[[[],[]]]]
[3,1,3,1,1] => [[],[[],[[]]]]
[3,3,1,1,1] => [[],[],[],[[]]]
[1,1,1,3,4] => [[],[],[[[]]]]
[1,1,1,4,3] => [[],[],[[[]]]]
[1,1,3,1,4] => [[],[[[[]]]]]
[1,1,3,4,1] => [[],[[[[]]]]]
[1,1,4,1,3] => [[],[[],[[]]]]
[1,1,4,3,1] => [[],[[[[]]]]]
[1,3,1,1,4] => [[[]],[[[]]]]
[1,3,1,4,1] => [[[[],[[]]]]]
[1,3,4,1,1] => [[],[[[[]]]]]
[1,4,1,1,3] => [[[]],[[],[]]]
[1,4,1,3,1] => [[[],[[[]]]]]
[1,4,3,1,1] => [[[[]]],[[]]]
[3,1,1,1,4] => [[],[[]],[[]]]
[3,1,1,4,1] => [[],[[],[[]]]]
[3,1,4,1,1] => [[],[[],[[]]]]
[3,4,1,1,1] => [[],[],[[[]]]]
[4,1,1,1,3] => [[],[[]],[[]]]
[4,1,1,3,1] => [[[[]]],[[]]]
[4,1,3,1,1] => [[],[[[[]]]]]
[4,3,1,1,1] => [[],[[]],[[]]]
[1,1,1,3,5] => [[],[],[[],[]]]
[1,1,1,5,3] => [[],[],[[],[]]]
[1,1,3,1,5] => [[],[[[],[]]]]
[1,1,3,5,1] => [[],[[],[],[]]]
[1,1,5,1,3] => [[],[[[],[]]]]
[1,1,5,3,1] => [[],[[],[],[]]]
[1,3,1,1,5] => [[],[[],[[]]]]
[1,3,1,5,1] => [[[],[[],[]]]]
[1,3,5,1,1] => [[],[[],[],[]]]
[1,5,1,1,3] => [[[]],[[],[]]]
[1,5,1,3,1] => [[[],[[],[]]]]
[1,5,3,1,1] => [[],[[],[],[]]]
[3,1,1,1,5] => [[],[],[[],[]]]
[3,1,1,5,1] => [[],[[],[[]]]]
[3,1,5,1,1] => [[],[[[],[]]]]
[3,5,1,1,1] => [[],[],[[],[]]]
[5,1,1,1,3] => [[],[],[[],[]]]
[5,1,1,3,1] => [[],[[],[[]]]]
[5,1,3,1,1] => [[],[[[],[]]]]
[5,3,1,1,1] => [[],[],[[],[]]]
[1,1,1,4,4] => [[],[],[],[[]]]
[1,1,4,1,4] => [[],[[],[],[]]]
[1,1,4,4,1] => [[],[],[[],[]]]
[1,4,1,1,4] => [[],[[],[],[]]]
[1,4,1,4,1] => [[[],[],[],[]]]
[1,4,4,1,1] => [[],[],[[],[]]]
[4,1,1,1,4] => [[],[],[[],[]]]
[4,1,1,4,1] => [[],[[],[],[]]]
[4,1,4,1,1] => [[],[[],[],[]]]
[4,4,1,1,1] => [[],[],[],[[]]]
[1,1,1,4,5] => [[],[],[[[]]]]
[1,1,1,5,4] => [[],[],[[[]]]]
[1,1,4,1,5] => [[],[[],[[]]]]
[1,1,4,5,1] => [[],[[[[]]]]]
[1,1,5,1,4] => [[],[[[[]]]]]
[1,1,5,4,1] => [[],[[[[]]]]]
[1,4,1,1,5] => [[[]],[[],[]]]
[1,4,1,5,1] => [[[],[[[]]]]]
[1,4,5,1,1] => [[],[[[[]]]]]
[1,5,1,1,4] => [[[[]]],[[]]]
[1,5,1,4,1] => [[[[],[[]]]]]
[1,5,4,1,1] => [[[[]]],[[]]]
[4,1,1,1,5] => [[],[[]],[[]]]
[4,1,1,5,1] => [[[]],[[[]]]]
[4,1,5,1,1] => [[],[[[[]]]]]
[4,5,1,1,1] => [[],[],[[[]]]]
[5,1,1,1,4] => [[],[[]],[[]]]
[5,1,1,4,1] => [[[]],[[],[]]]
[5,1,4,1,1] => [[],[[],[[]]]]
[5,4,1,1,1] => [[],[[]],[[]]]
[1,1,2,2,2] => [[],[],[],[[]]]
[1,2,1,2,2] => [[[]],[[],[]]]
[1,2,2,1,2] => [[],[[[],[]]]]
[1,2,2,2,1] => [[],[[]],[[]]]
[2,1,1,2,2] => [[],[[]],[[]]]
[2,1,2,1,2] => [[[],[[],[]]]]
[2,1,2,2,1] => [[[]],[[],[]]]
[2,2,1,1,2] => [[],[],[[[]]]]
[2,2,1,2,1] => [[],[[],[[]]]]
[2,2,2,1,1] => [[],[],[],[[]]]
[1,1,2,2,3] => [[],[],[[],[]]]
[1,1,2,3,2] => [[],[[],[[]]]]
[1,1,3,2,2] => [[],[],[[[]]]]
[1,2,1,2,3] => [[[],[],[[]]]]
[1,2,1,3,2] => [[[[],[[]]]]]
[1,2,2,1,3] => [[[]],[[[]]]]
[1,2,2,3,1] => [[],[[],[[]]]]
[1,2,3,1,2] => [[[],[],[[]]]]
[1,2,3,2,1] => [[[],[[],[]]]]
[1,3,1,2,2] => [[],[[[[]]]]]
[1,3,2,1,2] => [[[[],[[]]]]]
[1,3,2,2,1] => [[],[[],[[]]]]
[2,1,1,2,3] => [[],[[],[[]]]]
[2,1,1,3,2] => [[],[[[],[]]]]
[2,1,2,1,3] => [[[[]],[[]]]]
[2,1,2,3,1] => [[[[[],[]]]]]
[2,1,3,1,2] => [[[[[[]]]]]]
[2,1,3,2,1] => [[[],[],[[]]]]
[2,2,1,1,3] => [[],[],[[[]]]]
[2,2,1,3,1] => [[],[[[[]]]]]
[2,2,3,1,1] => [[],[],[[[]]]]
[2,3,1,1,2] => [[[]],[[],[]]]
[2,3,1,2,1] => [[[],[[[]]]]]
[2,3,2,1,1] => [[],[[],[[]]]]
[3,1,1,2,2] => [[],[],[[[]]]]
[3,1,2,1,2] => [[[[],[[]]]]]
[3,1,2,2,1] => [[[]],[[[]]]]
[3,2,1,1,2] => [[],[[[],[]]]]
[3,2,1,2,1] => [[[],[],[[]]]]
[3,2,2,1,1] => [[],[],[[],[]]]
[1,1,2,2,4] => [[],[[]],[[]]]
[1,1,2,4,2] => [[],[[[[]]]]]
[1,1,4,2,2] => [[],[],[[[]]]]
[1,2,1,2,4] => [[[],[[[]]]]]
[1,2,1,4,2] => [[[[[[]]]]]]
[1,2,2,1,4] => [[[]],[[[]]]]
[1,2,2,4,1] => [[[]],[[[]]]]
[1,2,4,1,2] => [[[],[[[]]]]]
[1,2,4,2,1] => [[[[[[]]]]]]
[1,4,1,2,2] => [[],[[[],[]]]]
[1,4,2,1,2] => [[[[[[]]]]]]
[1,4,2,2,1] => [[[]],[[[]]]]
[2,1,1,2,4] => [[],[[[[]]]]]
[2,1,1,4,2] => [[],[[[[]]]]]
[2,1,2,1,4] => [[[[]],[[]]]]
[2,1,2,4,1] => [[[[[[]]]]]]
[2,1,4,1,2] => [[[[[],[]]]]]
[2,1,4,2,1] => [[[[]],[[]]]]
[2,2,1,1,4] => [[],[],[[[]]]]
[2,2,1,4,1] => [[],[[[],[]]]]
[2,2,4,1,1] => [[],[],[[[]]]]
[2,4,1,1,2] => [[[]],[[[]]]]
[2,4,1,2,1] => [[[[[[]]]]]]
[2,4,2,1,1] => [[[[]]],[[]]]
[4,1,1,2,2] => [[],[[]],[[]]]
[4,1,2,1,2] => [[[[[],[]]]]]
[4,1,2,2,1] => [[[[]]],[[]]]
[4,2,1,1,2] => [[[[]]],[[]]]
[4,2,1,2,1] => [[[[],[[]]]]]
[4,2,2,1,1] => [[],[[]],[[]]]
[1,1,2,2,5] => [[],[[]],[[]]]
[1,1,2,5,2] => [[],[[[],[]]]]
[1,1,5,2,2] => [[],[],[[[]]]]
[1,2,1,2,5] => [[[],[[[]]]]]
[1,2,1,5,2] => [[[[[[]]]]]]
[1,2,2,1,5] => [[[]],[[[]]]]
[1,2,2,5,1] => [[[]],[[[]]]]
[1,2,5,1,2] => [[[],[[[]]]]]
[1,2,5,2,1] => [[[[],[[]]]]]
[1,5,1,2,2] => [[],[[[[]]]]]
[1,5,2,1,2] => [[[[[[]]]]]]
[1,5,2,2,1] => [[[]],[[[]]]]
[2,1,1,2,5] => [[],[[[[]]]]]
[2,1,1,5,2] => [[],[[[[]]]]]
[2,1,2,1,5] => [[[[]],[[]]]]
[2,1,2,5,1] => [[[[[[]]]]]]
[2,1,5,1,2] => [[[[[[]]]]]]
[2,1,5,2,1] => [[[[]],[[]]]]
[2,2,1,1,5] => [[],[],[[[]]]]
[2,2,1,5,1] => [[],[[[[]]]]]
[2,2,5,1,1] => [[],[],[[[]]]]
[2,5,1,1,2] => [[[]],[[[]]]]
[2,5,1,2,1] => [[[[[[]]]]]]
[2,5,2,1,1] => [[],[[[],[]]]]
[5,1,1,2,2] => [[],[[]],[[]]]
[5,1,2,1,2] => [[[[],[[]]]]]
[5,1,2,2,1] => [[[[]]],[[]]]
[5,2,1,1,2] => [[],[[[[]]]]]
[5,2,1,2,1] => [[[[[],[]]]]]
[5,2,2,1,1] => [[],[],[[[]]]]
[1,1,2,3,3] => [[],[],[[],[]]]
[1,1,3,2,3] => [[],[[[[]]]]]
[1,1,3,3,2] => [[],[[]],[[]]]
[1,2,1,3,3] => [[[]],[[[]]]]
[1,2,3,1,3] => [[[],[[[]]]]]
[1,2,3,3,1] => [[[]],[[],[]]]
[1,3,1,2,3] => [[[[[],[]]]]]
[1,3,1,3,2] => [[[],[[[]]]]]
[1,3,2,1,3] => [[[],[[],[]]]]
[1,3,2,3,1] => [[[[[[]]]]]]
[1,3,3,1,2] => [[[]],[[[]]]]
[1,3,3,2,1] => [[[]],[[],[]]]
[2,1,1,3,3] => [[],[[]],[[]]]
[2,1,3,1,3] => [[[[],[[]]]]]
[2,1,3,3,1] => [[[]],[[[]]]]
[2,3,1,1,3] => [[[]],[[[]]]]
[2,3,1,3,1] => [[[[],[[]]]]]
[2,3,3,1,1] => [[],[[]],[[]]]
[3,1,1,2,3] => [[],[[],[[]]]]
[3,1,1,3,2] => [[],[[[[]]]]]
[3,1,2,1,3] => [[[[[[]]]]]]
[3,1,2,3,1] => [[[],[[],[]]]]
[3,1,3,1,2] => [[[[]],[[]]]]
[3,1,3,2,1] => [[[[],[[]]]]]
[3,2,1,1,3] => [[],[[[],[]]]]
[3,2,1,3,1] => [[[],[[[]]]]]
[3,2,3,1,1] => [[[[]]],[[]]]
[3,3,1,1,2] => [[],[[]],[[]]]
[3,3,1,2,1] => [[],[[[[]]]]]
[3,3,2,1,1] => [[],[],[[],[]]]
[1,1,2,3,4] => [[],[[],[],[]]]
[1,1,2,4,3] => [[],[[[[]]]]]
[1,1,3,2,4] => [[],[[],[[]]]]
[1,1,3,4,2] => [[],[[[[]]]]]
[1,1,4,2,3] => [[],[[[[]]]]]
[1,1,4,3,2] => [[],[[[],[]]]]
[1,2,1,3,4] => [[[[]],[[]]]]
[1,2,1,4,3] => [[[[],[[]]]]]
[1,2,3,1,4] => [[[],[[[]]]]]
[1,2,3,4,1] => [[[],[],[[]]]]
[1,2,4,1,3] => [[[[],[[]]]]]
[1,2,4,3,1] => [[[[[[]]]]]]
[1,3,1,2,4] => [[[],[[[]]]]]
[1,3,1,4,2] => [[[[[],[]]]]]
[1,3,2,1,4] => [[[[],[[]]]]]
[1,3,2,4,1] => [[[],[[[]]]]]
[1,3,4,1,2] => [[[[],[[]]]]]
[1,3,4,2,1] => [[[[[[]]]]]]
[1,4,1,2,3] => [[[],[[],[]]]]
[1,4,1,3,2] => [[[],[[[]]]]]
[1,4,2,1,3] => [[[[[[]]]]]]
[1,4,2,3,1] => [[[[[],[]]]]]
[1,4,3,1,2] => [[[[[[]]]]]]
[1,4,3,2,1] => [[[[],[],[]]]]
[2,1,1,3,4] => [[],[[[[]]]]]
[2,1,1,4,3] => [[],[[[],[]]]]
[2,1,3,1,4] => [[[[[[]]]]]]
[2,1,3,4,1] => [[[[[[]]]]]]
[2,1,4,1,3] => [[[[[],[]]]]]
[2,1,4,3,1] => [[[],[[[]]]]]
[2,3,1,1,4] => [[[]],[[[]]]]
[2,3,1,4,1] => [[[[[],[]]]]]
[2,3,4,1,1] => [[],[[[],[]]]]
[2,4,1,1,3] => [[[]],[[],[]]]
[2,4,1,3,1] => [[[[]],[[]]]]
[2,4,3,1,1] => [[[]],[[[]]]]
[3,1,1,2,4] => [[[[]]],[[]]]
[3,1,1,4,2] => [[],[[[],[]]]]
[3,1,2,1,4] => [[[[[[]]]]]]
[3,1,2,4,1] => [[[[[[]]]]]]
[3,1,4,1,2] => [[[[],[[]]]]]
[3,1,4,2,1] => [[[],[[[]]]]]
[3,2,1,1,4] => [[],[[[],[]]]]
[3,2,1,4,1] => [[[],[[],[]]]]
[3,2,4,1,1] => [[[[]]],[[]]]
[3,4,1,1,2] => [[[]],[[],[]]]
[3,4,1,2,1] => [[[[]],[[]]]]
[3,4,2,1,1] => [[[[]]],[[]]]
[4,1,1,2,3] => [[[]],[[],[]]]
[4,1,1,3,2] => [[[[]]],[[]]]
[4,1,2,1,3] => [[[[[[]]]]]]
[4,1,2,3,1] => [[[[],[[]]]]]
[4,1,3,1,2] => [[[[[[]]]]]]
[4,1,3,2,1] => [[[[],[[]]]]]
[4,2,1,1,3] => [[[[]]],[[]]]
[4,2,1,3,1] => [[[[]],[[]]]]
[4,2,3,1,1] => [[],[[],[[]]]]
[4,3,1,1,2] => [[[[]]],[[]]]
[4,3,1,2,1] => [[[[]],[[]]]]
[4,3,2,1,1] => [[],[[],[],[]]]
[1,1,2,3,5] => [[],[[],[[]]]]
[1,1,2,5,3] => [[],[[[[]]]]]
[1,1,3,2,5] => [[],[[[[]]]]]
[1,1,3,5,2] => [[],[[],[[]]]]
[1,1,5,2,3] => [[],[[[[]]]]]
[1,1,5,3,2] => [[],[[],[[]]]]
[1,2,1,3,5] => [[[[[],[]]]]]
[1,2,1,5,3] => [[[[[],[]]]]]
[1,2,3,1,5] => [[[],[[],[]]]]
[1,2,3,5,1] => [[[],[[],[]]]]
[1,2,5,1,3] => [[[[[],[]]]]]
[1,2,5,3,1] => [[[[[],[]]]]]
[1,3,1,2,5] => [[[[[[]]]]]]
[1,3,1,5,2] => [[[[],[[]]]]]
[1,3,2,1,5] => [[[[],[[]]]]]
[1,3,2,5,1] => [[[[]],[[]]]]
[1,3,5,1,2] => [[[],[],[[]]]]
[1,3,5,2,1] => [[[],[[[]]]]]
[1,5,1,2,3] => [[[[],[[]]]]]
[1,5,1,3,2] => [[[[[],[]]]]]
[1,5,2,1,3] => [[[[[[]]]]]]
[1,5,2,3,1] => [[[],[[[]]]]]
[1,5,3,1,2] => [[[],[],[[]]]]
[1,5,3,2,1] => [[[],[[],[]]]]
[2,1,1,3,5] => [[],[[],[[]]]]
[2,1,1,5,3] => [[],[[],[[]]]]
[2,1,3,1,5] => [[[[],[[]]]]]
[2,1,3,5,1] => [[[[],[],[]]]]
[2,1,5,1,3] => [[[[],[[]]]]]
[2,1,5,3,1] => [[[[],[],[]]]]
[2,3,1,1,5] => [[],[[],[[]]]]
[2,3,1,5,1] => [[[[],[[]]]]]
[2,3,5,1,1] => [[],[[],[[]]]]
[2,5,1,1,3] => [[],[[],[[]]]]
[2,5,1,3,1] => [[[[],[[]]]]]
[2,5,3,1,1] => [[],[[],[[]]]]
[3,1,1,2,5] => [[[[]]],[[]]]
[3,1,1,5,2] => [[],[[],[[]]]]
[3,1,2,1,5] => [[[],[[[]]]]]
[3,1,2,5,1] => [[[[[[]]]]]]
[3,1,5,1,2] => [[[],[[[]]]]]
[3,1,5,2,1] => [[[],[[[]]]]]
[3,2,1,1,5] => [[],[[[],[]]]]
[3,2,1,5,1] => [[[],[[[]]]]]
[3,2,5,1,1] => [[[[]]],[[]]]
[3,5,1,1,2] => [[[]],[[],[]]]
[3,5,1,2,1] => [[[],[[[]]]]]
[3,5,2,1,1] => [[],[[[[]]]]]
[5,1,1,2,3] => [[[]],[[],[]]]
[5,1,1,3,2] => [[],[[],[[]]]]
[5,1,2,1,3] => [[[],[[[]]]]]
[5,1,2,3,1] => [[[[],[[]]]]]
[5,1,3,1,2] => [[[],[[[]]]]]
[5,1,3,2,1] => [[[],[[],[]]]]
[5,2,1,1,3] => [[],[[[[]]]]]
[5,2,1,3,1] => [[[[[[]]]]]]
[5,2,3,1,1] => [[],[[[[]]]]]
[5,3,1,1,2] => [[[]],[[],[]]]
[5,3,1,2,1] => [[[],[[[]]]]]
[5,3,2,1,1] => [[[]],[[],[]]]
[1,1,2,4,4] => [[],[],[[[]]]]
[1,1,4,2,4] => [[],[[[[]]]]]
[1,1,4,4,2] => [[],[[]],[[]]]
[1,2,1,4,4] => [[[]],[[[]]]]
[1,2,4,1,4] => [[[[[],[]]]]]
[1,2,4,4,1] => [[[[]]],[[]]]
[1,4,1,2,4] => [[[],[[[]]]]]
[1,4,1,4,2] => [[[],[],[[]]]]
[1,4,2,1,4] => [[[[]],[[]]]]
[1,4,2,4,1] => [[[],[[[]]]]]
[1,4,4,1,2] => [[],[[],[[]]]]
[1,4,4,2,1] => [[],[[[[]]]]]
[2,1,1,4,4] => [[],[[]],[[]]]
[2,1,4,1,4] => [[[[],[],[]]]]
[2,1,4,4,1] => [[],[[],[[]]]]
[2,4,1,1,4] => [[],[[],[[]]]]
[2,4,1,4,1] => [[[[],[],[]]]]
[2,4,4,1,1] => [[],[[]],[[]]]
[4,1,1,2,4] => [[[[]]],[[]]]
[4,1,1,4,2] => [[],[[],[[]]]]
[4,1,2,1,4] => [[[],[[[]]]]]
[4,1,2,4,1] => [[[],[[[]]]]]
[4,1,4,1,2] => [[[],[],[[]]]]
[4,1,4,2,1] => [[[],[[[]]]]]
[4,2,1,1,4] => [[[[]]],[[]]]
[4,2,1,4,1] => [[[[],[[]]]]]
[4,2,4,1,1] => [[],[[[[]]]]]
[4,4,1,1,2] => [[],[[]],[[]]]
[4,4,1,2,1] => [[],[[[[]]]]]
[4,4,2,1,1] => [[],[[]],[[]]]
[1,1,2,4,5] => [[],[[],[[]]]]
[1,1,2,5,4] => [[],[[[[]]]]]
[1,1,4,2,5] => [[],[[],[[]]]]
[1,1,4,5,2] => [[],[[],[[]]]]
[1,1,5,2,4] => [[],[[[[]]]]]
[1,1,5,4,2] => [[],[[],[[]]]]
[1,2,1,4,5] => [[[[]],[[]]]]
[1,2,1,5,4] => [[[[],[[]]]]]
[1,2,4,1,5] => [[[[[[]]]]]]
[1,2,4,5,1] => [[[],[[],[]]]]
[1,2,5,1,4] => [[[[],[[]]]]]
[1,2,5,4,1] => [[[[],[[]]]]]
[1,4,1,2,5] => [[[],[],[[]]]]
[1,4,1,5,2] => [[[],[],[[]]]]
[1,4,2,1,5] => [[[[],[[]]]]]
[1,4,2,5,1] => [[[[]],[[]]]]
[1,4,5,1,2] => [[[[],[[]]]]]
[1,4,5,2,1] => [[[[]],[[]]]]
[1,5,1,2,4] => [[[[[],[]]]]]
[1,5,1,4,2] => [[[],[[[]]]]]
[1,5,2,1,4] => [[[[],[[]]]]]
[1,5,2,4,1] => [[[[[],[]]]]]
[1,5,4,1,2] => [[[[[[]]]]]]
[1,5,4,2,1] => [[[],[[],[]]]]
[2,1,1,4,5] => [[],[[[[]]]]]
[2,1,1,5,4] => [[],[[[],[]]]]
[2,1,4,1,5] => [[[[[],[]]]]]
[2,1,4,5,1] => [[[[[[]]]]]]
[2,1,5,1,4] => [[[[[[]]]]]]
[2,1,5,4,1] => [[[],[[[]]]]]
[2,4,1,1,5] => [[[[]]],[[]]]
[2,4,1,5,1] => [[[],[[[]]]]]
[2,4,5,1,1] => [[],[[],[[]]]]
[2,5,1,1,4] => [[[]],[[],[]]]
[2,5,1,4,1] => [[[],[],[[]]]]
[2,5,4,1,1] => [[[]],[[],[]]]
[4,1,1,2,5] => [[],[[[],[]]]]
[4,1,1,5,2] => [[],[[[],[]]]]
[4,1,2,1,5] => [[[[[[]]]]]]
[4,1,2,5,1] => [[[[]],[[]]]]
[4,1,5,1,2] => [[[[[[]]]]]]
[4,1,5,2,1] => [[[],[[[]]]]]
[4,2,1,1,5] => [[],[[],[[]]]]
[4,2,1,5,1] => [[[],[[[]]]]]
[4,2,5,1,1] => [[],[[[[]]]]]
[4,5,1,1,2] => [[[]],[[],[]]]
[4,5,1,2,1] => [[[[]],[[]]]]
[4,5,2,1,1] => [[],[[[[]]]]]
[5,1,1,2,4] => [[],[[[],[]]]]
[5,1,1,4,2] => [[[]],[[[]]]]
[5,1,2,1,4] => [[[[[[]]]]]]
[5,1,2,4,1] => [[[[]],[[]]]]
[5,1,4,1,2] => [[[[],[[]]]]]
[5,1,4,2,1] => [[[[[[]]]]]]
[5,2,1,1,4] => [[],[[],[[]]]]
[5,2,1,4,1] => [[[],[],[[]]]]
[5,2,4,1,1] => [[],[[],[[]]]]
[5,4,1,1,2] => [[[[]]],[[]]]
[5,4,1,2,1] => [[[],[[[]]]]]
[5,4,2,1,1] => [[[]],[[],[]]]
[1,1,3,3,3] => [[],[],[],[[]]]
[1,3,1,3,3] => [[],[[],[[]]]]
[1,3,3,1,3] => [[],[[[],[]]]]
[1,3,3,3,1] => [[],[[]],[[]]]
[3,1,1,3,3] => [[],[],[[[]]]]
[3,1,3,1,3] => [[[],[[],[]]]]
[3,1,3,3,1] => [[[]],[[],[]]]
[3,3,1,1,3] => [[],[[]],[[]]]
[3,3,1,3,1] => [[],[[],[[]]]]
[3,3,3,1,1] => [[],[],[],[[]]]
[1,1,3,3,4] => [[],[[]],[[]]]
[1,1,3,4,3] => [[],[[[[]]]]]
[1,1,4,3,3] => [[],[],[[[]]]]
[1,3,1,3,4] => [[[[]],[[]]]]
[1,3,1,4,3] => [[[[[[]]]]]]
[1,3,3,1,4] => [[[]],[[[]]]]
[1,3,3,4,1] => [[[[]]],[[]]]
[1,3,4,1,3] => [[[],[[[]]]]]
[1,3,4,3,1] => [[[[[[]]]]]]
[1,4,1,3,3] => [[],[[[],[]]]]
[1,4,3,1,3] => [[[[[[]]]]]]
[1,4,3,3,1] => [[[]],[[[]]]]
[3,1,1,3,4] => [[[[]]],[[]]]
[3,1,1,4,3] => [[],[[[[]]]]]
[3,1,3,1,4] => [[[[]],[[]]]]
[3,1,3,4,1] => [[[[[[]]]]]]
[3,1,4,1,3] => [[[[],[[]]]]]
[3,1,4,3,1] => [[[[]],[[]]]]
[3,3,1,1,4] => [[],[[]],[[]]]
[3,3,1,4,1] => [[],[[[],[]]]]
[3,3,4,1,1] => [[],[],[[[]]]]
[3,4,1,1,3] => [[[]],[[[]]]]
[3,4,1,3,1] => [[[[[[]]]]]]
[3,4,3,1,1] => [[[]],[[[]]]]
[4,1,1,3,3] => [[],[[]],[[]]]
[4,1,3,1,3] => [[[[[],[]]]]]
[4,1,3,3,1] => [[[[]]],[[]]]
[4,3,1,1,3] => [[[[]]],[[]]]
[4,3,1,3,1] => [[[[],[[]]]]]
[4,3,3,1,1] => [[],[[]],[[]]]
[1,1,3,3,5] => [[],[],[[],[]]]
[1,1,3,5,3] => [[],[[],[[]]]]
[1,1,5,3,3] => [[],[],[[],[]]]
[1,3,1,3,5] => [[[],[],[[]]]]
[1,3,1,5,3] => [[[[],[],[]]]]
[1,3,3,1,5] => [[[]],[[],[]]]
[1,3,3,5,1] => [[],[[],[],[]]]
[1,3,5,1,3] => [[[],[],[],[]]]
[1,3,5,3,1] => [[[],[[],[]]]]
[1,5,1,3,3] => [[],[[],[[]]]]
[1,5,3,1,3] => [[[],[],[[]]]]
[1,5,3,3,1] => [[],[[],[],[]]]
[3,1,1,3,5] => [[],[[],[[]]]]
[3,1,1,5,3] => [[],[[],[],[]]]
[3,1,3,1,5] => [[[],[],[[]]]]
[3,1,3,5,1] => [[[[],[],[]]]]
[3,1,5,1,3] => [[[],[[],[]]]]
[3,1,5,3,1] => [[[],[],[],[]]]
[3,3,1,1,5] => [[],[],[[],[]]]
[3,3,1,5,1] => [[],[[],[[]]]]
[3,3,5,1,1] => [[],[],[[],[]]]
[3,5,1,1,3] => [[],[[],[],[]]]
[3,5,1,3,1] => [[[],[],[[]]]]
[3,5,3,1,1] => [[],[[],[[]]]]
[5,1,1,3,3] => [[],[],[[],[]]]
[5,1,3,1,3] => [[[],[],[[]]]]
[5,1,3,3,1] => [[[]],[[],[]]]
[5,3,1,1,3] => [[[]],[[],[]]]
[5,3,1,3,1] => [[[],[],[[]]]]
[5,3,3,1,1] => [[],[],[[],[]]]
[1,1,3,4,4] => [[],[],[[[]]]]
[1,1,4,3,4] => [[],[[[[]]]]]
[1,1,4,4,3] => [[],[[]],[[]]]
[1,3,1,4,4] => [[],[[[[]]]]]
[1,3,4,1,4] => [[[[[],[]]]]]
[1,3,4,4,1] => [[[[]]],[[]]]
[1,4,1,3,4] => [[[],[[[]]]]]
[1,4,1,4,3] => [[[],[],[[]]]]
[1,4,3,1,4] => [[[[]],[[]]]]
[1,4,3,4,1] => [[[[]],[[]]]]
[1,4,4,1,3] => [[],[[],[[]]]]
[1,4,4,3,1] => [[],[[[[]]]]]
[3,1,1,4,4] => [[],[],[[[]]]]
[3,1,4,1,4] => [[[[],[],[]]]]
[3,1,4,4,1] => [[[]],[[],[]]]
[3,4,1,1,4] => [[],[[],[[]]]]
[3,4,1,4,1] => [[[[],[],[]]]]
[3,4,4,1,1] => [[],[[]],[[]]]
[4,1,1,3,4] => [[[[]]],[[]]]
[4,1,1,4,3] => [[],[[],[[]]]]
[4,1,3,1,4] => [[[],[[[]]]]]
[4,1,3,4,1] => [[[],[[[]]]]]
[4,1,4,1,3] => [[[],[],[[]]]]
[4,1,4,3,1] => [[[],[[[]]]]]
[4,3,1,1,4] => [[[[]]],[[]]]
[4,3,1,4,1] => [[[[],[[]]]]]
[4,3,4,1,1] => [[[[]]],[[]]]
[4,4,1,1,3] => [[],[[]],[[]]]
[4,4,1,3,1] => [[],[[[[]]]]]
[4,4,3,1,1] => [[],[[]],[[]]]
[1,1,3,4,5] => [[],[[[],[]]]]
[1,1,3,5,4] => [[],[[],[[]]]]
[1,1,4,3,5] => [[],[[[[]]]]]
[1,1,4,5,3] => [[],[[[[]]]]]
[1,1,5,3,4] => [[],[[],[[]]]]
[1,1,5,4,3] => [[],[[[],[]]]]
[1,3,1,4,5] => [[[[[[]]]]]]
[1,3,1,5,4] => [[[[],[[]]]]]
[1,3,4,1,5] => [[[[[[]]]]]]
[1,3,4,5,1] => [[[],[[],[]]]]
[1,3,5,1,4] => [[[],[],[[]]]]
[1,3,5,4,1] => [[[],[[[]]]]]
[1,4,1,3,5] => [[[],[[],[]]]]
[1,4,1,5,3] => [[[],[[],[]]]]
[1,4,3,1,5] => [[[[],[[]]]]]
[1,4,3,5,1] => [[[[],[[]]]]]
[1,4,5,1,3] => [[[[[],[]]]]]
[1,4,5,3,1] => [[[[],[[]]]]]
[1,5,1,3,4] => [[[[],[[]]]]]
[1,5,1,4,3] => [[[[[[]]]]]]
[1,5,3,1,4] => [[[],[],[[]]]]
[1,5,3,4,1] => [[[],[[[]]]]]
[1,5,4,1,3] => [[[[[[]]]]]]
[1,5,4,3,1] => [[[],[[],[]]]]
[3,1,1,4,5] => [[[[]]],[[]]]
[3,1,1,5,4] => [[],[[],[[]]]]
[3,1,4,1,5] => [[[],[[],[]]]]
[3,1,4,5,1] => [[[[[[]]]]]]
[3,1,5,1,4] => [[[],[[[]]]]]
[3,1,5,4,1] => [[[],[[[]]]]]
[3,4,1,1,5] => [[[[]]],[[]]]
[3,4,1,5,1] => [[[[[[]]]]]]
[3,4,5,1,1] => [[],[[[],[]]]]
[3,5,1,1,4] => [[[]],[[],[]]]
[3,5,1,4,1] => [[[],[[],[]]]]
[3,5,4,1,1] => [[[]],[[[]]]]
[4,1,1,3,5] => [[[]],[[],[]]]
[4,1,1,5,3] => [[],[[],[[]]]]
[4,1,3,1,5] => [[[[],[[]]]]]
[4,1,3,5,1] => [[[[],[],[]]]]
[4,1,5,1,3] => [[[[],[[]]]]]
[4,1,5,3,1] => [[[[],[],[]]]]
[4,3,1,1,5] => [[],[[],[[]]]]
[4,3,1,5,1] => [[[[[],[]]]]]
[4,3,5,1,1] => [[[]],[[],[]]]
[4,5,1,1,3] => [[],[[],[[]]]]
[4,5,1,3,1] => [[[[],[[]]]]]
[4,5,3,1,1] => [[],[[],[[]]]]
[5,1,1,3,4] => [[],[[],[[]]]]
[5,1,1,4,3] => [[[]],[[[]]]]
[5,1,3,1,4] => [[[],[[[]]]]]
[5,1,3,4,1] => [[[],[[[]]]]]
[5,1,4,1,3] => [[[],[[],[]]]]
[5,1,4,3,1] => [[[[[[]]]]]]
[5,3,1,1,4] => [[[]],[[],[]]]
[5,3,1,4,1] => [[[],[[],[]]]]
[5,3,4,1,1] => [[],[[[[]]]]]
[5,4,1,1,3] => [[[[]]],[[]]]
[5,4,1,3,1] => [[[[[[]]]]]]
[5,4,3,1,1] => [[[]],[[],[]]]
[1,2,2,2,2] => [[],[],[],[[]]]
[2,1,2,2,2] => [[],[[]],[[]]]
[2,2,1,2,2] => [[],[[]],[[]]]
[2,2,2,1,2] => [[],[],[[[]]]]
[2,2,2,2,1] => [[],[],[],[[]]]
[1,2,2,2,3] => [[],[],[[],[]]]
[1,2,2,3,2] => [[],[[],[[]]]]
[1,2,3,2,2] => [[],[[[],[]]]]
[1,3,2,2,2] => [[],[],[[[]]]]
[2,1,2,2,3] => [[],[[],[[]]]]
[2,1,2,3,2] => [[[],[[],[]]]]
[2,1,3,2,2] => [[],[[],[[]]]]
[2,2,1,2,3] => [[],[[[],[]]]]
[2,2,1,3,2] => [[],[[],[[]]]]
[2,2,2,1,3] => [[],[],[[[]]]]
[2,2,2,3,1] => [[],[],[[[]]]]
[2,2,3,1,2] => [[],[[],[[]]]]
[2,2,3,2,1] => [[],[[[],[]]]]
[2,3,1,2,2] => [[],[[],[[]]]]
[2,3,2,1,2] => [[[],[[],[]]]]
[2,3,2,2,1] => [[],[[],[[]]]]
[3,1,2,2,2] => [[],[[]],[[]]]
[3,2,1,2,2] => [[[]],[[],[]]]
[3,2,2,1,2] => [[],[[],[[]]]]
[3,2,2,2,1] => [[],[],[[],[]]]
[1,2,2,2,4] => [[],[[]],[[]]]
[1,2,2,4,2] => [[[]],[[[]]]]
[1,2,4,2,2] => [[],[[[[]]]]]
[1,4,2,2,2] => [[],[[]],[[]]]
[2,1,2,2,4] => [[[]],[[[]]]]
[2,1,2,4,2] => [[[[[[]]]]]]
[2,1,4,2,2] => [[[[]]],[[]]]
[2,2,1,2,4] => [[],[[[[]]]]]
[2,2,1,4,2] => [[],[[[[]]]]]
[2,2,2,1,4] => [[],[],[[[]]]]
[2,2,2,4,1] => [[],[],[[[]]]]
[2,2,4,1,2] => [[],[[[[]]]]]
[2,2,4,2,1] => [[],[[[[]]]]]
[2,4,1,2,2] => [[],[[[[]]]]]
[2,4,2,1,2] => [[[[[[]]]]]]
[2,4,2,2,1] => [[],[[[[]]]]]
[4,1,2,2,2] => [[],[],[[[]]]]
[4,2,1,2,2] => [[[[]]],[[]]]
[4,2,2,1,2] => [[],[[[[]]]]]
[4,2,2,2,1] => [[],[],[[[]]]]
[1,2,2,2,5] => [[],[[]],[[]]]
[1,2,2,5,2] => [[[]],[[],[]]]
[1,2,5,2,2] => [[],[[],[[]]]]
[1,5,2,2,2] => [[],[[]],[[]]]
[2,1,2,2,5] => [[[]],[[[]]]]
[2,1,2,5,2] => [[[[],[[]]]]]
[2,1,5,2,2] => [[[[]]],[[]]]
[2,2,1,2,5] => [[],[[[[]]]]]
[2,2,1,5,2] => [[],[[[[]]]]]
[2,2,2,1,5] => [[],[],[[[]]]]
[2,2,2,5,1] => [[],[],[[[]]]]
[2,2,5,1,2] => [[],[[[[]]]]]
[2,2,5,2,1] => [[],[[],[[]]]]
[2,5,1,2,2] => [[],[[[[]]]]]
[2,5,2,1,2] => [[[],[[[]]]]]
[2,5,2,2,1] => [[[]],[[],[]]]
[5,1,2,2,2] => [[],[],[[[]]]]
[5,2,1,2,2] => [[[]],[[[]]]]
[5,2,2,1,2] => [[[]],[[[]]]]
[5,2,2,2,1] => [[],[[]],[[]]]
[1,2,2,3,3] => [[],[],[[],[]]]
[1,2,3,2,3] => [[[],[],[[]]]]
[1,2,3,3,2] => [[[]],[[],[]]]
[1,3,2,2,3] => [[],[[[[]]]]]
[1,3,2,3,2] => [[[[],[[]]]]]
[1,3,3,2,2] => [[],[[]],[[]]]
[2,1,2,3,3] => [[[]],[[],[]]]
[2,1,3,2,3] => [[[[]],[[]]]]
[2,1,3,3,2] => [[[]],[[],[]]]
[2,2,1,3,3] => [[],[[]],[[]]]
[2,2,3,1,3] => [[],[[[[]]]]]
[2,2,3,3,1] => [[],[[]],[[]]]
[2,3,1,2,3] => [[[],[],[[]]]]
[2,3,1,3,2] => [[[[[[]]]]]]
[2,3,2,1,3] => [[[[],[[]]]]]
[2,3,2,3,1] => [[[],[[[]]]]]
[2,3,3,1,2] => [[],[[[],[]]]]
[2,3,3,2,1] => [[[]],[[],[]]]
[3,1,2,2,3] => [[[]],[[],[]]]
[3,1,2,3,2] => [[[[[],[]]]]]
[3,1,3,2,2] => [[[]],[[[]]]]
[3,2,1,2,3] => [[[],[[],[]]]]
[3,2,1,3,2] => [[[],[],[[]]]]
[3,2,2,1,3] => [[],[[],[[]]]]
[3,2,2,3,1] => [[],[[[[]]]]]
[3,2,3,1,2] => [[[[],[[]]]]]
[3,2,3,2,1] => [[[],[],[[]]]]
[3,3,1,2,2] => [[],[],[[[]]]]
[3,3,2,1,2] => [[],[[],[[]]]]
[3,3,2,2,1] => [[],[],[[],[]]]
[1,2,2,3,4] => [[],[[],[],[]]]
[1,2,2,4,3] => [[[]],[[[]]]]
[1,2,3,2,4] => [[[],[[[]]]]]
[1,2,3,4,2] => [[[],[],[[]]]]
[1,2,4,2,3] => [[[],[[[]]]]]
[1,2,4,3,2] => [[[[[],[]]]]]
[1,3,2,2,4] => [[],[[],[[]]]]
[1,3,2,4,2] => [[[],[[[]]]]]
[1,3,4,2,2] => [[],[[[[]]]]]
[1,4,2,2,3] => [[[]],[[[]]]]
[1,4,2,3,2] => [[[[[[]]]]]]
[1,4,3,2,2] => [[],[[],[[]]]]
[2,1,2,3,4] => [[[[],[],[]]]]
[2,1,2,4,3] => [[[],[[[]]]]]
[2,1,3,2,4] => [[[],[[],[]]]]
[2,1,3,4,2] => [[[[[[]]]]]]
[2,1,4,2,3] => [[[[[[]]]]]]
[2,1,4,3,2] => [[[],[],[[]]]]
[2,2,1,3,4] => [[],[[[[]]]]]
[2,2,1,4,3] => [[],[[],[[]]]]
[2,2,3,1,4] => [[],[[[[]]]]]
[2,2,3,4,1] => [[],[[],[[]]]]
[2,2,4,1,3] => [[],[[],[[]]]]
[2,2,4,3,1] => [[],[[[[]]]]]
[2,3,1,2,4] => [[[[]],[[]]]]
[2,3,1,4,2] => [[[[],[[]]]]]
[2,3,2,1,4] => [[[[],[[]]]]]
[2,3,2,4,1] => [[[[[[]]]]]]
[2,3,4,1,2] => [[[],[],[[]]]]
[2,3,4,2,1] => [[[],[[[]]]]]
[2,4,1,2,3] => [[[[[],[]]]]]
[2,4,1,3,2] => [[[[]],[[]]]]
[2,4,2,1,3] => [[[[]],[[]]]]
[2,4,2,3,1] => [[[[],[[]]]]]
[2,4,3,1,2] => [[[[[[]]]]]]
[2,4,3,2,1] => [[[[],[],[]]]]
[3,1,2,2,4] => [[[[]]],[[]]]
[3,1,2,4,2] => [[[],[[[]]]]]
[3,1,4,2,2] => [[],[[],[[]]]]
[3,2,1,2,4] => [[[],[[[]]]]]
[3,2,1,4,2] => [[[],[[[]]]]]
[3,2,2,1,4] => [[],[[],[[]]]]
[3,2,2,4,1] => [[],[[[[]]]]]
[3,2,4,1,2] => [[[[[[]]]]]]
[3,2,4,2,1] => [[[],[[[]]]]]
[3,4,1,2,2] => [[],[[],[[]]]]
[3,4,2,1,2] => [[[[]],[[]]]]
[3,4,2,2,1] => [[],[[[[]]]]]
[4,1,2,2,3] => [[],[[],[[]]]]
[4,1,2,3,2] => [[[[],[[]]]]]
[4,1,3,2,2] => [[],[[[[]]]]]
[4,2,1,2,3] => [[[[],[[]]]]]
[4,2,1,3,2] => [[[[],[[]]]]]
[4,2,2,1,3] => [[],[[[[]]]]]
[4,2,2,3,1] => [[],[[[],[]]]]
[4,2,3,1,2] => [[[],[[],[]]]]
[4,2,3,2,1] => [[[[],[[]]]]]
[4,3,1,2,2] => [[[[]]],[[]]]
[4,3,2,1,2] => [[[],[],[[]]]]
[4,3,2,2,1] => [[],[[],[],[]]]
[1,2,2,3,5] => [[],[[],[[]]]]
[1,2,2,5,3] => [[[]],[[[]]]]
[1,2,3,2,5] => [[[],[[[]]]]]
[1,2,3,5,2] => [[[],[[[]]]]]
[1,2,5,2,3] => [[[],[[],[]]]]
[1,2,5,3,2] => [[[[[[]]]]]]
[1,3,2,2,5] => [[],[[[[]]]]]
[1,3,2,5,2] => [[[[],[[]]]]]
[1,3,5,2,2] => [[],[[[],[]]]]
[1,5,2,2,3] => [[[]],[[[]]]]
[1,5,2,3,2] => [[[[[[]]]]]]
[1,5,3,2,2] => [[[]],[[],[]]]
[2,1,2,3,5] => [[[[[],[]]]]]
[2,1,2,5,3] => [[[[[[]]]]]]
[2,1,3,2,5] => [[[[]],[[]]]]
[2,1,3,5,2] => [[[[[],[]]]]]
[2,1,5,2,3] => [[[[[[]]]]]]
[2,1,5,3,2] => [[[],[[],[]]]]
[2,2,1,3,5] => [[],[[[],[]]]]
[2,2,1,5,3] => [[],[[[],[]]]]
[2,2,3,1,5] => [[],[[[],[]]]]
[2,2,3,5,1] => [[],[[[],[]]]]
[2,2,5,1,3] => [[],[[[],[]]]]
[2,2,5,3,1] => [[],[[[],[]]]]
[2,3,1,2,5] => [[[[]],[[]]]]
[2,3,1,5,2] => [[[[],[[]]]]]
[2,3,2,1,5] => [[[[],[[]]]]]
[2,3,2,5,1] => [[[[[[]]]]]]
[2,3,5,1,2] => [[[],[[],[]]]]
[2,3,5,2,1] => [[[[[[]]]]]]
[2,5,1,2,3] => [[[[[],[]]]]]
[2,5,1,3,2] => [[[[],[[]]]]]
[2,5,2,1,3] => [[[],[[[]]]]]
[2,5,2,3,1] => [[[],[[[]]]]]
[2,5,3,1,2] => [[[[],[[]]]]]
[2,5,3,2,1] => [[[[],[[]]]]]
[3,1,2,2,5] => [[[[]]],[[]]]
[3,1,2,5,2] => [[[[],[[]]]]]
[3,1,5,2,2] => [[],[[[],[]]]]
[3,2,1,2,5] => [[[],[[[]]]]]
[3,2,1,5,2] => [[[],[[[]]]]]
[3,2,2,1,5] => [[],[[],[[]]]]
[3,2,2,5,1] => [[],[[[[]]]]]
[3,2,5,1,2] => [[[[[[]]]]]]
[3,2,5,2,1] => [[[],[[],[]]]]
[3,5,1,2,2] => [[],[[[],[]]]]
[3,5,2,1,2] => [[[[[[]]]]]]
[3,5,2,2,1] => [[[[]]],[[]]]
[5,1,2,2,3] => [[],[[],[[]]]]
[5,1,2,3,2] => [[[[],[[]]]]]
[5,1,3,2,2] => [[],[[[],[]]]]
[5,2,1,2,3] => [[[[],[[]]]]]
[5,2,1,3,2] => [[[[[],[]]]]]
[5,2,2,1,3] => [[[]],[[[]]]]
[5,2,2,3,1] => [[[[]]],[[]]]
[5,2,3,1,2] => [[[[[],[]]]]]
[5,2,3,2,1] => [[[[],[[]]]]]
[5,3,1,2,2] => [[],[[[],[]]]]
[5,3,2,1,2] => [[[[[],[]]]]]
[5,3,2,2,1] => [[],[[],[[]]]]
[1,2,2,4,4] => [[],[[]],[[]]]
[1,2,4,2,4] => [[[[],[[]]]]]
[1,2,4,4,2] => [[[[]]],[[]]]
[1,4,2,2,4] => [[[]],[[[]]]]
[1,4,2,4,2] => [[[[[],[]]]]]
[1,4,4,2,2] => [[],[],[[[]]]]
[2,1,2,4,4] => [[[[]]],[[]]]
[2,1,4,2,4] => [[[[[[]]]]]]
[2,1,4,4,2] => [[[]],[[[]]]]
[2,2,1,4,4] => [[],[[]],[[]]]
[2,2,4,1,4] => [[],[[[],[]]]]
[2,2,4,4,1] => [[],[[]],[[]]]
[2,4,1,2,4] => [[[],[[[]]]]]
[2,4,1,4,2] => [[[[],[[]]]]]
[2,4,2,1,4] => [[[[[[]]]]]]
[2,4,2,4,1] => [[[[]],[[]]]]
[2,4,4,1,2] => [[[]],[[[]]]]
[2,4,4,2,1] => [[[]],[[[]]]]
[4,1,2,2,4] => [[[[]]],[[]]]
[4,1,2,4,2] => [[[[[[]]]]]]
[4,1,4,2,2] => [[],[[[],[]]]]
[4,2,1,2,4] => [[[[[[]]]]]]
[4,2,1,4,2] => [[[[]],[[]]]]
[4,2,2,1,4] => [[],[[[[]]]]]
[4,2,2,4,1] => [[[[]]],[[]]]
[4,2,4,1,2] => [[[[[[]]]]]]
[4,2,4,2,1] => [[[[]],[[]]]]
[4,4,1,2,2] => [[],[],[[[]]]]
[4,4,2,1,2] => [[],[[[[]]]]]
[4,4,2,2,1] => [[],[],[[[]]]]
[1,2,2,4,5] => [[],[[[],[]]]]
[1,2,2,5,4] => [[[]],[[[]]]]
[1,2,4,2,5] => [[[[[[]]]]]]
[1,2,4,5,2] => [[[[]],[[]]]]
[1,2,5,2,4] => [[[[],[[]]]]]
[1,2,5,4,2] => [[[[[[]]]]]]
[1,4,2,2,5] => [[[]],[[],[]]]
[1,4,2,5,2] => [[[],[],[[]]]]
[1,4,5,2,2] => [[],[[],[[]]]]
[1,5,2,2,4] => [[[]],[[[]]]]
[1,5,2,4,2] => [[[],[[[]]]]]
[1,5,4,2,2] => [[[]],[[],[]]]
[2,1,2,4,5] => [[[[],[[]]]]]
[2,1,2,5,4] => [[[],[[[]]]]]
[2,1,4,2,5] => [[[[],[[]]]]]
[2,1,4,5,2] => [[[[],[[]]]]]
[2,1,5,2,4] => [[[[[[]]]]]]
[2,1,5,4,2] => [[[],[[],[]]]]
[2,2,1,4,5] => [[],[[[[]]]]]
[2,2,1,5,4] => [[],[[],[[]]]]
[2,2,4,1,5] => [[],[[[[]]]]]
[2,2,4,5,1] => [[],[[],[[]]]]
[2,2,5,1,4] => [[],[[],[[]]]]
[2,2,5,4,1] => [[],[[],[[]]]]
[2,4,1,2,5] => [[[[],[[]]]]]
[2,4,1,5,2] => [[[[[],[]]]]]
[2,4,2,1,5] => [[[[[],[]]]]]
[2,4,2,5,1] => [[[],[[[]]]]]
[2,4,5,1,2] => [[[],[[],[]]]]
[2,4,5,2,1] => [[[[[[]]]]]]
[2,5,1,2,4] => [[[[],[[]]]]]
[2,5,1,4,2] => [[[[]],[[]]]]
[2,5,2,1,4] => [[[],[],[[]]]]
[2,5,2,4,1] => [[[],[],[[]]]]
[2,5,4,1,2] => [[[],[[[]]]]]
[2,5,4,2,1] => [[[[],[[]]]]]
[4,1,2,2,5] => [[[]],[[],[]]]
[4,1,2,5,2] => [[[],[],[[]]]]
[4,1,5,2,2] => [[],[[],[[]]]]
[4,2,1,2,5] => [[[[[[]]]]]]
[4,2,1,5,2] => [[[],[[[]]]]]
[4,2,2,1,5] => [[],[[[],[]]]]
[4,2,2,5,1] => [[[[]]],[[]]]
[4,2,5,1,2] => [[[[[[]]]]]]
[4,2,5,2,1] => [[[[[],[]]]]]
[4,5,1,2,2] => [[],[[],[[]]]]
[4,5,2,1,2] => [[[],[[[]]]]]
[4,5,2,2,1] => [[[[]]],[[]]]
[5,1,2,2,4] => [[[]],[[],[]]]
[5,1,2,4,2] => [[[[]],[[]]]]
[5,1,4,2,2] => [[],[[[[]]]]]
[5,2,1,2,4] => [[[[[[]]]]]]
[5,2,1,4,2] => [[[],[[[]]]]]
[5,2,2,1,4] => [[],[[[],[]]]]
[5,2,2,4,1] => [[],[[[],[]]]]
[5,2,4,1,2] => [[[[]],[[]]]]
[5,2,4,2,1] => [[[[[[]]]]]]
[5,4,1,2,2] => [[[[]]],[[]]]
[5,4,2,1,2] => [[[],[[[]]]]]
[5,4,2,2,1] => [[],[[],[[]]]]
[1,2,3,3,3] => [[],[],[[],[]]]
[1,3,2,3,3] => [[[]],[[[]]]]
[1,3,3,2,3] => [[[]],[[[]]]]
[1,3,3,3,2] => [[],[[]],[[]]]
[2,1,3,3,3] => [[],[[]],[[]]]
[2,3,1,3,3] => [[],[[[[]]]]]
[2,3,3,1,3] => [[[]],[[[]]]]
[2,3,3,3,1] => [[],[[]],[[]]]
[3,1,2,3,3] => [[],[[],[[]]]]
[3,1,3,2,3] => [[[[[[]]]]]]
[3,1,3,3,2] => [[[]],[[[]]]]
[3,2,1,3,3] => [[[]],[[],[]]]
[3,2,3,1,3] => [[[[[[]]]]]]
[3,2,3,3,1] => [[[]],[[[]]]]
[3,3,1,2,3] => [[],[[[],[]]]]
[3,3,1,3,2] => [[],[[[[]]]]]
[3,3,2,1,3] => [[],[[],[[]]]]
[3,3,2,3,1] => [[],[[[[]]]]]
[3,3,3,1,2] => [[],[],[[[]]]]
[3,3,3,2,1] => [[],[],[[],[]]]
[1,2,3,3,4] => [[],[[],[],[]]]
[1,2,3,4,3] => [[[],[],[[]]]]
[1,2,4,3,3] => [[],[[[[]]]]]
[1,3,2,3,4] => [[[[[],[]]]]]
[1,3,2,4,3] => [[[],[[],[]]]]
[1,3,3,2,4] => [[],[[[],[]]]]
[1,3,3,4,2] => [[[[]]],[[]]]
[1,3,4,2,3] => [[[[],[[]]]]]
[1,3,4,3,2] => [[[[[],[]]]]]
[1,4,2,3,3] => [[],[[[[]]]]]
[1,4,3,2,3] => [[[[],[[]]]]]
[1,4,3,3,2] => [[[]],[[],[]]]
[2,1,3,3,4] => [[[[]]],[[]]]
[2,1,3,4,3] => [[[],[[[]]]]]
[2,1,4,3,3] => [[],[[],[[]]]]
[2,3,1,3,4] => [[[],[[[]]]]]
[2,3,1,4,3] => [[[[[[]]]]]]
[2,3,3,1,4] => [[[]],[[[]]]]
[2,3,3,4,1] => [[],[[],[[]]]]
[2,3,4,1,3] => [[[],[[[]]]]]
[2,3,4,3,1] => [[[],[[[]]]]]
[2,4,1,3,3] => [[],[[],[[]]]]
[2,4,3,1,3] => [[[[]],[[]]]]
[2,4,3,3,1] => [[],[[[[]]]]]
[3,1,2,3,4] => [[[[],[],[]]]]
[3,1,2,4,3] => [[[[[[]]]]]]
[3,1,3,2,4] => [[[[],[[]]]]]
[3,1,3,4,2] => [[[],[[[]]]]]
[3,1,4,2,3] => [[[[]],[[]]]]
[3,1,4,3,2] => [[[[],[[]]]]]
[3,2,1,3,4] => [[[],[[[]]]]]
[3,2,1,4,3] => [[[],[],[[]]]]
[3,2,3,1,4] => [[[[[[]]]]]]
[3,2,3,4,1] => [[[[[],[]]]]]
[3,2,4,1,3] => [[[[],[[]]]]]
[3,2,4,3,1] => [[[[]],[[]]]]
[3,3,1,2,4] => [[],[[[[]]]]]
[3,3,1,4,2] => [[],[[],[[]]]]
[3,3,2,1,4] => [[],[[],[[]]]]
[3,3,2,4,1] => [[],[[[[]]]]]
[3,3,4,1,2] => [[],[[],[[]]]]
[3,3,4,2,1] => [[],[[[[]]]]]
[3,4,1,2,3] => [[[],[],[[]]]]
[3,4,1,3,2] => [[[[[[]]]]]]
[3,4,2,1,3] => [[[[[[]]]]]]
[3,4,2,3,1] => [[[],[[],[]]]]
[3,4,3,1,2] => [[[[]],[[]]]]
[3,4,3,2,1] => [[[[],[],[]]]]
[4,1,2,3,3] => [[],[[],[[]]]]
[4,1,3,2,3] => [[[[[[]]]]]]
[4,1,3,3,2] => [[[[]]],[[]]]
[4,2,1,3,3] => [[[[]]],[[]]]
[4,2,3,1,3] => [[[[]],[[]]]]
[4,2,3,3,1] => [[[]],[[],[]]]
[4,3,1,2,3] => [[[[],[[]]]]]
[4,3,1,3,2] => [[[[]],[[]]]]
[4,3,2,1,3] => [[[],[],[[]]]]
[4,3,2,3,1] => [[[],[[[]]]]]
[4,3,3,1,2] => [[],[[[[]]]]]
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Created: Jun 16, 2023 at 12:30 by Martin Rubey
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Last Updated: Jun 16, 2023 at 13:38 by Martin Rubey