TopCoder Statistics - Problem Statement

Problem Statement

An ordered binary tree is a rooted binary tree in which each node X contains two pointers: X.left and X.right. Each of these pointers either points to the corresponding child node, or it has a special value "None" meaning that node X doesn't have the corresponding child.

I just taught Antonio some tree traversal techniques on ordered binary trees. I asked him to implement these tree traversals but I don't think he was paying attention, since he mixed them up and wrote the following pseudocode:

def order(v, mode):
    if v == None:
        return []
    if mode == "pre":
       return [v.label] + order(v.left, s[0]) + order(v.right, s[1])
    if mode == "in":
       return order(v.left, s[2]) + [v.label] + order(v.right, s[3])
    if mode == "post":
       return order(v.left, s[4]) + order(v.right, s[5]) + [v.label]

You are given the String[] s used in the pseudocode above. You are guaranteed that among {s[0], s[2], s[4]} and also among {s[1], s[3], s[5]} each of the strings "pre", "in", and "post" appears exactly once.

Let "root" be a variable that contains the root of an ordered binary tree with n nodes. The nodes are numbered 1 through n in no particular order.

Consider the scenario in which we executed Antonio's code on this tree three times by making the following function calls:

a1 = order(root, "pre")
a2 = order(root, "in")
a3 = order(root, "post")

You are given the int[]s a1, a2, a3. Is there a tree for which the above scenario is possible? In other words, is it possible to construct an ordered binary tree with n nodes such that Antonio's code would output the three given sequences a1, a2, a3 when called as shown above?

Return "Possible" if the scenario could have happened, or "Impossible" if there is no such tree.

Definition

Class:: InPrePost
Method:: isPossible
Parameters:: String[], int[], int[], int[]
Returns:: String
Method signature:: String isPossible(String[] s, int[] a1, int[] a2, int[] a3)
(be sure your method is public)

Constraints

s will contain exactly 6 elements.
Each element of s will be one of "pre", "in", "post".
Among {s[0], s[2], s[4]} and {s[1], s[3], s[5]}, each of "pre", "in", "post" appears exactly once.
a1 will have between 1 and 50 elements, inclusive.
a2,a3 will have the same length as a1.
Each of a1,a2,a3 will be a permutation of 1 to len(a1).

Examples

{"post", "in", "pre", "post", "in", "pre"}

{1,2,3,4,5}

{2,1,3,5,4}

{2,4,3,5,1}

Returns: "Possible"

A possible tree that could have generated these inputs looks as follows:
{"pre", "pre", "in", "in", "post", "post"}

{1,2,3,4}

{2,4,3,1}

{4,3,2,1}

Returns: "Possible"

It is allowed for nodes to have only one child.
{"post", "in", "pre", "post", "in", "pre"}

{1,2,3,4,5}

{2,1,3,5,4}

{1,4,3,5,2}

Returns: "Impossible"

This is impossible. Here is one reason: From a1 we can deduce that the root of the tree must have the label 1. However, from a3 we can deduce that the root of the tree must have the label 2. This is a contradiction.
{"post", "pre", "in", "post", "pre", "in"}

{1}

{1}

{1}

Returns: "Possible"
{"pre", "pre", "in", "in", "post", "post"}

{1,2,3,4,5,6,7,8,9,10}

{2,3,4,5,1,6,7,8,9,10}

{6,5,4,3,2,10,9,8,7,1}

Returns: "Impossible"
{"post","post","in","pre","pre","in"}

{9,4,8,3,7,5,6,1,2}

{3,8,7,4,6,5,9,2,1}

{6,7,3,8,4,5,1,2,9}

Returns: "Possible"
{"in","post","post","pre","pre","in"}

{10,4,9,2,6,1,5,8,7,3}

{5,9,1,4,6,2,7,8,10,3}

{8,1,9,4,5,2,6,7,3,10}

Returns: "Impossible"
{"pre","pre","in","post","post","in"}

{14,13,4,20,1,6,7,3,10,17,19,18,15,2,8,11,16,9,5,21,12}

{14,4,18,6,7,20,17,21,15,19,2,12,16,9,3,10,5,11,8,1,13}

{13,20,7,3,18,1,17,19,2,8,15,16,11,5,12,10,9,6,21,4,14}

Returns: "Impossible"
{"pre","post","in","in","post","pre"}

{10,39,16,29,20,38,22,4,8,35,9,1,28,33,37,6,21,7,14,17,5,25,23,15,34,18,11,36,19,31,12,3,32,24,30,13,26,2,27}

{37,33,29,1,9,35,6,34,4,22,21,38,7,20,14,17,5,28,25,23,15,31,18,11,19,32,12,8,16,3,36,24,13,30,39,10,26,2,27}

{37,33,28,1,9,6,35,8,4,21,22,7,38,5,17,18,20,12,19,11,14,34,15,23,25,36,31,29,13,24,32,3,30,16,39,27,2,26,10}

Returns: "Impossible"
{"post","post","in","in","pre","pre"}

{3,4,5,2,1}

{4,3,1,5,2}

{4,1,2,5,3}

Returns: "Possible"
{"pre","in","post","pre","in","post"}

{4,1,3,5,6,2}

{4,1,5,6,2,3}

{2,5,4,1,6,3}

Returns: "Impossible"
{"pre","pre","in","post","post","in"}

{5,3,6,4,2,7,1}

{5,6,4,7,2,3,1}

{7,5,1,4,2,3,6}

Returns: "Impossible"
{"post","pre","in","in","pre","post"}

{1,19,12,16,26,14,23,25,21,10,4,13,6,11,9,2,5,17,7,15,24,22,18,20,3,8}

{7,12,25,16,23,14,26,1,4,10,13,11,6,21,2,9,17,19,15,20,24,22,18,5,3,8}

{25,12,7,23,16,2,26,11,4,13,10,6,14,20,15,19,17,18,22,24,8,3,5,9,21,1}

Returns: "Impossible"
{"pre","post","post","in","in","pre"}

{5,8,1,20,14,17,12,2,22,23,6,3,16,4,18,21,10,13,19,7,9,15,11}

{3,6,16,23,22,4,2,12,18,17,14,10,21,20,1,8,5,13,19,7,9,15,11}

{3,6,23,16,22,2,4,12,17,18,14,20,21,10,1,8,11,15,9,7,19,13,5}

Returns: "Possible"
{"post","in","pre","post","in","pre"}

{15,21,24,7,17,22,5,3,23,38,8,35,6,12,14,31,26,30,40,2,33,9,25,20,36,4,13,32,27,16,28,34,11,19,37,18,1,39,29,41,10}

{39,32,9,30,6,8,23,3,5,38,22,35,17,12,26,31,14,7,2,40,33,24,36,20,25,4,13,21,19,34,28,16,11,27,1,18,37,15,41,29,10}

{27,13,40,14,35,38,3,23,5,8,22,6,12,17,31,26,30,7,2,9,33,4,20,36,25,24,32,21,11,28,34,16,19,39,18,1,37,10,41,29,15}

Returns: "Possible"
{"pre","pre","post","post","in","in"}

{3,1,4,2,5}

{1,3,2,5,4}

{1,4,5,2,3}

Returns: "Possible"
{"pre","post","post","in","in","pre"}

{20,6,18,21,15,14,3,19,9,16,26,24,25,12,11,1,28,17,2,13,22,4,5,7,8,10,23,27}

{25,15,26,16,9,13,19,3,11,1,28,17,14,24,12,2,21,18,22,4,5,10,8,7,6,20,23,27}

{25,15,26,16,9,19,12,28,1,11,3,14,17,27,21,2,13,5,4,22,18,6,7,8,24,10,23,20}

Returns: "Impossible"
{"pre","post","in","in","post","pre"}

{25,15,13,19,8,16,18,4,6,22,21,3,20,17,7,24,23,26,1,9,2,10,27,5,11,14,12}

{21,22,6,4,3,18,20,16,17,8,19,13,7,15,24,23,26,9,1,2,25,10,5,27,14,11,12}

{21,22,6,3,4,20,18,17,16,8,19,7,13,2,9,26,23,24,1,15,12,14,5,10,27,11,25}

Returns: "Possible"
{"post","post","in","in","pre","pre"}

{6,11,5,8,7,12,19,13,25,1,21,9,17,23,14,10,4,22,20,15,3,2,24,16,18}

{7,12,8,19,5,1,21,25,9,13,17,10,14,23,2,20,22,15,4,3,11,18,16,24,6}

{18,2,19,12,7,8,10,9,21,1,25,17,13,14,23,5,15,20,22,3,4,11,16,24,6}

Returns: "Possible"
{"in","post","post","in","pre","pre"}

{8,10,15,16,18,19,13,11,14,7,12,2,9,4,6,3,21,17,20,5,1}

{16,15,10,19,11,13,18,8,1,7,14,9,2,6,4,12,5,21,3,20,17}

{18,16,10,15,13,11,19,1,7,5,2,9,12,6,4,21,20,17,3,14,8}

Returns: "Possible"
{"in","post","post","pre","pre","in"}

{11,19,16,5,34,37,15,9,35,1,7,39,25,31,20,27,30,21,2,38,36,18,29,12,22,24,28,6,26,8,42,14,17,4,10,13,32,23,41,40,33,3}

{16,37,34,5,19,11,3,15,9,39,7,1,33,25,27,20,40,2,21,30,29,12,18,36,41,6,24,28,22,8,23,14,32,4,13,10,17,42,26,38,31,35}

{19,37,5,34,16,9,15,3,35,7,39,25,33,31,27,40,38,2,30,21,18,12,29,41,26,6,22,28,24,23,42,32,17,13,10,4,14,8,36,20,1,11}

Returns: "Possible"
{"post","pre","pre","post","in","in"}

{18,41,24,4,32,26,31,13,9,11,37,8,40,15,2,5,27,34,6,39,38,1,16,21,29,17,28,35,12,14,20,19,42,22,23,33,10,36,30,25,3,7}

{26,41,32,24,4,18,13,39,11,8,37,6,40,15,34,2,5,27,9,1,20,21,17,29,28,14,35,12,16,22,42,10,33,23,30,25,7,3,36,19,38,31}

{26,32,4,24,41,13,31,11,39,37,40,6,2,34,27,5,15,8,1,38,29,21,17,20,14,12,35,28,22,42,19,10,33,30,36,3,7,25,23,16,9,18}

Returns: "Possible"
{"post","in","pre","post","in","pre"}

{5,29,30,8,34,28,17,2,13,18,21,37,7,33,12,24,14,27,3,20,6,23,1,26,35,25,16,36,15,22,11,31,19,10,32,9,4}

{34,11,26,30,5,4,17,2,14,16,31,20,33,7,24,12,13,9,3,6,18,28,1,32,35,25,22,36,8,23,29,21,15,19,10,27,37}

{34,4,8,29,28,2,3,37,20,16,21,14,33,12,24,7,27,17,9,6,26,1,30,23,25,35,22,10,36,32,19,31,15,11,18,13,5}

Returns: "Impossible"
{"post","in","in","pre","pre","post"}

{21,44,36,15,41,7,30,39,32,40,13,46,19,1,42,34,43,6,2,45,35,20,8,22,16,14,26,17,27,24,33,18,29,25,11,31,12,23,5,28,38,10,4,3,9,37}

{30,39,15,32,46,41,13,40,38,45,19,11,36,1,27,34,43,2,29,18,16,8,10,22,14,35,6,17,24,23,33,25,42,44,7,28,26,12,5,31,21,37,3,20,4,9}

{15,29,42,9,32,39,30,34,41,40,13,19,1,38,4,43,7,27,45,36,20,8,16,22,35,14,18,33,24,31,17,26,44,11,25,12,2,46,5,28,6,23,10,3,37,21}

Returns: "Impossible"
{"pre","in","post","post","in","pre"}

{14,9,28,3,7,46,35,18,15,12,8,44,29,6,30,10,19,24,4,5,33,32,31,27,20,45,42,41,43,26,11,36,2,1,40,22,25,37,34,21,38,16,39,13,23,17}

{12,15,18,35,8,29,44,6,46,7,30,10,19,4,24,5,33,32,3,28,20,27,31,42,45,41,43,22,36,11,2,40,1,26,37,25,34,21,9,14,38,16,23,13,39,17}

{12,15,18,44,8,29,35,46,6,33,5,24,19,10,30,4,7,3,32,26,43,41,42,31,27,20,45,11,2,36,22,40,1,28,9,25,21,34,37,17,23,16,38,13,39,14}

Returns: "Possible"
{"post","post","in","pre","pre","in"}

{25,27,23,3,2,8,24,20,43,22,37,12,10,1,21,36,35,42,44,39,9,38,30,7,16,15,18,4,32,45,41,34,13,31,5,26,14,33,28,46,17,40,19,11,6,29}

{27,25,29,2,3,23,24,6,42,43,35,37,36,10,21,1,12,22,20,44,7,38,30,9,11,16,45,18,32,4,15,34,19,13,26,5,40,33,17,46,28,14,31,41,39,8}

{27,23,2,3,29,8,20,42,22,35,12,36,1,21,10,37,43,6,39,44,7,30,38,11,41,15,45,4,32,18,16,19,31,13,26,40,14,17,28,46,33,5,34,9,24,25}

Returns: "Possible"
{"pre","pre","in","in","post","post"}

{8,24,21,2,20,19,5,17,9,13,25,1,12,4,23,18,15,6,22,11,10,7,3,14,16}

{21,15,20,6,2,16,14,19,25,13,1,7,4,9,18,24,17,12,10,22,11,3,23,8,5}

{21,9,20,24,12,25,22,19,16,2,7,4,17,15,14,5,3,23,8,11,10,1,6,18,13}

Returns: "Impossible"
{"post","pre","in","in","pre","post"}

{44,43,5,30,23,28,8,7,40,11,45,41,46,22,42,29,50,16,4,48,36,35,9,27,37,20,12,34,47,24,21,38,18,33,13,26,10,6,14,25,15,19,17,31,1,39,32,3,49,2}

{44,29,5,30,42,23,28,22,8,46,41,45,11,40,7,43,16,12,4,20,48,37,27,9,35,36,50,34,24,33,18,38,21,47,25,26,14,6,10,13,19,15,31,39,1,17,32,3,49,2}

{29,42,30,5,22,28,23,46,8,41,45,11,40,7,12,16,20,4,37,48,27,9,35,36,33,24,18,38,21,25,14,26,6,10,19,39,31,1,2,49,3,32,17,15,13,47,34,50,43,44}

Returns: "Possible"
{"pre","in","in","post","post","pre"}

{24,18,27,12,13,15,25,19,17,2,22,23,21,26,3,10,7,14,8,11,16,6,4,5,1,20,9}

{27,9,13,7,19,25,17,18,2,26,8,24,3,22,10,21,12,23,14,11,6,16,4,15,1,20,5}

{17,25,7,3,9,5,27,19,8,21,22,2,24,12,10,6,13,4,16,11,14,23,18,1,15,20,26}

Returns: "Impossible"
{"post","in","pre","pre","in","post"}

{16,9,7,27,15,5,28,21,22,20,10,23,1,3,11,14,13,25,12,26,17,6,30,29,19,4,24,2,18,8}

{16,29,7,9,5,15,21,2,13,23,14,11,3,1,6,10,28,30,12,27,17,4,25,20,22,24,26,19,18,8}

{9,7,5,28,13,14,20,11,3,1,8,10,12,25,26,6,17,30,4,24,23,18,22,27,19,2,21,15,29,16}

Returns: "Impossible"
{"pre","in","in","post","post","pre"}

{21,36,20,31,14,16,22,30,11,19,32,3,9,23,24,2,37,34,6,35,12,1,13,15,7,33,28,4,5,26,18,17,25,10,29,8,27}

{16,14,22,11,30,31,32,19,20,23,9,3,34,2,37,24,36,1,12,35,6,21,15,13,33,7,27,4,8,18,26,10,25,17,29,5,28}

{16,30,22,11,14,19,32,31,24,3,23,9,34,37,2,20,6,12,35,1,36,28,7,13,15,33,27,5,26,18,8,10,25,29,17,4,21}

Returns: "Possible"
{"in","post","post","in","pre","pre"}

{4,10,15,1,13,9,5,14,3,8,12,7,11,6,2}

{11,1,9,12,13,14,5,10,2,4,3,8,6,7,15}

{7,8,11,1,2,10,14,5,3,12,6,9,15,13,4}

Returns: "Impossible"
{"in","in","post","pre","pre","post"}

{28,2,20,12,24,35,26,31,40,4,15,34,38,16,14,5,33,44,3,7,6,32,9,37,46,11,22,17,45,18,42,23,36,29,1,19,10,13,30,41,27,25,8,39,43,21}

{27,8,37,44,32,35,31,24,7,16,34,15,3,38,40,5,14,23,6,33,4,12,9,11,46,20,42,45,17,13,18,1,29,36,2,30,10,19,22,41,25,28,21,39,26,43}

{25,36,33,3,31,35,32,5,38,26,34,4,16,40,14,46,24,44,6,23,7,12,37,9,11,18,17,45,20,42,22,8,1,29,13,10,19,30,2,27,41,15,39,43,21,28}

Returns: "Impossible"
{"post","pre","in","in","pre","post"}

{20,32,14,5,23,26,18,24,16,33,8,21,40,27,37,13,7,42,41,2,28,4,10,17,11,3,19,39,43,34,31,30,6,15,38,36,35,29,9,1,22,12,25}

{29,24,7,36,8,1,21,9,40,23,13,37,42,41,5,28,33,2,14,10,3,32,19,39,22,43,11,34,17,38,30,6,31,15,20,26,27,4,16,12,35,25,18}

{1,10,20,42,27,8,35,29,24,36,21,26,40,12,4,23,41,5,2,7,14,37,34,17,43,19,22,11,39,32,15,6,30,31,25,13,3,38,9,16,33,18,28}

Returns: "Impossible"
{"post","post","in","in","pre","pre"}

{10,18,20,22,19,14,1,11,24,16,9,4,13,17,15,12,21,8,2,23,5,6,3,7}

{11,1,24,14,16,19,9,22,4,20,13,18,15,12,17,21,2,8,3,5,6,23,10,7}

{3,13,4,9,16,24,11,1,14,19,22,20,2,12,15,21,17,8,18,6,5,23,7,10}

Returns: "Possible"
{"in","pre","post","post","pre","in"}

{1,27,14,23,4,15,11,26,16,20,13,19,7,17,22,3,9,12,8,2,21,25,6,5,28,24,18,10}

{27,4,23,26,11,15,14,1,20,13,7,19,8,12,9,3,22,25,21,5,28,24,10,18,6,2,17,16}

{14,27,26,23,4,15,11,13,20,16,7,17,3,8,9,12,2,25,28,5,6,18,10,24,21,22,19,1}

Returns: "Possible"
{"post","post","pre","in","in","pre"}

{33,10,14,16,32,29,3,35,13,15,9,34,24,1,12,26,8,21,31,27,30,4,22,2,18,28,20,17,23,11,6,19,7,5,25,36}

{3,29,32,16,14,10,33,13,35,9,24,34,15,36,26,12,1,8,31,27,21,25,30,4,5,18,2,22,28,7,20,19,17,6,23,11}

{3,10,29,14,32,16,36,35,15,34,24,9,13,26,12,25,21,27,31,8,5,4,18,2,7,28,19,6,11,23,17,20,22,30,1,33}

Returns: "Possible"
{"pre","in","post","pre","in","post"}

{4,22,33,1,24,44,43,8,42,28,17,5,9,48,6,18,35,23,2,13,11,41,19,37,36,34,39,15,47,45,31,32,38,14,27,25,21,30,20,7,3,16,12,26,10,46,40,29}

{11,13,2,23,35,41,18,6,19,37,48,9,5,17,28,42,15,39,34,36,8,43,31,45,47,32,38,14,27,44,24,20,30,21,25,7,1,33,46,10,12,16,3,26,22,4,29,40}

{11,13,2,23,35,18,41,19,6,48,37,9,5,17,28,36,34,39,15,42,8,45,47,31,43,44,27,14,38,32,25,21,30,20,24,1,7,3,16,26,12,10,46,33,22,40,29,4}

Returns: "Possible"
{"post","pre","in","in","pre","post"}

{20,11,18,8,15,1,3,21,16,4,22,5,12,7,2,13,6,23,14,17,9,19,10}

{5,20,8,13,21,3,1,15,16,4,11,12,7,23,22,10,2,6,14,18,9,19,17}

{5,8,2,3,1,7,12,6,21,23,10,19,9,17,14,11,18,22,4,16,15,13,20}

Returns: "Impossible"
{"in","pre","post","post","pre","in"}

{7,12,20,21,14,3,18,27,17,4,1,11,19,22,10,5,15,26,29,13,8,16,23,9,28,24,6,2,25}

{8,10,11,17,18,3,27,14,4,21,1,19,20,22,5,12,13,26,15,29,24,9,28,6,23,25,2,16,7}

{16,5,19,4,27,3,18,14,17,21,11,1,22,20,10,12,8,29,26,15,13,25,28,9,24,23,6,2,7}

Returns: "Possible"
{"pre","pre","in","in","post","post"}

{8,6,31,19,34,17,28,24,35,25,16,37,33,23,12,13,11,1,22,14,38,27,10,32,20,26,4,18,21,9,7,30,5,29,2,15,36,3}

{6,31,8,34,17,28,19,35,25,16,37,33,23,24,12,13,1,22,11,14,27,10,32,20,38,4,26,9,21,7,18,30,5,29,2,15,36,3}

{31,6,28,17,34,23,33,37,16,25,35,22,1,20,32,10,27,4,9,7,21,3,36,15,2,29,5,30,18,26,38,14,11,13,12,24,19,8}

Returns: "Possible"
{"post","in","pre","post","in","pre"}

{22,41,47,33,28,1,12,9,19,18,26,38,29,27,5,11,34,31,21,25,42,6,4,23,7,16,14,24,35,30,36,39,43,15,44,40,3,8,37,10,45,46,2,13,17,32,20}

{20,41,40,29,13,23,12,1,19,28,18,38,33,27,5,6,15,43,34,25,42,11,47,9,45,16,14,7,4,31,36,39,30,21,44,35,3,8,37,32,2,26,24,17,46,10,22}

{10,7,11,38,19,12,9,1,13,18,6,35,5,27,33,42,43,14,26,34,28,40,23,47,15,16,24,41,21,39,36,31,30,4,44,3,29,37,8,25,46,2,45,17,32,20,22}

Returns: "Impossible"
{"in","pre","post","post","pre","in"}

{8,36,17,19,22,37,25,11,2,39,12,31,27,13,33,34,18,16,26,3,10,23,4,38,15,20,24,28,21,32,35,29,7,30,9,6,14,5,1}

{7,37,4,34,3,27,39,2,11,32,12,35,33,13,31,16,18,22,26,10,9,23,38,17,21,24,20,15,28,29,25,36,19,6,30,8,1,5,14}

{30,35,38,10,18,13,12,2,11,24,31,25,27,33,32,34,16,22,3,26,9,4,23,17,37,28,20,39,15,21,29,36,7,6,19,5,1,14,8}

Returns: "Impossible"
{"in","post","post","pre","pre","in"}

{24,25,7,21,22,35,32,31,10,12,30,19,42,16,46,27,3,39,13,20,14,38,33,23,6,18,1,28,37,44,4,41,9,5,17,29,36,26,15,40,2,8,45,43,11,34}

{21,7,22,25,24,34,35,12,32,10,6,27,30,42,46,15,19,20,38,14,13,39,11,28,33,31,1,18,23,44,43,36,4,9,29,17,5,41,16,45,40,8,2,26,37,3}

{25,21,22,7,32,12,6,10,35,34,3,27,19,30,46,16,42,13,38,14,20,11,37,28,23,33,1,18,31,43,26,4,36,41,29,5,17,9,40,45,2,8,15,44,39,24}

Returns: "Impossible"
{"pre","in","post","pre","in","post"}

{36,22,11,46,30,23,8,39,9,34,24,13,45,20,27,43,33,14,37,26,6,48,19,17,40,41,25,3,5,38,2,42,47,18,16,7,12,32,10,35,31,15,29,1,28,44,21,4}

{13,24,11,30,46,8,23,39,34,9,27,43,33,14,37,19,48,6,26,20,45,22,36,38,5,40,17,41,3,25,47,42,2,16,18,32,12,7,15,31,35,10,28,1,29,44,21,4}

{22,45,13,30,23,39,8,46,11,24,34,9,37,14,33,43,27,20,26,6,48,19,17,40,5,3,41,25,42,47,18,12,32,31,35,10,1,28,4,21,44,29,15,7,16,2,38,36}

Returns: "Possible"
{"in","post","post","in","pre","pre"}

{4,1,6,40,39,29,25,36,41,7,5,11,26,15,43,22,18,10,12,23,2,16,45,35,31,14,37,24,38,21,3,20,30,44,19,28,8,13,34,32,9,27,42,17,33}

{10,39,40,29,6,1,7,41,36,25,15,11,5,26,18,22,43,45,16,2,23,31,35,24,37,21,3,38,14,12,4,20,33,8,28,19,44,9,34,32,13,30,17,27,42}

{12,6,40,29,39,15,25,7,36,41,11,26,5,1,10,43,18,22,16,2,23,14,35,31,37,38,3,21,24,45,33,20,13,8,44,28,19,32,34,9,17,42,27,30,4}

Returns: "Possible"
{"post","pre","in","in","pre","post"}

{26,29,43,47,6,9,38,23,16,22,8,39,3,18,24,7,28,2,11,5,25,15,21,33,36,13,31,10,17,46,34,30,32,44,27,12,35,45,14,4,1,42,40,20,19,41,37}

{39,8,3,22,10,16,32,23,7,11,28,43,38,2,5,6,24,25,33,21,47,13,36,30,17,18,46,31,34,9,4,27,12,44,35,15,45,14,29,40,1,42,26,19,41,20,37}

{40,4,30,33,5,28,7,24,10,9,39,8,22,16,23,11,38,2,43,32,25,6,21,13,36,47,34,46,17,29,31,3,14,35,12,27,44,45,15,18,42,1,41,19,37,20,26}

Returns: "Impossible"
{"pre","post","post","in","in","pre"}

{22,19,29,15,16,2,5,36,28,11,17,8,9,14,26,18,6,10,24,23,12,33,34,4,7,21,30,1,32,27,13,31,20,3,35,25,37}

{33,12,23,24,10,6,18,26,14,9,34,8,17,4,7,21,11,28,30,1,36,5,2,16,32,27,3,20,31,13,15,29,35,25,37,19,22}

{33,12,23,24,10,6,18,26,14,34,9,8,7,4,17,11,21,30,28,36,1,5,2,27,32,16,15,13,31,20,3,37,25,35,29,19,22}

Returns: "Possible"
{"post","in","in","post","pre","pre"}

{47,48,27,40,26,18,37,1,11,25,22,44,10,13,19,21,20,39,23,42,46,29,30,38,4,24,15,9,31,45,5,8,49,41,34,2,35,17,43,16,3,14,6,36,28,32,7,33,12}

{40,27,48,47,26,12,25,11,1,37,33,10,13,44,21,19,20,7,23,42,29,46,32,38,4,28,31,9,15,36,5,49,8,6,2,35,34,17,14,16,3,43,41,45,24,30,39,22,18}

{40,48,27,18,26,12,25,1,11,22,44,13,10,33,21,39,20,7,30,29,46,42,38,32,24,28,31,9,45,5,36,49,41,34,35,2,6,43,14,3,16,17,8,15,4,23,19,37,47}

Returns: "Possible"
{"in","in","post","post","pre","pre"}

{9,18,38,30,35,28,29,5,34,49,24,32,46,36,37,41,42,31,10,19,21,25,11,20,1,14,17,44,27,45,3,48,22,13,2,39,8,23,7,40,6,33,50,43,12,4,16,47,15,26}

{27,36,29,35,30,28,5,38,34,32,24,46,49,25,19,31,10,42,21,41,37,18,11,1,20,17,44,14,13,48,22,3,45,9,15,7,8,23,39,33,6,40,2,43,50,4,12,47,16,26}

{45,37,5,35,28,30,29,34,38,36,46,24,32,49,21,10,31,42,19,41,25,20,11,1,18,27,44,17,14,22,48,3,13,26,40,23,8,39,7,6,33,12,50,43,4,2,15,47,16,9}

Returns: "Possible"
{"pre","in","in","post","post","pre"}

{48,29,30,7,4,20,11,24,27,43,45,31,41,40,25,9,3,13,36,1,28,37,39,38,23,49,10,21,26,22,6,5,2,47,17,32,12,34,16,44,35,18,14,46,42,15,33,8,19}

{24,27,11,20,4,7,45,43,31,9,40,25,41,30,3,13,1,36,29,28,37,39,38,23,48,49,21,10,22,26,6,17,47,2,5,32,16,34,12,35,44,15,42,46,14,18,19,8,33}

{27,24,11,20,4,41,31,43,45,40,9,25,7,36,13,3,1,30,23,38,39,37,28,29,33,18,44,12,32,5,6,26,10,49,21,22,2,47,17,16,34,35,14,46,42,15,8,19,48}

Returns: "Possible"
{"pre","pre","post","in","in","post"}

{4,15,45,23,9,30,8,2,11,22,44,26,25,41,7,14,32,46,33,16,34,12,40,21,28,5,42,17,24,38,48,37,1,39,20,3,13,6,35,10,36,29,47,18,19,49,43,27,31}

{45,23,30,19,18,49,25,7,34,16,33,46,32,14,41,26,22,8,9,15,4,21,28,40,12,48,38,24,17,42,5,37,3,20,39,1,6,13,10,35,36,29,11,47,27,43,44,2,31}

{23,45,15,9,18,2,3,13,49,22,25,26,7,17,14,32,30,33,16,34,21,40,28,42,41,24,38,48,39,19,8,6,10,11,44,43,27,31,20,47,29,36,35,46,1,37,5,12,4}

Returns: "Impossible"
{"post","in","in","pre","pre","post"}

{4,38,11,7,17,1,12,10,29,35,5,19,36,9,13,24,25,20,28,39,37,32,23,3,14,26,15,30,33,6,21,27,22,8,34,18,16,31,2}

{28,7,11,38,36,10,12,1,5,35,14,4,19,13,9,25,24,20,17,26,29,3,23,32,37,39,15,30,27,21,6,33,22,8,34,18,16,31,2}

{9,7,19,38,4,30,11,1,24,26,39,3,34,32,37,33,6,21,2,31,16,18,23,17,22,27,12,15,5,8,20,25,28,36,14,35,29,10,13}

Returns: "Impossible"
{"post","in","pre","post","in","pre"}

{4,8,23,9,34,3,40,32,28,20,48,41,6,30,29,24,44,43,14,13,16,38,47,49,18,12,1,21,2,50,39,36,5,27,37,45,7,31,25,11,26,46,15,42,17,35,33,19,22,10}

{21,34,23,9,8,3,48,32,28,20,40,44,29,30,6,24,41,16,14,13,43,49,47,38,18,1,12,4,50,2,10,36,7,45,37,27,5,15,26,11,25,46,31,42,22,35,19,33,17,39}

{41,34,9,23,40,3,32,48,20,28,8,44,29,30,24,6,21,16,13,14,12,47,49,18,38,1,43,39,50,2,5,36,7,45,37,27,10,25,26,11,15,46,17,42,22,33,19,35,31,4}

Returns: "Possible"
{"post","pre","pre","in","in","post"}

{32,7,34,31,48,16,15,44,1,42,43,39,17,3,40,19,18,29,9,11,21,47,45,13,41,24,46,20,23,22,50,30,14,25,12,10,4,36,27,35,8,26,2,5,37,49,33,38,28,6}

{32,37,42,1,36,15,16,48,46,34,43,19,38,3,17,39,18,11,45,9,23,20,31,24,41,13,12,22,21,25,29,14,30,50,47,10,44,4,27,8,35,26,2,5,7,28,49,40,33,6}

{42,1,36,15,16,48,46,19,38,45,17,11,9,33,20,31,24,41,13,35,47,12,29,14,30,50,44,8,28,6,23,40,49,18,5,2,26,25,27,4,10,22,21,3,7,39,43,34,37,32}

Returns: "Impossible"
{"in","post","post","pre","pre","in"}

{5,4,3,2,8,10,13,1,11,6,7,9,12,14}

{9,1,10,8,2,13,3,6,11,4,7,12,5,14}

{12,11,13,8,2,10,3,1,6,7,4,9,14,5}

Returns: "Possible"
{"pre","post","post","pre","in","in"}

{2,10,11,8,7,4,9,5,6,1,12,3}

{2,3,11,12,7,1,9,6,5,4,8,10}

{3,10,12,8,1,4,6,5,9,7,11,2}

Returns: "Possible"
{"in","pre","pre","in","post","post"}

{10,9,4,8,7,1,5,11,14,16,13,2,15,6,17,3,12}

{17,13,11,1,7,8,5,4,16,14,2,9,6,15,10,12,3}

{7,1,5,8,11,16,14,4,2,13,6,15,9,17,12,3,10}

Returns: "Possible"
{"post","in","in","post","pre","pre"}

{30,31,34,36,43,27,6,35,18,4,23,7,42,15,13,32,33,1,9,3,5,37,22,17,21,14,44,19,16,29,24,41,40,25,8,26,2,10,12,39,20,11,38,28}

{31,4,36,43,18,6,35,27,34,30,7,23,32,15,13,42,28,1,3,9,5,37,38,19,14,44,21,17,16,24,29,11,40,25,20,26,2,39,12,10,8,41,22,33}

{4,31,34,18,43,27,35,6,36,33,23,32,42,13,15,7,1,28,3,22,37,5,38,19,21,44,14,41,24,29,16,11,8,25,26,20,10,39,12,2,40,17,9,30}

Returns: "Possible"
{"pre","in","post","post","in","pre"}

{21,4,14,19,20,7,17,13,28,5,29,12,22,6,16,15,10,8,25,2,3,11,24,26,9,1,27,23,18}

{22,2,29,5,28,6,13,21,7,20,19,15,10,8,25,12,16,4,3,11,24,26,9,1,27,23,14,17,18}

{22,12,29,10,28,11,6,24,7,25,8,5,15,16,20,19,2,23,4,13,9,26,21,1,3,14,27,18,17}

Returns: "Impossible"
{"post","pre","pre","post","in","in"}

{4,13,14,8,11,3,12,6,7,2,15,1,10,9,5}

{9,12,14,8,11,3,13,6,10,15,2,1,7,4,5}

{6,8,14,12,3,11,13,9,1,2,15,7,10,5,4}

Returns: "Possible"
{"pre","post","post","pre","in","in"}

{12,24,19,18,3,4,5,13,29,27,22,20,23,16,8,21,25,9,6,17,1,7,11,14,10,15,26,28,2}

{19,24,12,2,18,4,29,5,13,3,8,23,16,20,22,28,21,9,26,6,17,1,11,15,10,14,7,25,27}

{24,19,4,3,29,13,5,18,2,27,20,8,16,23,21,28,25,17,6,26,7,1,15,14,10,11,9,22,12}

Returns: "Possible"
{"pre","in","in","post","post","pre"}

{6,3,4,15,12,10,9,1,7,16,8,14,2,13,11,5}

{6,3,5,12,15,11,9,13,7,2,8,14,16,1,10,4}

{4,3,5,12,10,11,1,13,16,2,14,8,7,9,15,6}

Returns: "Possible"
{"post","in","pre","post","in","pre"}

{2,13,5,12,7,10,9,4,8,11,3,1,6,14}

{6,4,7,12,5,10,9,13,11,8,3,1,2,14}

{1,9,12,7,10,5,4,3,11,8,13,6,14,2}

Returns: "Possible"
{"pre","post","post","pre","in","in"}

{25,4,3,34,33,32,2,27,20,37,11,8,29,38,5,31,6,7,22,40,28,41,30,24,17,39,9,26,1,35,14,36,12,16,19,43,18,10,15,42,23,13,21}

{33,3,34,4,25,21,32,27,20,5,37,38,8,29,11,2,30,31,41,7,28,40,22,6,17,13,39,1,26,9,12,35,36,14,19,23,18,42,15,10,43,16,24}

{4,33,34,3,27,2,5,20,11,38,29,8,37,32,21,24,30,6,41,22,28,40,7,31,9,1,26,39,13,16,12,14,36,35,23,43,42,10,15,18,19,17,25}

Returns: "Possible"
{"in","post","post","in","pre","pre"}

{7,8,1,12,2,11,9,6,4,3,10,5}

{7,5,1,8,10,12,3,2,11,4,9,6}

{5,1,10,3,4,11,6,9,2,12,8,7}

Returns: "Possible"
{"in","in","pre","post","post","pre"}

{8,12,7,1,11,4,14,2,13,3,9,5,15,10,6}

{12,1,7,8,4,11,6,2,10,3,15,5,9,13,14}

{1,7,12,14,11,4,6,13,10,9,15,5,3,2,8}

Returns: "Possible"
{"in","pre","pre","in","post","post"}

{26,24,39,38,11,22,1,4,20,2,21,33,29,5,36,14,18,35,15,10,3,16,13,6,34,23,19,12,32,8,37,9,7,17,30,28,25,27,31}

{17,12,10,35,5,21,2,20,4,1,33,22,29,18,14,36,11,38,15,34,13,16,3,6,39,19,23,24,7,9,37,8,32,30,26,31,27,25,28}

{20,4,2,1,33,21,29,22,14,36,18,5,11,35,15,38,16,13,6,3,34,10,19,23,39,12,37,9,8,7,32,24,30,17,27,25,31,28,26}

Returns: "Possible"
{"post","post","in","pre","pre","in"}

{8,2,7,11,9,3,6,10,5,12,13,1,4}

{2,8,4,9,11,1,3,10,13,12,5,6,7}

{2,4,7,9,1,6,3,13,5,12,10,11,8}

Returns: "Possible"
{"pre","pre","in","in","post","post"}

{24,14,21,23,17,25,19,10,18,11,16,20,3,6,2,15,5,1,4,22,9,12,7,26,8,13}

{21,23,14,17,25,24,18,11,10,16,20,3,6,2,19,5,15,1,22,4,9,12,7,26,8,13}

{23,21,25,17,14,11,18,2,6,3,20,16,10,5,22,13,8,26,7,12,9,4,1,15,19,24}

Returns: "Possible"
{"pre","post","post","in","in","pre"}

{48,11,40,1,29,5,25,22,17,3,33,20,34,9,46,6,42,23,27,47,4,15,12,19,43,14,45,26,13,2,16,36,39,35,38,8,21,41,31,18,24,44,10,28,37,30,32,7}

{42,6,46,9,34,20,33,23,3,17,22,25,27,47,15,4,5,29,12,19,43,14,45,38,36,16,2,13,26,35,39,1,40,8,21,41,31,18,24,44,28,10,11,48,37,30,7,32}

{42,6,46,9,34,20,33,3,23,17,22,15,47,27,4,25,5,45,14,43,19,12,29,1,26,13,2,16,36,38,35,39,44,24,18,31,41,21,8,40,11,10,28,7,30,37,32,48}

Returns: "Possible"
{"post","in","pre","post","in","pre"}

{32,30,45,44,43,22,31,38,33,19,3,46,29,6,37,5,35,4,1,12,16,17,14,18,13,2,24,21,41,42,34,27,9,28,39,26,25,7,40,15,20,10,36,23,11,8}

{33,30,45,38,43,31,22,44,32,19,46,3,8,5,37,6,17,1,4,16,12,35,14,18,13,11,42,21,41,24,27,34,23,28,39,26,36,7,10,15,20,40,25,9,2,29}

{30,33,44,38,22,31,43,45,29,3,46,19,6,5,37,8,17,1,12,16,4,2,13,18,14,24,42,41,21,11,27,9,23,25,26,39,36,40,10,20,15,7,28,34,35,32}

Returns: "Possible"
{"pre","post","post","in","in","pre"}

{13,40,22,17,12,15,42,28,37,14,44,25,24,47,8,26,2,43,35,5,7,6,36,20,3,19,31,9,48,11,4,45,39,38,21,10,29,33,18,32,23,34,41,46,16,30,1,27}

{20,36,6,7,5,35,43,2,26,8,47,24,25,44,3,14,37,19,28,42,31,48,9,15,12,11,4,45,39,38,21,10,17,22,29,33,40,13,18,23,32,34,41,46,27,1,30,16}

{20,36,6,7,5,35,43,2,26,8,47,24,25,44,14,3,19,37,28,31,42,15,9,48,21,38,39,45,4,11,12,17,10,33,29,22,40,27,46,41,34,23,18,32,1,30,16,13}

Returns: "Possible"
{"post","pre","in","post","pre","in"}

{17,32,14,18,27,41,1,30,9,7,35,19,6,37,34,25,40,29,39,36,12,28,31,23,3,33,38,5,11,22,13,21,43,2,44,15,26,24,10,42,16,4,45,8,20}

{14,32,27,18,13,39,30,41,1,19,7,9,35,34,37,25,29,40,6,36,31,3,23,28,38,33,22,11,5,12,17,20,26,2,15,44,10,42,24,43,45,16,4,8,21}

{13,14,18,27,32,12,6,1,41,7,9,19,35,30,29,34,25,37,40,36,39,22,3,31,23,38,33,28,5,11,2,26,44,15,43,42,10,24,20,4,16,8,45,21,17}

Returns: "Possible"
{"pre","post","post","in","in","pre"}

{29,4,6,1,25,18,8,20,31,10,14,22,9,34,13,19,23,3,32,21,28,26,27,24,17,5,2,30,15,7,11,12,33,16}

{9,22,14,34,32,31,20,8,13,27,28,21,10,3,23,18,25,26,19,24,17,1,6,16,2,30,4,29,15,7,11,12,33,5}

{9,22,14,10,34,31,20,27,13,8,18,23,3,32,21,28,24,19,26,25,1,17,2,16,6,4,30,5,33,12,11,7,15,29}

Returns: "Impossible"
{"post","pre","in","in","pre","post"}

{25,37,13,24,45,1,19,42,6,47,50,31,40,43,17,8,14,26,41,29,33,5,28,10,23,15,16,11,4,44,22,38,30,3,18,36,9,48,32,46,2,21,12,35,27,34,39,7,49,20}

{24,13,11,25,50,47,6,10,19,1,45,5,29,40,41,36,14,8,17,43,31,15,23,42,44,33,16,30,3,22,37,4,26,38,28,18,32,48,9,46,2,21,27,35,12,34,39,7,49,20}

{24,13,22,50,47,6,42,19,1,5,29,41,40,26,14,8,17,43,15,23,10,44,30,38,49,36,4,28,32,48,20,11,7,39,34,12,35,27,21,2,46,9,18,3,37,16,33,31,45,25}

Returns: "Impossible"
{"post","pre","pre","post","in","in"}

{12,41,13,50,19,35,6,38,27,32,40,20,42,4,36,11,25,45,34,9,2,43,17,37,39,23,33,44,24,48,14,18,49,16,7,46,31,29,30,28,22,3,8,15,26,47,10,5,21,1}

{11,41,33,37,38,6,35,25,26,50,42,5,40,14,4,27,1,34,46,30,23,39,36,17,44,48,24,9,18,7,16,49,19,31,28,2,3,22,32,15,47,20,43,21,10,8,29,13,45,12}

{50,33,41,34,35,6,24,25,11,29,5,14,4,42,26,1,30,47,38,40,23,36,37,9,48,39,44,19,7,18,49,21,13,28,2,45,3,32,15,8,10,16,17,20,46,22,31,43,27,12}

Returns: "Impossible"
{"pre","post","post","in","in","pre"}

{40,14,30,3,4,8,25,43,36,13,31,7,44,45,22,20,23,26,19,39,18,5,21,15,6,35,12,10,24,38,27,1,32,16,29,41,37,2,42,33,17,28,34,9,11}

{4,8,25,43,3,30,44,36,13,31,7,14,40,45,22,11,26,19,18,39,23,20,21,15,6,5,10,35,12,38,24,17,32,33,16,41,29,2,42,37,1,27,28,9,34}

{25,8,4,3,43,30,14,31,13,36,44,7,11,22,45,19,26,23,18,39,9,28,17,24,10,5,6,15,21,12,35,38,32,1,29,41,16,33,2,37,42,27,34,20,40}

Returns: "Possible"
{"post","in","pre","post","in","pre"}

{8,27,31,24,13,7,4,34,1,36,5,17,12,32,35,14,10,30,23,2,25,18,21,38,29,11,9,26,3,20,33,15,37,16,39,22,6,28,19}

{8,27,4,24,7,13,31,19,32,36,12,17,5,1,10,14,35,30,2,23,28,18,29,38,21,6,9,26,22,20,39,15,16,37,33,3,11,25,34}

{34,31,4,13,7,24,27,1,32,5,12,17,36,19,10,14,25,23,2,30,18,28,29,38,11,9,6,3,22,33,39,37,16,15,20,26,21,35,8}

Returns: "Possible"
{"pre","post","post","in","in","pre"}

{17,22,33,34,6,28,12,25,15,4,23,9,8,30,36,26,31,14,11,29,7,41,40,16,2,3,37,5,32,39,24,13,38,35,1,20,27,18,10,21,19}

{29,11,14,31,26,36,7,30,8,9,23,41,40,4,15,13,32,5,37,3,2,16,24,39,25,12,38,35,1,28,6,34,33,20,27,18,10,22,17,21,19}

{29,11,14,31,26,36,30,7,8,9,41,23,4,40,15,25,16,2,3,37,5,32,13,24,39,1,35,38,12,28,6,34,10,18,27,20,33,22,19,21,17}

Returns: "Possible"
{"in","pre","post","post","pre","in"}

{46,5,44,34,29,15,36,21,23,14,11,17,35,8,31,37,19,18,42,33,4,20,9,10,41,32,38,24,26,30,27,40,6,7,45,28,2,12,39,13,22,1,43,16,25,3}

{46,44,34,15,23,36,21,17,11,14,8,33,31,42,37,18,19,41,10,9,20,4,38,7,24,6,26,40,30,27,45,12,2,13,1,43,16,3,25,22,39,28,32,35,29,5}

{44,5,24,21,36,15,29,11,17,33,42,18,19,37,31,8,35,20,41,9,10,7,6,40,27,30,26,23,38,32,28,12,39,43,1,22,25,3,16,13,2,45,4,14,34,46}

Returns: "Impossible"
{"post","in","pre","post","in","pre"}

{21,31,32,26,29,36,15,4,18,1,33,20,23,8,25,42,37,10,41,6,3,13,38,39,28,44,11,27,34,7,12,2,17,14,9,43,5,16,40,24,30,45,19,35,22}

{35,8,1,36,29,26,4,15,18,32,23,20,33,31,41,37,42,10,25,19,14,7,11,28,39,44,38,27,34,9,2,12,17,3,5,43,13,30,40,24,16,45,6,21,22}

{25,33,15,29,36,38,4,1,18,32,20,23,8,31,10,37,42,41,35,9,12,27,44,28,39,11,26,7,34,13,2,14,17,3,43,5,19,24,40,30,45,16,6,22,21}

Returns: "Impossible"
{"post","pre","pre","post","in","in"}

{6,44,29,47,46,2,10,33,14,31,22,23,45,19,4,8,16,42,24,13,26,30,3,40,38,5,11,15,32,21,27,1,18,43,34,36,35,17,20,25,39,7,28,9,41,12,37}

{6,47,29,45,2,23,10,22,33,31,14,46,42,8,16,4,13,32,30,3,15,40,11,38,5,26,1,27,35,36,34,43,17,25,9,7,28,39,12,37,41,20,18,21,24,19,44}

{47,29,44,45,23,22,31,14,33,10,2,19,42,16,8,13,24,30,32,15,11,5,38,40,3,21,1,35,43,36,34,18,25,20,7,9,28,41,37,12,39,17,27,26,4,46,6}

Returns: "Possible"
{"pre","post","post","in","in","pre"}

{18,30,1,28,22,42,24,21,2,3,43,6,25,47,41,37,32,34,20,14,49,45,23,48,38,44,35,17,15,10,16,33,31,36,9,27,5,12,46,29,8,13,39,19,4,40,26,7,11}

{35,44,38,48,23,45,49,14,20,17,34,32,15,10,16,37,41,47,25,33,31,36,4,27,6,43,5,3,2,21,24,42,22,12,46,29,8,13,39,19,9,26,40,28,1,7,30,18,11}

{35,44,38,48,23,45,49,15,20,34,17,16,10,14,32,37,41,47,26,36,31,33,25,6,27,43,3,5,2,21,24,42,4,19,39,13,8,1,46,12,22,28,40,9,29,30,7,11,18}

Returns: "Impossible"
{"in","post","post","in","pre","pre"}

{14,39,11,38,4,32,6,37,1,5,36,35,40,12,18,24,17,41,21,25,34,2,33,13,8,30,22,7,3,29,23,9,42,15,27,10,28,20,26,43,19,16,31}

{11,39,14,32,4,38,31,6,1,36,5,37,16,40,21,41,18,17,24,25,2,13,30,8,33,34,12,35,22,19,7,43,29,3,26,23,20,9,28,42,10,15,27}

{39,11,31,38,32,4,16,1,37,36,5,12,40,41,17,24,18,34,25,33,8,30,13,2,21,19,22,43,29,26,20,28,10,27,15,42,9,23,3,7,35,6,14}

Returns: "Possible"
{"in","pre","post","post","pre","in"}

{35,16,39,24,7,29,18,11,28,37,32,4,34,6,14,40,19,23,8,25,9,27,1,30,5,22,31,33,21,38,3,17,13,12,2,10,15,20,26,36}

{27,11,29,7,24,18,20,32,37,4,28,16,9,8,40,14,6,23,19,17,25,1,35,26,13,38,33,31,21,3,22,34,12,10,2,5,39,15,36,30}

{1,28,18,7,24,29,20,11,4,32,37,16,27,25,23,14,40,6,19,8,17,9,39,34,21,33,31,3,38,22,12,13,5,10,2,15,26,30,36,35}

Returns: "Impossible"
{"pre","pre","in","post","post","in"}

{24,45,39,3,13,17,41,9,26,20,7,32,25,15,30,4,40,29,8,6,18,16,33,36,43,14,10,11,35,23,12,44,28,5,2,1,19,31,22,21,27,37,34,38,42,46}

{45,3,41,17,26,9,7,25,32,20,13,39,24,40,29,4,6,8,16,36,33,10,11,14,23,35,44,28,12,43,18,30,2,19,31,1,5,21,27,38,34,46,42,37,22,15}

{39,17,41,13,26,20,32,25,7,9,3,45,4,29,40,30,6,16,18,36,14,11,10,43,23,12,28,44,35,33,8,15,1,31,19,2,21,22,37,38,42,46,34,27,5,24}

Returns: "Possible"
{"in","in","post","pre","pre","post"}

{13,12,27,14,8,30,25,6,26,9,34,18,3,7,42,11,28,20,4,35,33,1,10,46,15,24,36,40,16,2,23,32,31,17,41,29,43,44,38,19,5,21,45,22,37,39}

{19,16,33,20,7,34,26,6,9,25,18,30,3,42,8,28,11,4,14,45,24,46,15,10,1,27,43,40,23,2,12,36,41,17,31,29,44,32,38,39,22,35,37,21,5,13}

{34,2,1,4,42,18,9,6,26,25,5,3,30,7,11,28,8,20,45,14,33,15,46,24,10,43,27,16,40,23,12,19,38,29,17,41,31,44,36,32,37,22,35,39,21,13}

Returns: "Impossible"
{"post","in","pre","pre","in","post"}

{14,13,20,11,3,9,21,30,29,38,27,17,46,39,15,31,7,24,40,25,45,28,4,19,47,8,33,1,12,43,26,32,34,35,37,10,42,6,18,22,41,16,23,44,5,2,36}

{30,36,21,46,31,3,11,20,35,38,14,15,39,13,8,27,7,24,29,40,16,19,4,28,17,47,1,33,32,25,43,12,10,9,37,34,6,42,45,22,41,18,23,44,5,2,26}

{29,25,21,9,13,37,11,20,35,15,39,46,17,40,28,4,8,33,32,36,43,31,34,3,6,26,2,5,22,23,16,41,44,45,42,10,12,1,47,19,18,30,24,7,27,38,14}

Returns: "Impossible"
{"in","post","pre","pre","post","in"}

{18,13,36,32,15,20,14,29,22,38,23,17,9,24,34,27,5,26,16,35,21,2,31,10,19,37,28,7,11,12,6,33,8,25,30,39,3,1,4}

{1,33,37,10,2,16,26,5,9,17,23,38,34,27,24,22,29,14,35,20,21,15,31,19,32,36,6,11,28,7,12,13,3,30,8,25,39,18,4}

{23,17,38,27,34,24,9,22,5,29,26,14,35,16,21,20,2,31,15,19,10,32,37,12,7,28,11,6,36,33,39,25,8,30,3,13,1,4,18}

Returns: "Possible"
{"in","in","post","pre","pre","post"}

{33,6,15,18,37,42,21,23,17,31,11,1,22,39,30,41,38,40,5,12,36,7,20,19,26,35,8,2,28,24,4,32,29,16,27,34,10,13,14,25,9,3}

{6,37,20,15,31,36,1,23,19,42,12,5,33,24,13,41,30,39,22,17,4,40,18,11,26,35,21,28,2,8,7,32,29,27,38,34,10,16,14,25,9,3}

{40,6,18,37,12,42,19,23,17,31,5,24,34,41,30,16,22,1,4,20,15,28,2,8,39,3,33,25,14,13,10,38,27,29,32,11,21,35,26,7,36,9}

Returns: "Impossible"
{"post","pre","pre","in","in","post"}

{35,41,15,23,6,18,17,38,10,3,2,9,30,12,1,27,37,26,31,16,29,21,14,22,5,28,24,8,34,33,32,25,36,40,13,7,19,4,39,11,20}

{26,18,15,23,6,41,17,10,2,9,3,38,37,27,30,1,12,35,14,16,21,29,31,36,8,24,28,5,34,25,33,32,22,20,7,13,19,39,4,11,40}

{38,23,15,18,6,17,41,3,10,9,2,26,37,12,30,1,27,16,14,29,21,34,8,28,24,5,36,32,33,25,4,7,19,13,39,20,11,40,22,31,35}

Returns: "Possible"
{"in","post","pre","in","post","pre"}

{8,31,7,21,25,11,15,5,1,19,34,22,2,37,10,13,38,9,20,3,14,30,18,35,33,23,27,39,26,28,4,32,17,6,29,36,12,16,24}

{26,20,14,13,37,2,22,34,19,39,5,15,24,25,10,21,35,38,9,3,30,7,18,23,33,27,31,1,12,28,32,8,16,36,6,17,29,4,11}

{19,39,30,31,22,15,2,11,37,18,25,10,3,9,38,20,21,34,14,5,7,27,23,33,35,1,13,32,12,28,26,24,4,29,17,6,36,16,8}

Returns: "Impossible"
{"post","in","pre","pre","in","post"}

{1,11,20,9,10,13,14,18,12,23,16,19,15,8,22,17,7,3,6,2,4,5,21}

{4,15,10,9,20,14,13,12,18,16,23,19,11,22,8,6,3,2,7,17,1,21,5}

{17,18,9,10,13,14,20,12,15,19,23,16,8,22,11,2,3,6,7,4,5,21,1}

Returns: "Possible"
{"post","post","in","in","pre","pre"}

{20,32,23,12,40,29,19,5,22,13,11,1,34,8,18,33,45,2,17,27,4,37,39,26,31,28,10,9,44,30,7,6,15,43,24,41,14,21,46,16,36,35,42,25,38,3}

{32,23,2,40,12,19,29,13,22,5,45,8,1,34,11,18,33,20,27,4,17,37,3,31,10,28,9,6,30,44,7,26,15,36,16,24,46,41,14,21,43,25,42,35,39,38}

{2,23,32,40,45,19,13,22,5,29,8,34,1,33,18,11,12,3,4,27,37,17,25,6,9,10,28,31,30,7,44,36,15,16,46,21,14,41,24,43,26,42,35,38,39,20}

Returns: "Possible"
{"post","post","in","in","pre","pre"}

{21,26,3,33,32,12,19,18,31,22,9,23,13,2,4,6,10,8,16,30,29,1,14,24,7,5,17,11,28,25,27,20,15}

{21,26,9,3,22,33,31,32,18,12,19,15,10,13,6,4,2,23,8,20,30,16,27,14,1,29,25,24,28,7,11,5,17}

{15,9,22,31,18,19,12,32,33,3,26,10,6,4,2,13,20,8,30,27,14,1,25,28,11,17,5,7,24,29,16,23,21}

Returns: "Possible"
{"pre","pre","post","in","in","post"}

{34,38,47,7,48,4,26,32,25,43,36,12,24,23,8,46,5,37,6,31,33,45,35,28,11,2,16,19,3,10,13,17,20,40,9,41,21,22,29,39,27,15,1,14,30,18,44,42}

{37,5,46,8,23,24,31,6,12,36,33,45,43,25,35,32,26,11,28,4,48,3,10,19,16,2,7,47,17,13,1,15,27,39,29,22,21,41,30,14,9,40,18,20,38,34,42,44}

{37,5,46,8,23,24,12,31,6,33,36,43,45,25,32,35,26,4,11,28,48,7,3,19,10,16,2,17,13,47,38,1,15,27,39,29,22,21,30,14,41,9,18,40,20,42,44,34}

Returns: "Possible"
{"post","post","in","pre","pre","in"}

{1,15,9,25,3,27,6,18,7,11,35,26,41,36,24,31,29,19,10,39,28,38,23,14,37,34,32,43,22,20,8,21,30,40,44,4,5,16,42,33,12,17,2,13}

{44,3,6,18,25,28,7,26,35,9,24,22,41,29,31,15,12,4,20,14,17,38,11,34,37,43,32,39,36,21,8,30,19,40,27,5,10,42,16,33,13,2,23,1}

{13,29,26,18,42,6,3,7,11,25,35,34,43,24,9,31,38,23,28,14,39,22,41,37,32,20,36,10,30,12,8,4,19,5,40,27,21,33,16,44,15,17,2,1}

Returns: "Impossible"
{"in","in","pre","pre","post","post"}

{14,1,17,9,8,4,15,6,21,18,7,3,11,13,19,5,16,20,2,10,12}

{12,17,9,8,14,1,13,21,6,4,18,11,19,20,5,16,7,10,15,2,3}

{8,9,17,12,16,6,21,13,20,18,5,7,11,4,2,15,3,10,19,1,14}

Returns: "Impossible"
{"pre","post","post","pre","in","in"}

{26,19,23,3,25,32,30,35,33,29,8,14,6,7,21,5,13,18,1,15,9,17,34,31,16,4,22,10,11,24,28,20,12,2,27}

{30,35,33,14,29,8,32,25,21,7,6,3,23,17,13,5,1,18,9,15,34,19,26,27,31,16,22,4,28,24,11,10,2,12,20}

{35,30,32,14,33,8,29,21,6,7,25,3,5,18,1,13,17,15,9,23,19,34,31,27,20,28,4,16,22,10,11,24,2,12,26}

Returns: "Possible"
{"in","in","post","pre","pre","post"}

{44,28,31,12,8,11,26,22,3,17,19,5,37,16,40,39,24,38,9,15,49,30,1,43,18,20,14,10,41,21,35,47,29,27,7,42,34,36,13,25,23,45,48,33,4,6,46,2,32}

{8,12,31,28,44,3,22,26,11,40,24,39,16,37,5,19,17,49,38,15,9,1,30,21,41,10,43,14,20,18,27,34,42,7,29,47,35,36,23,25,13,45,48,6,4,33,46,2,32}

{28,31,12,8,22,26,11,19,5,37,16,39,40,24,15,38,9,1,41,43,10,14,20,18,47,29,7,27,42,34,25,23,4,33,32,2,46,6,48,45,13,36,35,21,30,49,17,3,44}

Returns: "Possible"
{"in","post","pre","in","post","pre"}

{39,1,17,18,16,34,14,15,46,5,50,3,47,27,42,44,8,49,30,26,21,2,32,22,23,31,37,11,35,43,12,24,45,41,9,6,13,40,20,28,19,4,38,7,36,10,33,48,25,29}

{1,18,16,17,39,5,46,15,14,34,29,3,47,50,42,27,25,8,30,21,26,49,44,32,2,48,23,37,31,22,43,35,11,33,24,45,12,10,9,41,6,36,13,7,40,38,20,4,28,19}

{17,16,18,1,29,5,34,46,14,15,47,3,25,42,27,49,26,21,30,8,48,32,2,31,37,23,33,43,11,35,45,24,10,9,36,6,7,38,4,19,28,20,40,13,41,12,22,44,50,39}

Returns: "Possible"
{"post","pre","in","in","pre","post"}

{21,45,8,25,7,12,34,10,41,14,26,4,38,3,16,31,28,33,39,20,37,29,30,43,11,35,40,42,27,22,24,36,18,13,5,9,15,23,17,6,1,2,44,46,47,32,19}

{12,7,34,41,10,4,26,19,8,3,16,44,38,31,28,32,18,30,21,43,11,37,40,35,20,1,39,22,45,27,36,24,5,9,13,6,23,46,17,29,33,15,2,47,42,14,25}

{19,18,26,41,42,34,7,10,12,14,38,16,3,2,28,31,4,8,36,1,40,11,30,43,29,37,35,20,45,22,27,39,33,5,13,24,17,9,46,23,15,44,47,6,32,25,21}

Returns: "Impossible"
{"pre","post","post","pre","in","in"}

{1,46,49,38,39,31,4,16,26,21,5,33,29,28,36,2,3,35,19,20,30,40,48,44,8,25,37,50,43,9,32,23,45,17,15,42,41,7,27,22,10,6,34,18,13,24,47,11,12,14}

{46,1,14,49,21,39,26,4,16,31,38,5,36,2,3,28,29,12,35,19,48,23,44,32,25,9,50,43,37,8,40,30,11,45,17,15,22,27,7,41,47,6,10,18,24,13,34,42,20,33}

{46,38,21,31,26,16,4,39,49,14,33,5,2,36,28,3,19,35,12,20,48,40,23,8,32,37,9,43,50,25,44,17,45,11,42,15,7,22,27,47,34,6,10,24,13,18,41,30,29,1}

Returns: "Possible"
{"post","post","in","pre","pre","in"}

{9,43,37,29,26,19,38,28,21,20,6,8,10,34,46,48,11,35,4,47,24,16,40,17,36,33,13,44,27,32,5,30,42,1,18,49,31,7,15,12,14,39,25,41,45,2,3,50,23,22}

{6,8,20,10,21,34,28,46,38,48,19,35,11,26,47,4,29,33,36,40,17,16,24,49,18,30,32,44,13,27,5,1,42,37,39,14,7,31,12,15,43,23,50,2,41,25,45,3,9,22}

{23,39,49,47,35,48,46,34,10,8,6,20,21,28,38,19,11,26,4,40,16,17,36,24,33,29,42,5,27,13,44,32,30,1,18,37,15,31,7,12,14,43,3,45,25,41,2,50,22,9}

Returns: "Possible"
{"pre", "pre", "in", "in", "post", "post" }

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }

{2, 3, 4, 5, 1, 6, 7, 8, 9, 10 }

{6, 5, 4, 3, 2, 10, 9, 8, 7, 1 }

Returns: "Impossible"
{"post", "in", "pre", "post", "in", "pre" }

{1, 2, 3, 4, 5 }

{2, 1, 3, 5, 4 }

{1, 4, 3, 5, 2 }

Returns: "Impossible"
{"post", "in", "pre", "post", "in", "pre" }

{1, 2, 3, 4, 5 }

{2, 1, 3, 5, 4 }

{2, 4, 3, 5, 1 }

Returns: "Possible"
{"in", "pre", "post", "post", "pre", "in" }

{1, 2, 3 }

{3, 2, 1 }

{3, 2, 1 }

Returns: "Impossible"

Statistics

Problem Statement for "InPrePost"

Problem Statement

Definition

Constraints

Examples