Hypertrees

Problem code: HYPER

All submissions for this problem are available.

A hypergraph is a generalization of a graph, where an edge can connect any number of vertices. A k-uniform hypergraph is a hypergraph such that all its hyperedges have size k. For more information, see Wikipedia.

Let's call a particular hypergraph a hypertree if it is connected (that is, you can move from any vertex to any other vertex using only its hyperedges) and removing any of its hyperedges makes the hypergraph disconnected (note that this definition of hypertrees differs from the standard one).

Given just one integer N, find the number of 3-uniform hypertrees on N vertices. Two 3-uniform hypertrees are considered different if a hyperedge (u, v, w) exists such that it is present in exactly one of these hypertrees (note that the order of vertices in the hyperedge doesn't matter, and neither does the order of hyperedges in the hypertree).

Input

The first line of the input contains an integer T -- the number of test cases (at most 15). Then T lines follow, each contains an integer N (3 ≤ N ≤ 17).

Important! Please include all code used in solving this problem in your solution.

Output

For each test case output one line containing the requested number. It's guaranteed that this number won't exceed 263-1.

Examples

Input:
4
3
4
5
8

Output:
1
6
25
93268

Explanation:

There is just one 3-uniform hypertree on 3 vertices: {(1,2,3)}. There are six of them on 4 vertices: {(1,2,3), (1,2,4)}, {(1,2,3), (1,3,4)}, {(1,2,3), (2,3,4)}, {(1,2,4), (1,3,4)}, {(1,2,4), (2,3,4)}, {(1,3,4), (2,3,4)}. Two of the 25 possible hypertrees on 5 vertices are {(1,2,3), (3,4,5)} and {(1,2,3), (1,2,4), (1,2,5)}.

Author: gennady.korotkevich
Tester: pieguy
Editorial http://discuss.codechef.com/problems/HYPER
Date Added: 30-09-2011
Time Limit: 1 sec
Source Limit: 50000 Bytes
Languages: ADA, ASM, BASH, BF, C, C99 strict, CAML, CLOJ, CLPS, CPP 4.0.0-8, CPP 4.3.2, CS2, D, ERL, FORT, FS, GO, HASK, ICK, ICON, JAR, JAVA, JS, LISP clisp, LISP sbcl, LUA, NEM, NICE, NODEJS, PAS fpc, PAS gpc, PERL, PERL6, PHP, PIKE, PRLG, PYTH, PYTH 3.1.2, RUBY, SCALA, SCM guile, SCM qobi, ST, TCL, TEXT, WSPC


Comments

the huge difference between

cyberax @ 3 Dec 2011 01:38 AM
the huge difference between this definition of hypertrees and the well-known one is very confusing. in the kind of trees described in this statement, cycles are permitted (ex: V={1,2,3} E={{1,2,3},{1,2,4},{1,2,5}} has cycles). so these are not really trees actually. maybe it should not be called that way, in order not to disturb people. anyway. a pretty difficult problem.

i dono the exact concept of

ugishadow @ 10 Dec 2011 06:39 PM
i dono the exact concept of this problem....

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