p1671_Rhyme Schemes

Rhyme Schemes

Time Limit: 1000MSMemory Limit: 10000KTotal Submissions: 674Accepted: 376Special Judge

Description

Therhyme scheme for a poem (or stanza of a longer poem) tells which linesof the poem rhyme with which other lines. For example, a limerick suchas If computers that you build are quantum
Then spies of all factions will want 'em
Our codes will all fail
And they'll read our email
`Til we've crypto that's quantum and daunt 'em

Jennifer and Peter Shor (http://www.research.att.com/~shor/notapoet.html)

Has a rhyme scheme of aabba, indicating that the first, second and fifth lines rhyme and the third and fourth lines rhyme.
For a poem or stanza of four lines, there are 15 possible rhyme schemes:
aaaa, aaab, aaba, aabb, aabc, abaa, abab, abac, abba, abbb, abbc, abca, a bcb, abcc, and abcd.
Write a program to compute the number of rhyme schemes for a poem or stanza of N lines where N is an input value.

Input

Inputwill consist of a sequence of integers N, one per line, ending with a 0(zero) to indicate the end of the data. N is the number of lines in apoem.

Output

Foreach input integer N, your program should output the value of N,followed by a space, followed by the number of rhyme schemes for a poemwith N lines as a decimal integer with at least 12 correct significantdigits (use double precision floating point for your computations).

Sample Input

1
2
3
4
20
30
10
0

Sample Output

1 1
2 2
3 5
4 15
20 51724158235372
30 846749014511809120000000
10 115975

Source

Greater New York 2003