The rhyme scheme for a poem (or stanza of a longer poem) tells which lines of the poem rhyme with which other lines. For example, a limerick such as
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
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
Input will consist of a sequence of integers N (<= 50), one per line, ending with a 0 (zero) to indicate the end of the data. N is the number of lines in a poem.
Output
For each input integer N, your program should output the value of N, followed by a space, followed by the number of rhyme schemes for a poem with N lines.
Sample Input
1
2
3
4
20
30
10
0
Sample Output
1 1
2 2
3 5
4 15
20 51724158235372
30 846749014511809332450147
10 115975
