Given a string of characters, we can permute the individual characters to make new strings. If we consider an ordering on the characters, say alphabetic, then the strings themselves can be ordered. Then any given permutation can be given a unique number designating its position in that ordering. For example, the string acab gives rise to the following 12 distinct permutations:
| aabc | 1 | acab | 5 | bcaa | 9 |
| aacb | 2 | acba | 6 | caab | 10 |
| abac | 3 | baac | 7 | caba | 11 |
| abca | 4 | baca | 8 | cbaa | 12 |
Thus the string acab can be characterised in this sequence as 5.
Write a program that will read in a string and determine its position in the ordered sequence of permutations of its constituent characters. Note that numbers of permutations can get very large; however, we guarantee that no string will be given whose position is more than 231 - 1.
Input will consist of a series of lines, each line containing one string. Each string will consist of up to 20 lower case letters, not necessarily distinct. The file will be terminated by a line consisting of a single #.
Output will consist of a series of lines, one for each line of the input. Each line will consist of the position of the string in its sequence, right justified in a field of width 10.
bacaa abc cba #
15
1
6