P8620 [Lanqiao Cup 2014 National A] Permutation Index
Description
If we use the $4$ letters a b c d to form a string, there are $4! = 24$ possibilities. If we sort them, each string corresponds to an index:
```text
abcd 0
abdc 1
acbd 2
acdb 3
adbc 4
adcb 5
bacd 6
badc 7
bcad 8
bcda 9
bdac 10
bdca 11
cabd 12
cadb 13
cbad 14
cbda 15
cdab 16
cdba 17
...
```
Now you are given a string formed by no more than 10 pairwise distinct lowercase letters. Can you find the index of this string among all permutations?
Input Format
One line, a string.
Output Format
One line, an integer, representing the index of the given string among all strings generated by permuting its letters. Note: the smallest index is $0$.
Explanation/Hint
Time limit: 1 second, 256M. Lanqiao Cup, the 5th National Finals, 2014.
Translated by ChatGPT 5