Sometimes the programmers have very strange ways of hiding their passwords. Billy "Hacker" Geits chooses a string S composed of L (5 <= L <= 100,000) lowercase letters ('a'..'z') with length L. Then he makes and sorts all L-1 one-letter left cyclic shifts of the string. He then takes as a password one prefix of the lexicographically first of the obtained strings (including S).
For example consider the string "alabala". The sorted cyclic one-letter left shifts (including the initial string) are:
aalabal
abalaal
alaalab
alabala
balaala
laalaba
labalaa
Lexicographically, first string is 'aalabal'. The first letter of this string ('a') is the 'a' that was in position 6 in the initial string (counting the first letter in the string as position 0).
Write a program that, for given string S, finds the start position of the first letter of the sorted list of cyclic shifts of the string. If the first element appears more than once in the sorted list, then the program should output the smallest possible initial position.