You are given a string s consisting of lowercase Latin letters. Character c is called k-dominant iff each substring of s with length at least k contains this character c.

You have to find minimum k such that there exists at least one k-dominant character.

-----Input-----

The first line contains string s consisting of lowercase Latin letters (1 ≤ |s| ≤ 100000).

-----Output-----

Print one number — the minimum value of k such that there exists at least one k-dominant character.

-----Examples-----

Input abacaba

Output 2

Input zzzzz

Output 1

Input abcde

Output 3