As an experiment the Educational Codeforces Round 33 will be rated for Div. 2. ×

C. K-Dominant Character
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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