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
import string

s = input()

ans = len( s ) // 2 + 1

for a in list( string.ascii_lowercase ):
    last = -1
    l = 0
    for i , c in enumerate( list( s ) ):
        if a == c:
            l = max( l, i - last )
            last = i
    l = max( l , len( s ) - last )
    ans = min( ans, l )

print( ans )
