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
from sys import stdin, stdout

s = stdin.readline().rstrip('\n')

from collections import defaultdict
characters = defaultdict(list)
for i, c in enumerate(s):
    characters[c].append(i)


k = []
for c, positions in characters.iteritems():
    positions = [-1] + positions + [len(s)]
    current_k = max([(end - start) for start, end in zip(positions, positions[1:])])
    k.append(current_k)

print >>stdout, min(k)