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 collections


def solution():
    d = collections.defaultdict(list)
    s = str(raw_input())
    for i, c in enumerate(s):
        d[c].append(i)
    res = len(s)
    for key, value in d.items():
        if len(value) == 0:
            continue
        segment = [value[0] + 1, len(s) - value[-1]]
        for i in range(len(value))[1:]:
            segment.append(value[i] - value[i - 1])
        res = min(res, max(segment))
    return res


if __name__ == '__main__':
    print solution()
