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 sys
from collections import Counter


def max_d(string, alpha, occur):
    if occur == 1:
        return len(string) // 2 + 1
    prev = -1
    max_d = 0
    for index, i in enumerate(s):
        if i == alpha:
            if index - prev > max_d:
                max_d = index - prev
            prev = index
    return max(max_d, len(s) - prev)


s = sys.stdin.readline().rstrip()
c = Counter(s)
print(min(max_d(s, k, v) for k, v in c.items()))
