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 functools import reduce
str = input()
main_res = float('inf')

x = {}

for i in str:
    if not i in x:
        arr = list(map(lambda x: len(x), str.split(i)))
        res = reduce(lambda x, y: max([x, y]), arr)
        x[i] = res
        if res < main_res:
            main_res = res

print(main_res + 1)