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
inp = input()
places = {}
for ind, l in enumerate(inp):
    if l not in places:
        places[l] = [-1]
    places[l].append(ind)
for l in places:
    places[l].append(len(inp))
print(min(
    max([j-i for i, j in zip(places[l][:-1], places[l][1:])])
    for l in places
))