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
s = list(input())

n = len(s)
idx = [[-1] for _ in range(26)]
for i in range(n):
    idx[ord(s[i]) - ord('a')].append(i)
for i in range(26):
    idx[i].append(n)

print(min(map(lambda ls: max(map(lambda i: ls[i + 1] - ls[i], range(len(ls) - 1))), idx)))
