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 string
s = input()
les = len(s)
ans = les
for c in string.ascii_lowercase:
    l, a = -1, 0
    for i in range(les):
        if s[i] == c:
            a = max(a, i-l)
            l = i
    a = max(a, les-l)
    ans = min(ans, a)
print(ans)