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 = input()
t = sorted(list(set(s)))
a1 = []
for k in t:
    t1, dk = [], 0
    for i in range(len(s)):
        if s[i]==k:
            t1.append(i+1-dk)
            dk = i+1
    t1.append(len(s)+1-dk)
    a1.append(max(t1))
print(min(a1))