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
#!/bin/python
import sys
s = raw_input()
alphabet = "abcdefghijklmnopqrstuvwxyz"
k = len(s)
for c in alphabet:
    nb_c = 1
    t =[]
    for e in s:
        if e==c:
            t.append(nb_c)
            nb_c = 1
        else:
            nb_c+=1
    t.append(nb_c)
    if t !=[]:
        k = min(k,max(t))
print(k)      