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()
d={x:[0,-1] for x in string.ascii_lowercase}
for i in range(len(s)):
    d[s[i]][0]=max(i-d[s[i]][1],d[s[i]][0])
    d[s[i]][1]=i
a=[]
for i in d:
    d[i][0]=max(len(s)-d[i][1],d[i][0])
    a.append(d[i][0])
a.sort()
print(a[0])