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()
c=[]
f=0
for i in s:
    if i not in c:
        c.append(i)
j=[]
for i in c :
    n=0
    m=0
    for i2 in i+s+i:
        if i2==i:
            n+=1
            if n>m:
                m=n
            n=0
        else:
            n+=1
    j.append(m)
print(min(j))
