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
n = input()
l = len(n)
dist = {x:0 for x in string.ascii_lowercase}
last = {x:-1 for x in string.ascii_lowercase}
for i in range(l):
    dist[n[i]] = max(dist[n[i]], i - last[n[i]])
    last[n[i]] = i
for i in dist.keys():
    dist[i] = max(dist[i], l - last[i])
print(min(dist.values()))