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()
n = len(s)
lst = [-1] * 26
dis = [0] * 26
for i in range(n):
    x = ord(s[i]) - 97
    dis[x] = max(dis[x], i - lst[x])
    lst[x] = i
for i in range(26):
    dis[i] = max(dis[i], n - lst[i])
print(min(dis))