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()
Len = len(s)
min_k = Len
for ch in set(s):
    last_idx, freq = -1, 0
    for i in range(Len):
        if s[i] == ch:
            freq = max(freq, i-last_idx)
            last_idx = i
    freq = max(freq, Len-last_idx)
    min_k = min(min_k, freq)
print(min_k)
