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 = raw_input()
ans = len(s)
for c in xrange(ord('a'), ord('z') + 1):
    c = chr(c)
    last, cand = 0, 0
    for index, ch in enumerate(c + s + c):
        if ch == c:
            cand = max(cand, index - last)
            last = index
    ans = min(ans, cand)
print ans
