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()
letters = list(set(s))
letter_ans = []
for letter in letters:
    index = []
    num = -2
    while num != -1:
        num = s.find(letter, max(0, num + 1))
        index.append(num)
    index.pop()
    max_sub = 0
    for i in range(1, len(index)):
        max_sub = max(index[i] - index[i-1], max_sub)
    max_sub = max(len(s) - index[-1], max_sub, index[0] + 1)
    letter_ans.append(max_sub)
print(min(letter_ans))
