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()

import string

dct = {ch: -1 for ch in string.ascii_lowercase}
distances = {ch: [] for ch in string.ascii_lowercase}
for i, ch in enumerate(s):
   distances[ch].append(i - dct[ch])
   dct[ch] = i

dct = {ch: -1 for ch in string.ascii_lowercase}
distances_backward = {ch: [] for ch in string.ascii_lowercase}

for i, ch in enumerate(s[::-1]):
   distances_backward[ch].append(i - dct[ch])
   dct[ch] = i

ans = 10**9
for ch in set(s):
    m1 = max(distances[ch])
    m2 = max(distances_backward[ch])
    m = max(m1, m2)
    if m < ans:
        ans = m
print(ans)
