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(); pos = {}; gap = {}; res = []

for i in range(len(s)):
    if s[i] not in pos:
        pos[s[i]] = i
        gap[s[i]] = i + 1
    else:
        if i - pos[s[i]] > gap[s[i]]:
            gap[s[i]] = i - pos[s[i]]
        pos[s[i]] = i

for i in gap:
    if len(s) - pos[i] > gap[i]:
        gap[i] = len(s) - pos[i]

for key, val in gap.items():
    if s.count(key) > 1: res.append(val)
try: print(min(min(res), len(s) // 2 + 1))
except: print(len(s) // 2 + 1)
