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
import string

s = input()

def max_dist(s, c):
	pos = [-1]
	for i, val in enumerate(s):
		if val == c:
			pos.append(i)
	pos.append(len(s))
	return max(pos[i+1] - pos[i] for i in range(len(pos) - 1))

print(min(max_dist(s, c) for c in string.ascii_lowercase))