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 = str(raw_input())
a = [0]*(26)
visited = [False]*(26)
firstOcc = [0]*26
lastOcc = [0]*26
n = len(s)
mi = 1000001
for i in range(26):
	t =1
	r =1
	for j in range(n):
		x = ord(s[j])-ord('a')
		if x!=i:
			t+=1
		else:
			r = max(t,r)
			t = 1
		r = max(r,t)
	mi = min(r,mi)
print mi