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
i=input()
s=set(i)
def F(c):
	l=[i+1 for i,x in enumerate(i) if x==c]
	d=(y-x for x,y in zip(l,l[1:]))
	return max(l[0],len(i)-l[-1]+1,*d)
print(min(map(F,s)))