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(input())
n = len(s)
ans = 10**18
for i in range(26):
    c = chr(i+ord('a'))
    temp = -1
    p = []
    for j in range(n):
        if s[j] == c:
            p.append(j-temp)
            temp = j
    else:
        p.append(n-temp)
    #print(p)
    if p:
        ans = min(ans, max(p))
print(ans)
