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 = raw_input()
D = [-1] * 26
Prev = [-1] * 26
for i in range(len(S)):
    idx = ord(S[i]) - 97
    if Prev[idx] == -1:
        D[idx] = i - Prev[idx]
        Prev[idx] = i
    else:
        D[idx] = max(i - Prev[idx], D[idx])
        Prev[idx] = i
        
for i in range(26):
    D[i] = max(len(S) - Prev[i], D[i])

ret = (len(S) /2) + 1
for i in range(26):
    if D[i] != -1: ret = min(ret, D[i])
print ret