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 sys

s = [ord(c) - 97 for c in input()]
n = len(s)


def solve(k):
    count, res = [0]*26, [1]*26
    for i in range(k):
        count[s[i]] += 1
    for cc in range(26):
        if count[cc] == 0:
            res[cc] = 0

    for i in range(k, n):
        count[s[i]] += 1
        count[s[i-k]] -= 1

        for cc in range(26):
            if count[cc] == 0:
                res[cc] = 0

    return max(res) > 0


ok, ng = n, 0
while abs(ok - ng) > 1:
    mid = (ok + ng) >> 1
    if solve(mid):
        ok = mid
    else:
        ng = mid

print(ok)
