Shrinking

Snuke can change a string t of length N into a string t' of length N - 1 under the following rule:

• For each i (1 ≤ i ≤ N - 1), the i-th character of t' must be either the i-th or (i + 1)-th character of t.

There is a string s consisting of lowercase English letters. Snuke's objective is to apply the above operation to s repeatedly so that all the characters in s are the same. Find the minimum necessary number of operations.

Constraints

• 1 ≤ |s| ≤ 100
• s consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:

s

Output

Print the minimum necessary number of operations to achieve the objective.

Examples

Input

serval

Output

3

Input

jackal

Output

2

Input

zzz

Output

0

Input

whbrjpjyhsrywlqjxdbrbaomnw

Output

8

inputFormat

Input

Input is given from Standard Input in the following format:

s

outputFormat

Output

Print the minimum necessary number of operations to achieve the objective.

Examples

Input

serval

Output

3

Input

jackal

Output

2

Input

zzz

Output

0

Input

whbrjpjyhsrywlqjxdbrbaomnw

Output

8

样例

serval

3