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
#include <bits/stdc++.h>
using namespace std;
string s;
int main() {
  cin >> s;
  int p[26];
  int d[26] = {0};
  int lg = int(s.length());
  for (int i = 0; i < 26; ++i) {
    p[i] = -1;
  }
  int index;
  for (int i = 0; i < lg; ++i) {
    index = s[i] - 'a';
    d[index] = max(d[index], i - p[index]);
    p[index] = i;
  }
  for (int i = 0; i < 26; ++i) {
    d[i] = max(d[i], lg - p[i]);
  }
  int dk = 1e9;
  for (int i = 0; i < 26; ++i) {
    dk = min(dk, d[i]);
  }
  dk = min(dk, lg / 2 + 1);
  cout << dk;
  return 0;
}
