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;
int main() {
  string s;
  cin >> s;
  s = " " + s;
  int n = s.size();
  vector<int> v[26];
  for (int i = 1; i < n; i++) v[s[i] - 'a'].push_back(i);
  int ans = n - 1;
  for (int i = 0; i < 26; i++) {
    int sb = 0, l = 0;
    for (int j = 0; j < v[i].size(); j++) {
      sb = max(sb, v[i][j] - l);
      l = v[i][j];
    }
    if (v[i].size() > 0) ans = min(ans, max(sb, n - v[i][v[i].size() - 1]));
  }
  cout << ans << endl;
  return 0;
}
