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() {
  cin.tie(0);
  ios_base::sync_with_stdio(0);
  string s;
  cin >> s;
  int length = s.size();
  vector<int> arr[26];
  for (int i = 0; i < length; i++) {
    arr[s[i] - 'a'].push_back(i);
  }
  int hi = INT_MAX;
  for (int i = 0; i < 26; i++) {
    if (arr[i].empty()) continue;
    int lo = arr[i][0] + 1;
    for (int j = 1; j < (int)arr[i].size(); j++) {
      lo = max(lo, arr[i][j] - arr[i][j - 1]);
    }
    lo = max(lo, length - arr[i].back());
    hi = min(hi, lo);
  }
  cout << hi;
}
