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() {
  ios::sync_with_stdio(0);
  string s;
  cin >> s;
  int n = s.length();
  map<char, vector<int>> mp;
  for (int i = 0; i < n; i++) {
    mp[s[i]].push_back(i);
  }
  int ans = 1e6;
  for (char c = 'a'; c <= 'z'; c++) {
    int mx = 0;
    int nn = mp[c].size();
    if (nn == 0) continue;
    for (int i = 0; i <= nn; i++) {
      if (i == 0)
        mx = max(mx, mp[c][i] + 1);
      else if (i == nn)
        mx = max(n - mp[c][i - 1], mx);
      else
        mx = max(mx, mp[c][i] - mp[c][i - 1]);
    }
    if (mx != 0) ans = min(ans, mx);
  }
  cout << min(ans, n / 2 + 1) << endl;
  return 0;
}
