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;
  map<char, vector<int> > idx;
  for (char c = 'a'; c <= 'z'; ++c) idx[c].push_back(-1);
  for (int i = 0; i < (int)s.size(); ++i) {
    idx[s[i]].push_back(i);
  }
  for (char c = 'a'; c <= 'z'; ++c) idx[c].push_back(s.size());
  int ans = s.size() / 2 + 1;
  for (char c = 'a'; c <= 'z'; ++c) {
    int ansi = 0;
    for (int i = 1; i < (int)idx[c].size(); ++i) {
      ansi = max(ansi, idx[c][i] - idx[c][i - 1]);
    }
    ans = min(ans, ansi);
  }
  printf("%d\n", ans);
  return 0;
}
