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_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  string s;
  cin >> s;
  map<char, int> dis;
  map<char, int> last;
  map<char, int> cnt;
  int n = s.size();
  for (int i = 0; i < n; i++) {
    last[s[i]] = -1;
  }
  for (int i = 0; i < n; i++) {
    if (last[s[i]] != -1) {
      dis[s[i]] = max(dis[s[i]], i - last[s[i]]);
    } else {
      dis[s[i]] = i + 1;
    }
    last[s[i]] = i;
  }
  for (int i = 0; i < n; i++) {
    dis[s[i]] = max(dis[s[i]], n - last[s[i]]);
  }
  int ans = n / 2 + 1;
  for (int i = 0; i < n; i++) {
    if (dis[s[i]] != 0) {
      ans = min(ans, dis[s[i]]);
    }
  }
  cout << ans << '\n';
  return 0;
}
