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;
char str[1000005];
int vis[305];
int ans[305];
int main() {
  scanf("%s", str + 1);
  int tmp = 1e7;
  int len = strlen(str + 1);
  for (int i = 1; i <= len; i++) {
    ans[str[i]] = max(ans[str[i]], i - vis[str[i]]);
    vis[str[i]] = i;
  }
  for (int i = 0; i <= 300; i++)
    if (ans[i]) {
      ans[i] = max(ans[i], len + 1 - vis[i]);
      tmp = min(tmp, ans[i]);
    }
  if (tmp == 1e7) {
    tmp = len / 2 + 1;
  }
  printf("%d\n", tmp);
  return 0;
}
