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;
const int INF = 0x3f3f3f3f;
int main() {
  char a[100010];
  int loc[26], len[26], las[26];
  memset(loc, -1, sizeof loc);
  memset(len, 0, sizeof len);
  memset(las, INF, sizeof las);
  scanf("%s", a);
  int lena = strlen(a);
  for (int i = 0; i < lena; i++) {
    int x = a[i] - 'a';
    len[x] = max(len[x], i - loc[x]);
    las[x] = min(las[x], lena - i);
    loc[x] = i;
  }
  int ans = INF;
  for (int i = 0; i < 26; i++) {
    if (len[i] != 0) ans = min(ans, max(len[i], las[i]));
  }
  printf("%d\n", ans);
}
