You are given an array of n integer numbers a0, a1, ..., an - 1. Find the distance between two closest (nearest) minimums in it. It is guaranteed that in the array a minimum occurs at least two times.

Input

The first line contains positive integer n (2 ≤ n ≤ 105) — size of the given array. The second line contains n integers a0, a1, ..., an - 1 (1 ≤ ai ≤ 109) — elements of the array. It is guaranteed that in the array a minimum occurs at least two times.

Output

Print the only number — distance between two nearest minimums in the array.

Examples

Input

2
3 3


Output

1


Input

3
5 6 5


Output

2


Input

9
2 1 3 5 4 1 2 3 1


Output

3
#include <bits/stdc++.h>
using namespace std;
int lol[100002];
int main() {
  int n, nr, i, m;
  cin >> n >> m;
  lol[0] = 1;
  lol[1] = 0;
  for (i = 1; i < n; i++) {
    cin >> nr;
    if (nr == m)
      lol[++lol[0]] = i;
    else if (nr < m) {
      m = nr;
      lol[0] = 1;
      lol[1] = i;
    }
  }
  nr = lol[2] - lol[1];
  for (i = 3; i <= lol[0]; i++)
    if (lol[i] - lol[i - 1] < nr) nr = lol[i] - lol[i - 1];
  cout << nr;
  return 0;
}
