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;
const int N = 1e5 + 5;
const int INF = 1e9;
int a[N], n;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  int minimum, distance, j;
  minimum = distance = j = INF;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    if (a[i] < minimum) {
      minimum = a[i];
      distance = INF;
      j = i;
    } else if (a[i] == minimum) {
      distance = min(distance, abs(j - i));
      j = i;
    }
  }
  cout << distance << '\n';
  return 0;
}
