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 a[100000];
int main() {
  int n, min1 = 100000;
  cin >> n;
  for (int i = 0; i < n; i++) cin >> a[i];
  int x = a[0], y = 0;
  for (int i = 1; i < n; i++) {
    if (x > a[i]) {
      x = a[i];
      y = i;
    }
  }
  for (int i = 0; i < n; i++)
    if (x == a[i] && y != i) {
      min1 = min(min1, abs(y - i));
      y = i;
    }
  cout << min1 << endl;
  return 0;
}
