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 main() {
  int n, i, f1 = 0, x = 0, y = 0;
  cin >> n;
  long long a[n], min1 = 1000000001, min2 = min1;
  for (i = 0; i < n; i++) {
    cin >> a[i];
    if (a[i] < min1) {
      min1 = a[i];
    }
  }
  for (i = 0; i < n; i++) {
    if (a[i] == min1 && f1 == 0) {
      x = i;
      f1 = 1;
    } else if (a[i] == min1 && f1 == 1) {
      y = i;
      if (y - x < min2) min2 = y - x;
      x = y;
    }
  }
  cout << min2;
  return 0;
}
