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[100005];
int main() {
  for (int i = 0; i < 100; i++) {
    int a = i;
  }
  int n;
  scanf("%d", &n);
  int minn = 100005;
  int minx = 1000000001;
  for (int i = 0; i < n; i++) {
    scanf("%d", &a[i]);
    minx = min(minx, a[i]);
  }
  int pre = -1;
  for (int i = 0; i < n; i++) {
    if (a[i] == minx && pre != -1) {
      minn = min(minn, i - pre);
      pre = i;
    } else if (pre == -1 && a[i] == minx)
      pre = i;
  }
  cout << minn << endl;
  return 0;
}
