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[100001];
int main() {
  int n, mini, temp;
  cin >> n;
  cin >> mini;
  int minindex = 0, maxindex = 0, flag = 1;
  for (int i = 1; i < n; i++) {
    cin >> temp;
    if (mini == temp) {
      maxindex = i;
      a[flag] = i;
      flag++;
    }
    if (temp < mini) {
      mini = temp;
      minindex = i;
      maxindex = i;
      flag = 0;
      a[flag] = i;
      flag++;
    }
  }
  sort(a, a + flag);
  for (int i = 0; i < flag - 1; i++) a[i] = a[i + 1] - a[i];
  temp = a[0];
  for (int i = 1; i < flag - 1; i++) {
    if (temp > a[i]) temp = a[i];
  }
  cout << temp;
  return 0;
}
