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() {
  long int n, i;
  cin >> n;
  long int a[n + 1], b[n + 1], min = 1000000005, j;
  for (i = 0; i < n; i++) {
    cin >> a[i];
    if (a[i] < min) min = a[i];
  }
  long int t;
  for (i = 0; i < n; i++) {
    if (a[i] == min) {
      t = i;
      break;
    }
  }
  long int p = 0;
  long int min1 = 1000000005;
  for (j = i + 1; j < n; j++) {
    if (a[j] == min) {
      b[p] = j - t;
      if (b[p] < min1) {
        min1 = b[p];
      }
      t = j;
      p++;
    }
  }
  cout << min1 << endl;
}
