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 long int n;
  cin >> n;
  long long int a[n], i, b[2], j, p;
  for (i = 0; i < n; i++) cin >> a[i];
  b[0] = 0, b[1] = 1000000;
  for (i = 1; i < n; i++) {
    if (a[i] < a[b[0]]) {
      b[0] = i;
      b[1] = 1000000;
    } else if (a[i] == a[b[0]]) {
      if (b[1] == 1000000)
        p = b[1] = i;
      else if ((b[1] - b[0]) > (i - p)) {
        b[0] = p;
        p = b[1] = i;
      } else
        p = i;
    }
  }
  cout << (b[1] - b[0]);
  return 0;
}
