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;
long long p[100005] = {0};
int main() {
  long long n, mn = 1e10;
  cin >> n;
  long long arr[n], small = 1e9 + 5, c = 0;
  ;
  for (long long i = 0; i < n; i++) {
    cin >> arr[i];
    small = min(small, arr[i]);
  }
  for (long long i = 0; i < n; i++) {
    if (arr[i] == small) {
      p[c] = i;
      c++;
    }
  }
  for (long long i = 0; i < n; i++) {
    if (p[i + 1] - p[i] < mn && p[i + 1] != 0) {
      mn = p[i + 1] - p[i];
    }
  }
  cout << mn;
  return 0;
}
