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 i, j, mi = 1e9, n, a[100100], l, r;
vector<long long> v;
int main() {
  cin >> n;
  for (i = 0; i < n; i++) {
    cin >> a[i];
    mi = min(mi, a[i]);
  }
  for (i = 0; i < n; i++)
    if (a[i] == mi) v.push_back(i + 1);
  l = v.size() - 1;
  mi = 1e9;
  for (i = 0; i < l; i++) mi = min(mi, v[i + 1] - v[i]);
  cout << mi;
}
