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() {
  int n;
  map<int, vector<int>> mp;
  cin >> n;
  int arr[n];
  int min = 1000000001;
  for (int i = 0; i < n; i++) {
    cin >> arr[i];
    mp[arr[i]].push_back(i);
    if (arr[i] < min) min = arr[i];
  }
  map<int, vector<int>>::iterator itr = mp.find(min);
  int ans = n + 2;
  vector<int> v1 = itr->second;
  for (int j = 1; j < v1.size(); j++) {
    if (v1[j] - v1[j - 1] < ans) ans = v1[j] - v1[j - 1];
  }
  cout << ans;
  return 0;
}
