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, a, mn = INT_MAX, ans = INT_MAX;
  cin >> n;
  map<int, int> mp;
  map<int, int> mp_ans;
  for (int i = 1; i <= n; i++) {
    cin >> a;
    if (mp[a] == 0)
      mp[a] = i;
    else {
      if (a <= mn) {
        mn = a;
        if (mp_ans[a] != 0) {
          ans = min(mp_ans[a], i - mp[a]);
          mp_ans[a] = ans;
        } else {
          mp_ans[a] = i - mp[a];
        }
      }
      mp[a] = i;
    }
  }
  cout << mp_ans[mn];
}
