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 int N, nrmax = 1000000001;
  int i, nr, curr = 0, spent = 0;
  cin >> N;
  long int v[N];
  for (i = 0; i < N; i++) {
    cin >> nr;
    if (nr == nrmax) {
      v[curr] = spent;
      curr++;
      spent = 0;
    }
    if (nr < nrmax) {
      nrmax = nr;
      curr = 0;
      spent = 0;
    }
    spent++;
  }
  nrmax = v[0];
  for (i = 1; i < curr; i++) {
    if (nrmax > v[i]) nrmax = v[i];
  }
  cout << nrmax;
}
