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 a[100020];
int main(void) {
  int n;
  int i;
  int o;
  vector<int> v;
  scanf("%d", &n);
  for (i = 1; i <= n; i++) scanf("%d", &a[i]);
  v.clear();
  for (i = 2, v.push_back(1), o = n; i <= n; i++) {
    if (a[i] == a[v.at(0)]) {
      o = min(o, i - v.at(v.size() - 1));
      v.push_back(i);
    }
    if (a[i] < a[v.at(0)]) {
      v.clear();
      v.push_back(i);
      o = n;
    }
  }
  printf("%d\n", o);
  return 0;
}
