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 n, ans = 1e9;
struct none {
  int s, id;
} a[100005];
bool cmp(none p, none q) {
  if (p.s != q.s) return p.s < q.s;
  return p.id < q.id;
}
int main(void) {
  cin >> n;
  for (int i = 0; i < n; i++) cin >> a[i].s, a[i].id = i;
  sort(a, a + n, cmp);
  for (int i = 0; i < n && a[i].s == a[i + 1].s; i++)
    ans = min(ans, a[i + 1].id - a[i].id);
  cout << ans;
}
