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>
const long long maxx = 1e9 + 10;
using namespace std;
long long n, a[100005], minn = maxx, i, min2, vt;
int main() {
  cin >> n;
  for (i = 1; i <= n; ++i) {
    cin >> a[i];
    if (a[i] < minn) minn = a[i];
  }
  for (i = 1; i <= n; ++i)
    if (a[i] == minn) break;
  vt = i;
  min2 = n;
  for (i += 1; i <= n; ++i)
    if (a[i] == minn) {
      if (i - vt < min2) min2 = i - vt;
      vt = i;
    }
  cout << min2;
  return 0;
}
