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 n, i, k, x = 0, y = 0, a, j = 0;
  cin >> n;
  for (i = 1; i <= n; i++) {
    cin >> a;
    if (x >= a || x == 0) {
      if (x == a)
        k = min(i - j, k);
      else
        k = i - j;
      x = a;
      if (x <= y || y == 0) {
        swap(x, y);
        j = i;
      }
    }
  }
  cout << k;
}
