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 MIN = 0x7fffffff;
int main() {
  int n, i, j, loc1, loc2 = 100010;
  int num[100050];
  scanf("%d", &n);
  for (i = 1; i <= n; i++) {
    cin >> num[i];
    if (num[i] < MIN) {
      MIN = num[i];
      loc1 = i;
    }
  }
  for (i = loc1 + 1; i <= n; i++) {
    if (num[i] == MIN) {
      loc2 = min(loc2, i - loc1);
      loc1 = i;
    }
  }
  cout << loc2 << endl;
  return 0;
}
