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() {
  int n;
  scanf("%d", &n);
  long long mi = LONG_LONG_MAX;
  int dif = INT_MAX;
  int prev = 0;
  for (int i = 0; i < n; i++) {
    long long a;
    scanf("%d", &a);
    if (i == 0) {
      mi = a;
      prev = 0;
    } else {
      if (a < mi) {
        mi = a;
        prev = i;
        dif = INT_MAX;
      } else if (a == mi) {
        dif = min(dif, i - prev);
        prev = i;
      }
    }
  }
  printf("%d\n", dif);
  return 0;
}
