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>
int main() {
  int n;
  scanf("%d", &n);
  int i;
  int min = 1000000000;
  int a[100001];
  for (i = 0; i < n; i++) {
    scanf("%d", &a[i]);
    if (a[i] < min) {
      min = a[i];
    }
  }
  int first = 1;
  int pre = 0;
  int answer = n;
  for (i = 0; i < n; i++) {
    if (min == a[i]) {
      if (first) {
        pre = i;
        first = 0;
      } else {
        if (i - pre < answer) {
          answer = i - pre;
        }
        pre = i;
      }
    }
  }
  printf("%d\n", answer);
  return 0;
}
