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;
  int a[100005], x, i;
  int minValue = 1000000001;
  int first, diff = 100005;
  scanf("%d", &n);
  for (i = 0; i < n; i++) {
    scanf("%d", &x);
    a[i] = x;
    minValue = min(minValue, x);
  }
  for (i = 0; i < n; i++) {
    if (a[i] == minValue) {
      first = i;
      break;
    }
  }
  for (i = 0; i < n; i++) {
    if (diff == 1) break;
    if (first != i && a[i] == minValue) {
      diff = min((i - first), diff);
      first = i;
    }
  }
  printf("%d\n", diff);
  return 0;
}
