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;
struct node {
  int id;
  int no;
} a[100001];
int n, tot = 1, minn = 2100000000;
bool cmp(node a, node b) {
  if (a.no != b.no) return a.no < b.no;
  return a.id < b.id;
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i].no);
    a[i].id = i;
  }
  sort(a + 1, a + n + 1, cmp);
  while (a[tot].no == a[tot + 1].no) {
    minn = min(minn, a[tot + 1].id - a[tot].id);
    tot++;
  }
  printf("%d", minn);
  return 0;
}
