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 n, a[100001], c[100001], d, m, x(1e9);
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) {
    scanf("%d", &a[i]);
    x = min(x, a[i]);
  }
  for (int i = 1; i <= n; ++i) {
    if (a[i] == x) {
      c[++d] = i;
    }
  }
  m = 1e9;
  for (int i = 2; i <= d; ++i) m = min(m, c[i] - c[i - 1]);
  printf("%d\n", m);
  return 0;
}
