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;
const int MOD = 1000000007;
const int MAX = 1000005;
int main(void) {
  int arr[100001], n, i, pos, mini, res, len;
  while (scanf("%d", &n) != EOF) {
    for (i = 0; i < n; i++) scanf("%d", &arr[i]);
    mini = arr[0];
    pos = 0;
    for (i = 1; i < n; i++) {
      if (mini > arr[i]) {
        mini = arr[i];
        pos = i;
      }
    }
    vector<int> v;
    v.push_back(pos);
    for (i = pos + 1; i < n; i++)
      if (mini == arr[i]) v.push_back(i);
    mini = 1e5;
    len = v.size();
    for (i = 1; i < len; i++) {
      res = v[i] - v[i - 1];
      if (mini > res) mini = res;
    }
    printf("%d\n", mini);
  }
  return 0;
}
