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 N = 1e5 + 5;
map<int, int> m;
int main() {
  int n;
  scanf("%d", &n);
  int mn = 1e6;
  int x;
  int g = 1e9;
  for (int i = 1; i <= n; i++) {
    scanf("%d", &x);
    if (!m[x]) {
      m[x] = i;
    } else {
      if (g >= x) {
        if (g == x)
          mn = min(mn, i - m[x]);
        else
          mn = i - m[x];
        m[x] = i;
        g = x;
      }
    }
  }
  printf("%d", mn);
  return 0;
}
