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>
int a[100050];
int main() {
  int n;
  while (~scanf("%d", &n)) {
    int minn = 1e9 + 7, p;
    for (int i = 1; i <= n; i++) {
      scanf("%d", &a[i]);
      if (a[i] < minn) {
        minn = a[i];
        p = i;
      }
    }
    int d = p, ans = 1e9 + 7;
    for (int i = p + 1; i <= n; i++) {
      if (a[i] == minn) {
        if (i - d < ans) {
          ans = i - d;
        }
        d = i;
      }
    }
    printf("%d\n", ans);
  }
}
