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 main() {
  int n, min = 1000000005, k, mindis = 1000000005, x1;
  scanf("%d", &n);
  x1 = 0;
  for (int i = 1; i <= n; i++) {
    scanf("%d", &k);
    if (k < min) {
      min = k;
      mindis = 1000000005;
      x1 = i;
    } else if (k == min) {
      if (x1 != 0) {
        if (i - x1 < mindis) mindis = i - x1;
        x1 = i;
      }
    }
  }
  printf("%d", mindis);
}
