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, i, a, j = 0, b, len;
  int chouba[100000], jix[100000];
  scanf("%d", &n);
  for (i = 0; i < n; i++) {
    scanf("%d", &chouba[i]);
  }
  a = chouba[0];
  for (i = 1; i < n; i++) {
    if (a > chouba[i]) a = chouba[i];
  }
  for (i = 0; i < n; i++) {
    if (chouba[i] == a) {
      jix[j] = i;
      j++;
    }
  }
  b = jix[1] - jix[0];
  for (i = 0; i < j - 1; i++) {
    if (jix[i + 1] - jix[i] < b) b = jix[i + 1] - jix[i];
  }
  printf("%d", b);
  return 0;
}
