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 n, t, i, d1, d2, a[100000];
int main() {
  while (~scanf("%d", &n)) {
    long long min = 10000000000;
    for (i = 0; i < n; i++) scanf("%d", &a[i]);
    for (i = 0; i < n; i++) {
      if (a[i] < min) min = a[i];
    }
    t = 0;
    d1 = 100000;
    for (i = 0; i < n; i++) {
      if (a[i] == min) {
        if (t == 0) {
          t++;
          d2 = 0;
        } else {
          if (d2 < d1) d1 = d2;
          d2 = 0;
        }
      }
      d2++;
    }
    printf("%d\n", d1);
  }
}
