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[100020] = {0};
int main() {
  int n, i, dis1, dis2 = 0, dis = 0, min;
  scanf("%d", &n);
  for (i = 1; i <= n; i++) {
    scanf("%d", &A[i]);
    if (min > A[i] || i == 1) min = A[i];
  }
  for (i = 1; i <= n; i++)
    if (A[i] == min) {
      if (dis2 == 0) dis2 = i;
      dis1 = dis2;
      dis2 = i;
      if (dis > dis2 - dis1 || dis == 0) dis = dis2 - dis1;
    }
  printf("%d", dis);
  return 0;
}
