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 nol;
  scanf("%d", &nol);
  int min = 1000000000;
  int number[100001];
  for (int i = 0; i < nol; i++) {
    scanf("%d", &number[i]);
    if (number[i] < min) {
      min = number[i];
    }
  }
  int tampung[100001];
  int a = 0;
  for (int i = 0; i < nol; i++) {
    if (number[i] == min) {
      tampung[a] = i;
      a++;
    }
  }
  min = 1000000000;
  for (int j = 0; j < a - 1; j++) {
    if (tampung[j + 1] - tampung[j] < min) {
      min = tampung[j + 1] - tampung[j];
    }
  }
  printf("%d\n", min);
  return 0;
}
