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>
using namespace std;
int main() {
  long long int n, i = 0;
  cin >> n;
  long long int A[n], B[n];
  while (i < n) {
    cin >> A[i];
    i++;
  }
  long long int min = A[0], k = 0;
  for (i = 0; i < n; i++) {
    if (A[i] < min) {
      min = A[i];
    }
  }
  for (i = 0; i < n; i++) {
    if (A[i] == min) {
      B[k] = i;
      k++;
    }
  }
  long long int min1 = B[1] - B[0];
  for (i = 0; i < k - 1; i++) {
    if ((B[i + 1] - B[i]) < min1) min1 = B[i + 1] - B[i];
  }
  cout << min1 << endl;
  return 0;
}
