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() {
  ios::sync_with_stdio(false);
  int n, i, cou, j, k, val;
  long long num, m, n2, m2;
  char RE;
RE:
  cin >> n;
  long long A[n], B[n];
  if (n < 2 && n > 100000) goto RE;
  for (i = 0; i < n; i++) {
    cin >> A[i];
  }
  m = A[0];
  j = 0;
  for (i = 1; i < n; i++) {
    if (m > A[i]) {
      m = min(m, A[i]);
      j = i;
    }
  }
  m2 = 0;
  k = 0;
  for (i = j; i < n; i++) {
    if (A[i] == m) {
      B[k] = i;
      k++;
      m2++;
    }
  }
  k = k - 1;
  cou = 1000000;
  for (i = 0; i < k; i++) {
    val = B[i + 1] - B[i];
    if (val < cou) cou = val;
  }
  cout << cou << endl;
}
