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() {
  int n, min1, ras = INT_MAX;
  cin >> n;
  int a[n];
  queue<int> v;
  cin >> a[0];
  min1 = a[0];
  v.push(0);
  for (int i = 1; i < n; i++) {
    cin >> a[i];
    if (min1 > a[i]) {
      while (!v.empty()) {
        v.pop();
      }
      v.push(i);
      min1 = a[i];
    } else {
      if (min1 == a[i] && v.size() == 2) {
        int kek = v.front();
        v.pop();
        ras = min(ras, v.front() - kek);
        v.push(i);
      }
      if (min1 == a[i] && v.size() == 1) {
        ras = i - v.front();
        v.push(i);
      }
    }
  }
  int kol = v.front();
  v.pop();
  ras = min(v.front() - kol, ras);
  cout << ras;
}
