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 a, b = 1, ans = 0x7fffffff, seg[100010], n;
vector<int> g;
int main() {
  cin >> n;
  a = n, b = 1;
  for (int i = 1; i <= n; i++) cin >> seg[i];
  for (int i = 1; i <= n; i++) {
    if (seg[i] < ans) ans = seg[i];
  }
  for (int i = 1; i <= n; i++) {
    if (seg[i] == ans) {
      g.push_back(i);
    }
  }
  ans = 0x7fffffff;
  for (int i = 1; i < g.size(); i++) {
    ans = min(ans, g[i] - g[i - 1]);
  }
  cout << ans;
  return 0;
}
