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;
signed main() {
  long long n, mx = LLONG_MAX, ans = LLONG_MAX, mn = LLONG_MAX;
  vector<long long> a(100005);
  map<long long, long long> m;
  cin >> n;
  for (long long i = 1; i <= n; i++) cin >> a[i], mn = min(mn, a[i]);
  for (long long i = 1; i <= n; i++) {
    if (m[a[i]] > 0 && a[i] == mn) ans = i - m[a[i]];
    m[a[i]] = i;
    mx = min(mx, ans);
  }
  cout << mx;
}
