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>
const int inf = 1e9 + 7;
const int N = 1e5 + 50;
int minn, wz, n, x, ans;
int main() {
  scanf("%d", &n);
  minn = inf;
  ans = n;
  for (int i = 1; i <= n; i++) {
    scanf("%d", &x);
    if (minn == x && ans > i - wz) ans = i - wz;
    if (minn == x) wz = i;
    if (minn > x) minn = x, wz = i, ans = n;
  }
  printf("%d\n", ans);
}
