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
import java.util.*;
public class minimums {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        long[] values = new long[N];
        for(int i=0;i<N;i++){
            values[i] = sc.nextInt();
        }
        long minimum = (long)(Math.pow(10,9)+1);
        for(int i=0;i<N;i++){
            if(values[i]<minimum){
                minimum = values[i];
            }
        }
        ArrayList<Integer> minindices = new ArrayList<>();
        for(int i=0;i<N;i++){
            if(values[i]==minimum){
                minindices.add(i);
            }
        }
        int mindistance = 1000000;
        for(int i=0;i<minindices.size()-1;i++){
            if(minindices.get(i+1)-minindices.get(i)<mindistance){
                mindistance = minindices.get(i+1)-minindices.get(i);
            }
        }
        System.out.println(mindistance);
    }
}
