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.*;
import java.lang.*;
import java.io.*;
 
///*
public class Solution{
    public static void main (String[] args) throws java.lang.Exception{
        Scanner in = new Scanner(System.in);
            int n=in.nextInt();
            Data d[] = new Data[n];
            for(int i=0;i<n;i++){
                d[i]=new Data(in.nextInt(),i);
            }
            Arrays.sort(d,new Com());
            int min =n+1;
            for(int i=1;i<n;i++){
                if(d[i-1].a==d[i].a){
                    if(min>d[i].b-d[i-1].b){
                        min=d[i].b-d[i-1].b;
                    }
                }
                else{
                    break;
                }
            }
            System.out.println(min);
        }
}
class Data{
    int a,b;
    public Data(int a,int b){
        this.a= a;
        this.b=b;
    }
}
class Com implements Comparator<Data>{
    public int compare(Data a,Data b){
        if(a.a>b.a){
            return 1;
        }
        if(a.a<b.a){
            return -1;
        }
        if(a.b>b.b){
            return 1;
        }
        if(a.b<b.b){
            return -1;
        }
        return 0;
    }
}
//*/
/*
class Solution{
    public static void main (String[] args) throws java.lang.Exception{
        Scanner in = new Scanner(System.in);
        int t=in.nextInt();
        while(t-->0){
            int n=in.nextInt();
        }
    }
}
*/
/*
class Solution{
    public static void main (String[] args) throws java.lang.Exception{
        Scanner in = new Scanner(System.in);
        int t=in.nextInt();
        while(t-->0){
            int n=in.nextInt();
        }
    }
}
*/
/*
class Solution{
    public static void main (String[] args) throws java.lang.Exception{
        Scanner in = new Scanner(System.in);
        int t=in.nextInt();
        while(t-->0){
            int n=in.nextInt();
        }
    }
}
*/
/*
class Solution{
    public static void main (String[] args) throws java.lang.Exception{
        Scanner in = new Scanner(System.in);
        int t=in.nextInt();
        while(t-->0){
            int n=in.nextInt();
        }
    }
}
        arr[j]=arr[i]^arr[j];
        arr[i]=arr[i]^arr[j];
        a2[i]=a2[i]^a2[j];
        a2[j]=a2[i]^a2[j];
        a2[i]=a2[i]^a2[j];
    }    
}
*/
