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 Main
{
public static void main(String[] ar)
{
Scanner sc = new Scanner(System.in);
int n = sc.nextInt();
int[] arr = new int[n];
int min = Integer.MAX_VALUE;
for(int i=0; i<n;i++)
{
arr[i] = sc.nextInt();
if(arr[i] < min)
min = arr[i];
}

int x =-1;
int diff;
int mindiff=Integer.MAX_VALUE;
int pos=0;
for(int j=0; j<n;j++)
{
if(arr[j] == min && x==-1)
{
pos =j;
x=0;
}
else if(arr[j] == min && x!=-1)
{
diff = j-pos;
if(mindiff > diff)
mindiff = diff;
pos=j;
}
}
System.out.println(mindiff);

}

}