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.*;

/**
 *
 * @author m.zhaksygeldy
 */
public class MergeSort {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        Num[] nums = new Num[n];
        MergeSort c = new MergeSort();
        for (int i = 0; i < n; i++) {
            nums[i] = c.new Num(i, sc.nextInt());
        }
        
        Arrays.sort(nums);        
        int count = nums.length;
        Num min = nums[0];
        for (int i = 0; i < n - 1; i++) {
            if(count == nums.length) {
                min = nums[i];
            } 
            if(min.val == nums[i].val && nums[i].val == nums[i+1].val) {
                int currCount = nums[i+1].index - nums[i].index;
                count = Math.min(currCount, count);            
            } else if(count != nums.length){
                break;
            }
        }
        
        System.out.println(count);
    }
    
    public class Num implements Comparable<Num> {

        public int index;
        public int val;

        public Num(int index, int val) {
            this.index = index;
            this.val = val;
        }

        @Override
        public int compareTo(Num o) {
            if (val > o.val) {
                return 1;
            }
            if (val < o.val) {
                return -1;
            }
            return 0;
        }

    }
    
}
