Given an array a of length n, find another array, b, of length n such that:

  * for each i (1 ≤ i ≤ n) MEX(\\{b_1, b_2, …, b_i\})=a_i. 



The MEX of a set of integers is the smallest non-negative integer that doesn't belong to this set.

If such array doesn't exist, determine this.

Input

The first line contains an integer n (1 ≤ n ≤ 10^5) — the length of the array a.

The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ i) — the elements of the array a. It's guaranteed that a_i ≤ a_{i+1} for 1≤ i < n.

Output

If there's no such array, print a single line containing -1.

Otherwise, print a single line containing n integers b_1, b_2, …, b_n (0 ≤ b_i ≤ 10^6)

If there are multiple answers, print any.

Examples

Input


3
1 2 3


Output


0 1 2 

Input


4
0 0 0 2


Output


1 3 4 0 

Input


3
1 1 3


Output


0 2 1 

Note

In the second test case, other answers like [1,1,1,0], for example, are valid.

import java.util.*;

public class tt_1364C {

    public static void main(String[] args){

        Scanner sc = new Scanner(System.in);

        int n = sc.nextInt();
        int[] arr = new int[n];
        StringBuilder sb = new StringBuilder();
        for(int i=0; i<n; i++){
            arr[i] = sc.nextInt();
        }
        int[] res = new int[n];
        Deque<Integer> largerElements = new ArrayDeque<>(n);
        Deque<Integer> smallerElements = new ArrayDeque<>(n);
        for(int i=0; i<arr[n-1]; i++){
            smallerElements.addFirst(i);
        }
        for(int i=n-1; i>=1; i--){
            if(arr[i] != arr[i-1]){
                while(smallerElements.peek()>arr[i-1]){
                    largerElements.addLast(smallerElements.removeFirst());
                }
                res[i] = smallerElements.removeFirst();
                //sb.append(smallerElements.removeFirst()+" ");
            }
            else {
                if(largerElements.size()!=0){
                    res[i] = largerElements.removeFirst();
                    //sb.append(largerElements.removeFirst()+" ");
                }
                else {
                    System.out.println("here "+i);
                    res[i] = arr[n-1]+10;
                }
            }
        }
        if(largerElements.size()+smallerElements.size()<=1){
            int x = 0;
            if(largerElements.size()==1){
                x+=largerElements.remove();
            }
            else if(smallerElements.size()==1){
                x+=smallerElements.remove();
            }
            else {
                x+=(arr[n-1]+10);
            }
            res[0] = x;
            sb.append(x+" ");
            int index = 0;
            StringBuilder ss = new StringBuilder();
            for(int i=0; i<n; i++){
                if(res[i] == 153){
                    index = i;
                }
                ss.append(res[i]+" ");
            }
            System.out.println(ss.toString());
            /*System.out.println(index);
            int[] sm = new int[126];
            for(int i=0; i<index; i++){
                sm[i] = res[i];
            }
            Arrays.sort(sm);
            for(int xx: sm){
                System.out.print(xx+" ");
            }*/
        }
        else {
            System.out.println(-1);
        }
    }

}
