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.lang.reflect.Array;
import java.util.*;

public class Main {


    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int n = sc.nextInt();
        int[] a = new int[n];
        TreeMap<Integer, Integer> heap = new TreeMap<>();
        HashMap<Integer, Integer> cant = new HashMap<>();

        for (int i = 0; i <= 5; i++) {
            heap.put(i, 1);
        }
        for (int i = 0; i < n; i++) {
            a[i] = sc.nextInt();
            heap.remove(a[i]);
            cant.put(a[i], cant.getOrDefault(a[i], 0) + 1);
        }
        int[] b = new int[n];
        for (int i = 0; i < n; i++) {
            if (heap.isEmpty()){
                return;
            }
            int pointer = heap.firstKey();
            b[i] = pointer;

            heap.put(pointer, heap.getOrDefault(pointer, 0) - 1);
            if (heap.get(pointer) <= 0)
                heap.remove(pointer);

            cant.put(a[i], cant.get(a[i]) - 1);
            if (cant.containsKey(a[i]) && cant.get(a[i]) <= 0) {
                cant.remove(a[i]);
                heap.put(a[i], heap.getOrDefault(a[i], 0) + 1);
                if (heap.get(a[i]) <= 0)
                    heap.remove(a[i]);
            }

            System.out.print(b[i] + " ");
        }
        System.out.println();

    }
}
