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 test {
    public static void main (String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        
        int[] arr = new int[n];
        boolean[] num = new boolean[100001];
        int[] res = new int[n];

        boolean canDo = true;
        for (int i=0; i<n; i++) {
            arr[i] = sc.nextInt();
            if (arr[i]-i > 1) {
                canDo = false;
                break;
            }
            else {
                num[arr[i]] = true;
            }
        }

        if (canDo) {
            int j = 0;
            while (num[j]) {
                j += 1;
            }
            res[0] = j;
            num[j] = true;

            for (int i=1; i<n; i++) {
                if (arr[i] != arr[i-1]) {
                    res[i] = arr[i-1];
                }
                else {
                    while (num[j]) {
                        j += 1;
                    }
                    res[i] = j;
                    num[j] = true;
                }
            }

            for (int i=0; i<n; i++) {
                System.out.print(res[i] + " ");
            }
            System.out.println();
        }
        else {
            System.out.println(-1);
        }
    }
}