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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.*;

/**
 * @project: Codeforces649
 * @author: izhanatuly
 * @date: 13/06/2020
 */

public class C {
    static Scanner scanner;

    public static void main(String[] args) {
        scanner = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        runTestCase();
    }

    private static void runTestCase() {
        int n = scanner.nextInt();
        int[] nums = new int[n];
        for(int i=0; i<n; i++) {
            nums[i] = scanner.nextInt();
        }
        if(nums[0]>1) {
            System.out.println(-1);
            return;
        }
        int[] res = new int[n];
        boolean[] taken = new boolean[n+1];
        Queue<Integer> toTake = new LinkedList<>();
        for(int i=n-1; i>0; i--) {
            for(int g=nums[i]-1; g>=nums[i-1]; g--) {
                toTake.add(g);
            }
        }
        Arrays.fill(res, -1);
        for(int i=n-1; i>0; i--) {
            if(nums[i]==nums[i-1]) {
//                System.out.println(i + " " + toTake.peek());
                if(!toTake.isEmpty() && toTake.peek()>nums[i]) {
                    res[i] = toTake.poll();
                    taken[res[i]] = true;
                }
            }
        }
        for(int i=0; i<n; i++) if(res[i]==-1) {
            if(!toTake.isEmpty() && toTake.peek()<nums[i]) {
                res[i] = toTake.poll();
                taken[res[i]] = true;
            }
        }
        int numToTake = 0;
        for(int i=0; i<n; i++) if(res[i]==-1) {
            while(taken[numToTake]) {
                numToTake++;
            }
            res[i] = numToTake;
            taken[res[i]] = true;
        }
        StringBuilder sb = new StringBuilder();
        for(int num : res) {
            sb.append(num);
            sb.append(' ');
        }
        System.out.println(sb.toString());
    }
}