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 A {

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

        int n = sc.nextInt();

        int arr[] = new int[n];

        TreeSet<Integer> pq = new TreeSet<>();

        HashSet<Integer> set = new HashSet<>();

        int first = -1;

        for (int i = 0; i < n; i++) {
            int cur = sc.nextInt();
            arr[i] = cur;

            set.add(cur);

            if (i == 0) {
                first = cur;
            }
        }

        if (first != 0 && first != 1) {
            System.out.println(-1);
            return;
        }

        int ans[] = new int[n];

        for (int i = 0; i < n; i++) {

            int cur = arr[i];

            if (i != 0 && cur != arr[i - 1]) {
                ans[i] = arr[i - 1];
                continue;
            }

            pq.add(cur);

            int insert = (pq.size() == 0 ? 0 : pq.last()) + 1;

            while (set.contains(insert)) {
                insert++;
            }

            ans[i] = insert;
            pq.add(insert);

        }

        pq = new TreeSet<>();

        for (int i = 0; i <= n; i++) {
            pq.add(i);
        }

        pq.remove(ans[0]);

        sb.append(ans[0]).append(" ");

        for (int i = 0; i < n; i++) {
            if (pq.first() != arr[i]) {
                System.out.println(-1);
                return;
            }

            if (i == n - 1) {
                break;
            }

            sb.append(ans[i + 1]).append(" ");

            pq.remove(ans[i + 1]);
        }

        System.out.print(sb);
    }
}