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];

        ArrayList<Integer> al = new ArrayList<>();

        int first = -1;

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

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

            if (al.size() == 0) {
                al.add(cur);
                continue;
            }

            if (cur != al.get(al.size() - 1)) {
                al.add(cur);
            }
        }

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

        int ans[] = new int[n];

        ans[0] = (first == 0 ? 1 : 0);

        int index = 1;

        for (int i = 1; i < n; i++) {

            if (index == al.size()) {
                ans[i] = ans[i - 1];
                continue;
            }

            int next = al.get(index);

            int cur = arr[i];

            if (next == cur) {
                ans[i] = arr[i - 1];
                index++;
                continue;
            }

            if (ans[i - 1] < next - 1) {

                if (ans[i - 1] + 1 == cur) {
                    ans[i] = ans[i - 1] + 2;
                } else {
                    ans[i] = ans[i - 1] + 1;
                }

            } else {
                ans[i] = ans[i - 1];
            }

        }

        // PriorityQueue<Integer> pq = new PriorityQueue<>();

        TreeSet<Integer> 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);
    }
}