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.*;
import java.util.*;

public class C {
    //Solution by Sathvik Kuthuru
    public static void main(String[] args) {
        FastReader scan = new FastReader();
        PrintWriter out = new PrintWriter(System.out);
        Task solver = new Task();
        int t = 1;
        for(int tt = 1; tt <= t; tt++) solver.solve(tt, scan, out);
        out.close();
    }

    static class Task {

        public void solve(int testNumber, FastReader scan, PrintWriter out) {
            int n = scan.nextInt();
            int[] a = new int[n];
            for(int i = 0; i < n; i++) {
                a[i] = scan.nextInt();
            }
            if(a[0] >= 2) {
                out.println(-1);
                return;
            }
            int[] res = new int[n];
            Arrays.fill(res, Integer.MAX_VALUE / 10);
            res[0] = a[0] ^ 1;
            TreeMap<Integer, ArrayDeque<Integer>> unusued = new TreeMap<>();
            TreeSet<Integer> need = new TreeSet<>();
            for(int i = 0; i <= n + 100; i++) need.add(i);
            need.remove(res[0]);
            for(int i = 1; i < n; i++) {
                res[i] = res[i - 1];
                add(unusued, a[i], i);
                TreeMap<Integer, ArrayDeque<Integer>> temp = new TreeMap<>();
                while(need.first() != a[i]) {
                    int f = need.first();
                    Integer prev = unusued.higherKey(f);
                    if(prev != null) {
                        int get = remove(unusued, prev);
                        add(temp, prev, get);
                        res[get] = f;
                        need.pollFirst();
                        continue;
                    }
                    Integer next = unusued.lowerKey(f);
                    if(next != null) {
                        int get = remove(unusued, next);
                        add(temp, next, get);
                        res[get] = f;
                        need.pollFirst();
                        continue;
                    }
                    if(unusued.containsKey(f)) {
                        int currIndex = remove(unusued, f);
                        prev = temp.higherKey(f);
                        if(prev != null) {
                            int get = remove(temp, prev);
                            int t = res[get];
                            res[get] = f;
                            res[currIndex] = t;
                            add(temp, f, currIndex);
                            add(temp, prev, get);
                            need.pollFirst();
                            continue;
                        }
                        prev = temp.lowerKey(f);
                        if(prev != null) {
                            int get = remove(temp, prev);
                            int t = res[get];
                            res[get] = f;
                            res[currIndex] = t;
                            add(temp, f, currIndex);
                            add(temp, prev, get);
                            need.pollFirst();
                            continue;
                        }
                    }
                    out.println(-1);
                    return;
                }
            }
            for(int i : res) out.printf("%d ", i);
        }
    }

    static void add(TreeMap<Integer, ArrayDeque<Integer>> a, int v, int i) {
        ArrayDeque<Integer> curr = a.getOrDefault(v, new ArrayDeque());
        curr.addLast(i);
        if(!a.containsKey(v)) a.put(v, curr);
    }

    static int remove(TreeMap<Integer, ArrayDeque<Integer>> a, int v) {
        int ret = a.get(v).pollFirst();
        if(a.get(v).isEmpty()) a.remove(v);
        return ret;
    }

    static void shuffle(int[] a) {
        Random get = new Random();
        for (int i = 0; i < a.length; i++) {
            int r = get.nextInt(a.length);
            int temp = a[i];
            a[i] = a[r];
            a[r] = temp;
        }
    }

    static void shuffle(long[] a) {
        Random get = new Random();
        for (int i = 0; i < a.length; i++) {
            int r = get.nextInt(a.length);
            long temp = a[i];
            a[i] = a[r];
            a[r] = temp;
        }
    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public FastReader(String s) throws FileNotFoundException {
            br = new BufferedReader(new FileReader(new File(s)));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

}