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 Main {
    static int[][] canExit;
    static int[][] vis;

    static class Pair{
        int ind, val;
        Pair(int i, int v){
            ind=i;
            val=v;
        }
    }


    static void solve() throws Exception {
		int n = sc.nextInt();
		int[] arr = sc.intArr(n);
		int[] b = new int[n];
		for (int i=1;i<n;i++){
			if (arr[i]<arr[i-1] || arr[i]>i+1){
				pw.println(-1);
				return;
			}
		}
		HashSet<Integer> nextMax = new HashSet<>();

		for (int i=0;i<n;i++){
			nextMax.add(arr[i]);
			if (arr[i]>i+1){
				pw.println(-1);
				return;
			}
		}

		int[] res = new int[n];
		int curr = 0;
		int mex= 0;
		for (int i=0;i<n;i++){
			res[i] = Integer.MAX_VALUE;
			if (i!=0){
				if (arr[i]!=arr[i-1]){
					res[i]=arr[i-1];
					continue;
				}	
			}
			while (nextMax.contains(curr))curr++;
		
			res[i] = curr;
			curr++;

			
			
		}
		for (int i=0;i<n;i++){
			pw.print(res[i] + " ");
		}
    }



    static PrintWriter pw;
    static MScanner sc;

    public static void main(String[] args) throws Exception {

        pw = new PrintWriter(System.out);
        sc = new MScanner(System.in);

        ///int tests =sc.nextInt();
        int tests = 1;
        while (tests-- > 0){
            solve();
            pw.flush();
        }

    }

    static class MScanner {
        StringTokenizer st;
        BufferedReader br;

        public MScanner(InputStream system) {
            br = new BufferedReader(new InputStreamReader(system));
        }

        public MScanner(String file) throws Exception {
            br = new BufferedReader(new FileReader(file));
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        public int[] intArr(int n) throws IOException {
            int[] in = new int[n];
            for (int i = 0; i < n; i++)
                in[i] = nextInt();
            return in;
        }

        public long[] longArr(int n) throws IOException {
            long[] in = new long[n];
            for (int i = 0; i < n; i++)
                in[i] = nextLong();
            return in;
        }

        public int[] intSortedArr(int n) throws IOException {
            int[] in = new int[n];
            for (int i = 0; i < n; i++)
                in[i] = nextInt();
            shuffle(in);
            Arrays.sort(in);
            return in;
        }

        public long[] longSortedArr(int n) throws IOException {
            long[] in = new long[n];
            for (int i = 0; i < n; i++)
                in[i] = nextLong();
            shuffle(in);
            Arrays.sort(in);
            return in;
        }

        public Integer[] IntegerArr(int n) throws IOException {
            Integer[] in = new Integer[n];
            for (int i = 0; i < n; i++)
                in[i] = nextInt();
            return in;
        }

        public Long[] LongArr(int n) throws IOException {
            Long[] in = new Long[n];
            for (int i = 0; i < n; i++)
                in[i] = nextLong();
            return in;
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

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

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

        public char nextChar() throws IOException {
            return next().charAt(0);
        }

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

        public boolean ready() throws IOException {
            return br.ready();
        }

        public void waitForInput() throws InterruptedException {
            Thread.sleep(3000);
        }
    }

    static void shuffle(int[] in) {
        for (int i = 0; i < in.length; i++) {
            int idx = (int) (Math.random() * in.length);
            int tmp = in[i];
            in[i] = in[idx];
            in[idx] = tmp;
        }
    }

    static void shuffle(long[] in) {
        for (int i = 0; i < in.length; i++) {
            int idx = (int) (Math.random() * in.length);
            long tmp = in[i];
            in[i] = in[idx];
            in[idx] = tmp;
        }
    }
}
