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.*;
import java.io.*;
import java.io.BufferedReader;
import java.awt.Point;

public class Z_C{
	public static final long mod= 1000000007;
	public static Debug db;

	public static void main(String[] args) throws IOException {
		InputReader in = new InputReader(System.in);
		PrintWriter out = new PrintWriter(System.out);
		Autocompletion solver = new Autocompletion();
		db=new Debug(System.getSecurityManager()==null);
		solver.solve(1, in, out);
		out.close();
	}
	static class Autocompletion {

		public void solve(int testNumber, InputReader in, PrintWriter out) {
			int n=in.nextInt();
			int arr[]=in.nextIntArr(n);
			int ret[]=new int[n];
			int nope[]=new int[n+10000];
			ArrayList<Integer> set=new ArrayList<Integer>();
			for(int i=0;i<n;i++) {
				nope[arr[i]]=1;
				
			}
			for(int i=0;i<nope.length;i++) {
				if(nope[i]==0) {
					set.add(i);
				}
			}
			int now=0;
			
			int pointer=0;
			if(arr[0]==1) {
				pointer++;
			}
			db.debug("set", set);
			for(int i=0;i<n;i++) {
				if(arr[i]==now) {
					ret[i]=set.get(pointer);
					pointer++;
				}
				else {
					ret[i]=now;
					now=arr[i];
				}
			}
			for(int i=0;i<n;i++) {
				out.print(ret[i]+" ");
			}
			out.println();
		}
	}

	static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;
 
        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }
 
        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
 
        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong() {
        	return Long.parseLong(next());
        }
        public int[] nextIntArr(int n) {
        	int arr[]=new int[n];
        	for(int i=0;i<n;i++) {
        		arr[i]=this.nextInt();
        	}
        	return arr;
        }
    }
	public static class Debug {
        private boolean allowDebug;
 
        public Debug(boolean allowDebug) {
            this.allowDebug = allowDebug;
        }
 
        private void outputName(String name) {
            System.out.print(name + " = ");
        }
 
        public void debug(String name, int x) {
            if (!allowDebug) {
                return;
            }
 
            outputName(name);
            System.out.println("" + x);
        }
 
        public void debug(String name, long x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println("" + x);
        }
 
        public void debug(String name, double x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println("" + x);
        }
 
        public void debug(String name, int[] x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println(Arrays.toString(x));
        }
 
        public void debug(String name, long[] x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println(Arrays.toString(x));
        }
 
        public void debug(String name, double[] x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println(Arrays.toString(x));
        }
 
        public void debug(String name, Object x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println("" + x);
        }
 
        public void debug(String name, Object... x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println(Arrays.deepToString(x));
        }
    }
}
