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.*;
import java.math.*;

//Mann Shah [ DAIICT ].

public class Main {
	static long mod = (long) (1e9+7);
	static InputReader in;
    static PrintWriter out;
    static Debugger deb;  
    
    	public static void main(String args[] ) throws NumberFormatException, IOException  {
			
		in = new InputReader(System.in);
	    out = new PrintWriter(System.out);
	    deb = new Debugger();
	   
	    int n = in.nextInt();
	    int[] a = in.nextIntArray(n);
	    
	    TreeSet<Integer> hs = new TreeSet();
	    int[] f = new int[n+1];
	    for(int i=0;i<n;i++) {
	    		f[a[i]]=1;
	    		hs.add(a[i]);
	    }
	    int cur=0;
	    int[] ans = new int[n];
	    for(int i=0;i<n;i++) {
	    		if(hs.first() < a[i]) {
	    			ans[i] = hs.first();
	    			hs.remove(hs.first());
	    		}
	    		else {
	    			while(f[cur]==1) {
	    				cur++;
	    			}
	    			f[cur]=1;
	    			ans[i] = cur;
	    			cur++;
	    		}
	    }
	    for(int i=0;i<n;i++) {
	    		out.print(ans[i]+" ");
	    }
	    
	    out.close();
	}




/* TC space


 */	
		static class InputReader
	    {
	        private final InputStream stream;
	        private final byte[] buf = new byte[8192];
	        private int curChar, snumChars;
	        private SpaceCharFilter filter;

	        public InputReader(InputStream stream){
	                this.stream = stream;
	        }
	        public int snext(){
                if (snumChars == -1) throw new InputMismatchException();
                if (curChar >= snumChars){
                        curChar = 0;
                        try{
                                snumChars = stream.read(buf);
                        } catch (IOException e){
                                throw new InputMismatchException();
                        }
                        if (snumChars <= 0)
                                return -1;
                }
                return buf[curChar++];
	        }

	        public int nextInt(){
	                int c = snext();
	                while (isSpaceChar(c)){
	                    c = snext();
	                }
	                int sgn = 1;
	                if (c == '-'){
                        sgn = -1;
                        c = snext();
	                }
	                int res = 0;
	                do{
                        if (c < '0' || c > '9')
                                throw new InputMismatchException();
                        res *= 10;
                        res += c - '0';
                        c = snext();
	                } while (!isSpaceChar(c));
	                return res * sgn;
	        }

	        public long nextLong()
	        {
	                int c = snext();
	                while (isSpaceChar(c))
	                {
	                        c = snext();
	                }
	                int sgn = 1;
	                if (c == '-')
	                {
	                        sgn = -1;
	                        c = snext();
	                }
	                long res = 0;
	                do
	                {
	                        if (c < '0' || c > '9')
	                                throw new InputMismatchException();
	                        res *= 10;
	                        res += c - '0';
	                        c = snext();
	                } while (!isSpaceChar(c));
	                return res * sgn;
	        }

	        public int[] nextIntArray(int n)
	        {
	                int a[] = new int[n];
	                for (int i = 0; i < n; i++)
	                {
	                        a[i] = nextInt();
	                }
	                return a;
	        }

	        public long[] nextLongArray(int n)
	        {
	                long a[] = new long[n];
	                for (int i = 0; i < n; i++)
	                {
	                        a[i] = nextLong();
	                }
	                return a;
	        }
	        
	        public ArrayList<Integer> nextArrayList(int n){
	        			ArrayList<Integer> x = new ArrayList<Integer>();
	        			for(int i=0;i<n;i++) {
	        				int v = in.nextInt();
	        				x.add(v);
	        			}
	        			return x;
	        }

	        public String readString()
	        {
	                int c = snext();
	                while (isSpaceChar(c))
	                {
	                        c = snext();
	                }
	                StringBuilder res = new StringBuilder();
	                do
	                {
	                        res.appendCodePoint(c);
	                        c = snext();
	                } while (!isSpaceChar(c));
	                return res.toString();
	        }

	        public String nextLine()
	        {
	                int c = snext();
	                while (isSpaceChar(c))
	                        c = snext();
	                StringBuilder res = new StringBuilder();
	                do
	                {
	                        res.appendCodePoint(c);
	                        c = snext();
	                } while (!isEndOfLine(c));
	                return res.toString();
	        }

	        public boolean isSpaceChar(int c)
	        {
	                if (filter != null)
	                        return filter.isSpaceChar(c);
	                return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	        }

	        private boolean isEndOfLine(int c)
	        {
	                return c == '\n' || c == '\r' || c == -1;
	        }

	        public interface SpaceCharFilter
	        {
	                public boolean isSpaceChar(int ch);
	        }

	    }
		
		static class Debugger{
			public void n(int x) {
				out.println(x);
			}
			
			public void a(int[] a) {
		        StringBuilder sb = new StringBuilder();
		        for(int i=0;i<a.length;i++) {
		        		sb.append(a[i]+" ");
		        }
		        out.println(sb.toString());
			}
		}
	
		
}


class Pair { 
   int x; 
   int y; 
   // Constructor 
   public Pair(int x, int y) 
   { 
       this.x = x; 
       this.y = y; 
   } 
	@Override
	public boolean equals(Object o) {
	    if (this == o) return true;
	    if (!(o instanceof Pair)) return false;
	    Pair p = (Pair) o;
	    return x == p.x && y == p.y;
	}	
	@Override
	public int hashCode() {
		return (""+x+"-"+y).hashCode();
	}	
} 
