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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.PriorityQueue;
import java.util.StringTokenizer;
 
public class A {
	
	StringTokenizer st;
	BufferedReader file;
	PrintWriter pout = new PrintWriter(System.out);
	long MOD = 1000000007;

	
	public static void main(String[] args) throws Exception
	{
		new A().run();
	}	
	
	public void run() throws Exception
	{
		file = new BufferedReader(new InputStreamReader(System.in));
		int N = nextInt();
		int[] ints = readInts(N);
		boolean[] lastOcc = new boolean[N];
		boolean[] seen = new boolean[100001];
		for(int i = N - 1;i>=0;i--)
		{
			if(i - ints[i] < -1)
			{
				System.out.println(-1);
				return;
			}
			if(!seen[ints[i]])
			{
				lastOcc[i] = true;
				seen[ints[i]] = true;
			}
		}
		PriorityQueue<Integer> candidates = new PriorityQueue<Integer>();
		for(int i = 0;i<seen.length;i++)
		{
			if(!seen[i])
				candidates.add(i);
		}
		int[] ans = new int[N];
		for(int i = 0;i<N;i++)
		{
			ans[i] = candidates.poll();
			if(lastOcc[i])
				candidates.add(ints[i]);
		}
		for(int i = 0;i<ans.length;i++)
		{
			pout.print(ans[i]+" ");
		}
		pout.println();
		pout.flush();
	}
	
	public int gcd(int a, int b)
	{
		return BigInteger.valueOf(a).gcd(BigInteger.valueOf(b)).intValue();
	}
	
	public void newst()
	{
		try {
			st = new StringTokenizer(file.readLine());
		} catch (IOException e) {
			e.printStackTrace();
		}
	}
	
	public String readLine() throws IOException
	{
		return file.readLine();
	}
	
	public String next()
	{
		if(st == null || !st.hasMoreTokens())
			newst();
		return st.nextToken();
	}
	
	public int nextInt()
	{
		if(st == null || !st.hasMoreTokens())
			newst();
		return Integer.parseInt(st.nextToken());
	}
	
	public long nextLong()
	{
		if(st == null || !st.hasMoreTokens())
			newst();
		return Long.parseLong(st.nextToken());
	}
	
	public int[] readInts(int N)
	{
		int[] ints = new int[N];
		for(int i = 0;i<N;i++)
		{
			ints[i] = nextInt();
		}
		return ints;
	}
	
	public long[] readLongs(int N)
	{	
		long[] ints = new long[N];
		for(int i = 0;i<N;i++)
		{
			ints[i] = nextLong();
		}
		return ints;
	}
	
}