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.*;

public class C649C{
	static class FastReader {

        BufferedReader br;
        StringTokenizer st;

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

        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());
        }

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

	int[] nextIntArrayOne(int n) {
				int[] a = new int[n+1];
				for (int i = 1; i < n+1; i++)
					a[i] = nextInt();
				return a;
	}

        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;
        }
    }

	public static void main(String[] args) {
		FastReader s =new FastReader();
		
		StringBuilder str = new StringBuilder();
		
			int n = s.nextInt();
			int arr[] = s.nextIntArray(n);
			int ans[] = new int[n];
			Arrays.fill(ans, -1);
			Set<Integer> set = new HashSet<>((int)1e5);
			
			int max = Integer.MIN_VALUE;
			for(int i = 0;i<n;i++) {
				
				max = Math.max(max, arr[i]);
			}
			
			for(int i =0;i<=max;i++) {
				set.add(i);
			}
			for(int i =0;i<n;i++) {
				if(set.contains(arr[i])) set.remove(arr[i]);
			}
			
			for(int i = n - 1;i>0;i--) {
				if(arr[i] != arr[i - 1]) {
					ans[i] = arr[i - 1];
				}
			}
			int res[] = new int[set.size()];
			int k = 0;
			for(int p : set) {
				res[k++] = p;
			}
		
			
			
			int prv = 0;
			k = 0;
			for(int i = 0;i<n;i++) {
				if(ans[i] == -1) {
					if(k == res.length ) {
						ans[i] = prv;
					}else {
						prv = res[k++];
						ans[i] = prv;
					}
				}
			}
		for(int p : ans) str.append(p+" ");	
		
		System.out.println(str);
	}

	

}