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.
/*
JHope
*/
import java.util.*;
import java.io.*;
import java.math.*;

   public class C2
   {
      public static void main(String bts[]) throws Exception
      {
         BufferedReader infile = new BufferedReader(new InputStreamReader(System.in));  
         StringTokenizer st = new StringTokenizer(infile.readLine());
         int N = Integer.parseInt(st.nextToken());
         StringBuilder sb = new StringBuilder();
         int[] arr = new int[N];
         st = new StringTokenizer(infile.readLine());
         for(int i=0; i < N; i++)
            arr[i] = Integer.parseInt(st.nextToken());
         int[] res = new int[N];
         if(arr[0] >= 2)
         {
            System.out.println(-1);
            return;
         }
         //our heartbeats are in sync
         Arrays.fill(res, -1);
         res[0] = 1-arr[0];
         int prev = arr[0];
         for(int i=1; i < N; i++)
            if(prev != arr[i])
            {
               res[i] = prev;
               prev = arr[i];
            }
         TreeSet<Integer> set = new TreeSet<Integer>();
         for(int i=0; i <= 150000; i++)
            set.add(i);
         for(int x: res)
            if(x >= 0)
               set.remove(x);
         for(int i=0; i < N; i++)
            if(res[i] != -1)
            {
               int dex = i-1;
               while(dex >= 0 && res[dex] == -1)
               {
                  int val = set.first();
                  if(val < arr[i])
                  {
                     res[dex] = val;
                     set.remove(val);
                  }
                  else
                     res[dex] = 1;
                  dex--;
               }
            }
         int dex = N-1;
         while(res[dex] == -1)
         {
            int val = set.first();
            if(val < arr[N-1])
            {
               res[dex] = val;
               set.remove(val);
            }
            else
               res[dex] = 1;
            dex--;
         }
         for(int x: res)
            sb.append(x+" ");
         System.out.print(sb);
      }
   }