Problem:
Score : 400 points

Problem Statement

Snuke has an empty sequence a.

He will perform N operations on this sequence.

In the i-th operation, he chooses an integer j satisfying 1 \leq j \leq i, and insert j at position j in a (the beginning is position 1).

You are given a sequence b of length N. Determine if it is possible that a is equal to b after N operations. If it is, show one possible sequence of operations that achieves it.

Constraints

All values in input are integers.

1 \leq N \leq 100

1 \leq b_i \leq N

Input

Input is given from Standard Input in the following format:

N
b_1 \dots b_N

Output

If there is no sequence of N operations after which a would be equal to b, print -1.
If there is, print N lines. In the i-th line, the integer chosen in the i-th operation should be printed. If there are multiple solutions, any of them is accepted.

Sample Input 1

3
1 2 1

Sample Output 1

1
1
2

In this sequence of operations, the sequence a changes as follows:

After the first operation: (1)

After the second operation: (1,1)

After the third operation: (1,2,1)

Sample Input 2

2
2 2

Sample Output 2

-1

2 cannot be inserted at the beginning of the sequence, so this is impossible.

Sample Input 3

9
1 1 1 2 2 1 2 3 2

Sample Output 3

1
2
2
3
1
2
2
1
1

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;
import java.io.*;
import static java.lang.System.in;

public class Main {
    static int n,k;
    static long mod = 1000000000+7;
    static long[] fac,inv;
    static int[] id,size;
    //static long mod = 1000000000+7;
    //static HashSet<Integer>[] graph;
    //static ArrayList<Integer>[] graph;
    static ArrayList<Integer> ans = new ArrayList<>();
    static boolean flag = true;
    public static void main(String[] args)throws IOException {
        //BufferedReader reader = new BufferedReader(new InputStreamReader(in));
        //String[] buf = reader.readLine().split(" ");
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        //int[] b = new int[n+1];
        //for(int i=1;i<=n;i++) b[i]=sc.nextInt();
        // reverse the time line
        ArrayList<Integer> rec = new ArrayList<>();
        for(int i=0;i<n;i++) rec.add(sc.nextInt());
        LinkedList<Integer> ans = new LinkedList<>();
        while(rec.size()>0){
            int idx=-1;
            for(int i=rec.size()-1;i>=0;i--){
                if(rec.get(i)==i+1){
                    idx = i;
                    break;
                }
            }
            if(idx==-1) break;
            ans.addFirst(rec.get(idx));
            rec.remove(idx);
        }
        if(ans.size()!=n) System.out.println(-1);
        else{
            for(int w:ans) System.out.println(w);
        }
    }
}