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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Text;
using System.Linq;
using static System.Math;

class Program{
    static void Main(){
        int n = int.Parse(Console.ReadLine());
        int[] b = Console.ReadLine().Split().Select(int.Parse).ToArray();
        
        int[] ans = new int[n];
        for (int i = n - 1;i >= 0;i--){
            int c = i + 1;
            for (int j = n - 1;j >= 0;j--){
                if (b[j] == -1) continue;
                if (b[j] == c){
                    b[j] = -1;
                    ans[i] = c;
                    break;
                }
                c--;
            }
            if (ans[i] == 0){
                Console.WriteLine(-1);
                return;
            }
        }
        foreach (var i in ans) Console.WriteLine(i);
    }
}