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;

public class CSharp
{
    public static void Main()
    {
        Kyopuro chokudai = new Kyopuro();
        chokudai.AtCoder();
    }
}

public class Kyopuro
{
    public void AtCoder()
    {
        int n = int.Parse(Console.ReadLine());
        string[] s = Console.ReadLine().Split(' ');
        int[] b = new int[n];
        for (int i = 0; i < n; i++) b[i] = int.Parse(s[i]);
        int[] a = new int[n];
        int[] x = new int[n];
        bool[] f = new bool[n];
        for(int i=0; i<n; i++)
        {
            for(int j=i; j<n; j++)
            {
                if (b[j] < b[i]) x[i]++;
            }
        }
        int c = n - 1;
        int d = 0;
        bool ans = true;
        for(int i=0; i<n; i++)
        {
            c = n - 1;       
            while (c > -1)
            {
                ans = true;
                d = 0;
                if (!f[c])
                {
                    for (int j = 0; j < c; j++)
                    {
                        if (f[j]) d++;
                    }
                    if (d < b[c] - 1)
                    {
                        ans = false;
                    }
                    d = 0;
                    for(int j=c; j<n; j++)
                    {
                        if (f[j]) d++;
                    }
                    if (d < x[c])
                    {
                        ans = false;
                    }
                }
                else ans = false;
                
                if(ans)
                {
                    a[i] = b[c];
                    f[c] = true;
                    c = 0;
                }
                c--;
            }
        }
        ans = true;
        for (int i = 0; i < n; i++) if (!f[i]) ans = false;
        if (ans)
        {
            for (int i = 0; i < n; i++)
            {
                Console.WriteLine(a[i]);             
            }
        }
        else Console.WriteLine(-1);

    }
    public static void DebugWL(object x) { System.Diagnostics.Debug.WriteLine(x); }
}