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;
using System.Collections.Generic;
using System.Linq;
using System.Diagnostics;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using System.Numerics;
using System.IO;
using System.Runtime.InteropServices;
using static System.Math;
using static Math2;
using static io;
using static Utils;



public class CompetitiveProgramming
{

  public void Solve()
  {
    var N = Int1;
    var b = Ints.Select(x => x - 1).ToArray();
    var c = new List<int>(b);
    var ans = new List<int>();
    while (true)
    {
      if (c.Count == 0) break;
      bool exist = false;
      for (int i = c.Count - 1; i >= 0; --i)
      {
        if (c[i] == i)
        {
          c.RemoveAt(i);
          ans.Add(i + 1);
          exist = true;
          break;
        }
      }
      if (!exist)
      {
        Put(-1);
        return;
      }
    }
    ans.Reverse();
    VerticalPut(ans);
  }

}


public static class Math2
{
  public const int INF = 1 << 29;
  public const long INFL = 1L << 60;
  public const long MOD = 1000000007;
  public const int MOD2 = 998244353;

  public static long Power(long a, long b, long MOD = 1000000007)//i^N
  {
    long res = 1;
    while (b > 0)
    {
      if ((b & 1) != 0) res = res * a % MOD;
      a = a * a % MOD;
      b >>= 1;
    }
    return res;
  }
  public static long Power2(long a, long b)//i^N
  {
    long res = 1;
    while (b > 0)
    {
      if ((b & 1) != 0) res = res * a;
      a = a * a;
      b >>= 1;
    }
    return res;
  }
  public static long GCD(long a, long b)
  {
    while (b > 0)
    {
      var r = a % b;
      a = b;
      b = r;
    }
    return a;
  }
  public static long LCM(long a, long b) => (b / GCD(a, b)) * a;
  public static long Comb(long n, long r, int MOD = 1000000007)
  {
    if (r > n - r) r = n - r;
    long Nume = 1;
    long Deno = 1;

    if (r > n - r) r = n - r;
    for (long i = 1; i <= r; ++i)
    {
      Deno = (Deno * i) % MOD;
      Nume = Nume * (n - i + 1) % MOD;
    }
    return (Nume * inv(Deno)) % MOD;
  }
  public static long Comb2(long n, long r)
  {
    long Nume = 1;
    long Deno = 1;

    if (r > n - r) r = n - r;
    for (long i = 1; i <= r; ++i)
    {
      Deno *= i;
      Nume *= n - i + 1;
    }
    return Nume / Deno;
  }
  public static long inv(long x, int MOD = 1000000007)
  {
    return Power(x, MOD - 2, MOD);
  }
}
public static class Utils
{

  public static void Swap<T>(ref T A, ref T B)
  {
    T x = A;
    A = B;
    B = x;
  }
  public static int DigitSum(int N)
  {
    string s = N.ToString();
    int ret = 0;
    for (int i = 0; i < s.Length; ++i) ret += s[i] - '0';
    return ret;
  }
}
class Program
{
  static void Main(string[] args)
  {
    var CompetitiveProgramming = new CompetitiveProgramming();
    CompetitiveProgramming.Solve();
  }
}
public static class io
{
  public static string Str => Console.ReadLine();
  public static string[] Strs => Str.Split(' ');
  public static long[] Longs => Strs.Select(long.Parse).ToArray();
  public static int[] Ints => Strs.Select(int.Parse).ToArray();
  public static char[] Chars => Str.ToArray();
  public static double[] Doubles => Strs.Select(double.Parse).ToArray();
  public static long Long1 => Longs[0];
  public static int Int1 => Ints[0];
  public static char Char1 => Chars[0];
  public static double Double1 => Doubles[0];
  public static long[] VerticalRead(int N) { long[] A = new long[N]; for (int i = 0; i < N; ++i) A[i] = Long1; return A; }
  public static void Put(string a) => Console.WriteLine(a);
  public static void Put(params object[] i) => Put(string.Join(" ", i));
  public static void Put<T>(IEnumerable<T> a) => Put(string.Join(" ", a));
  public static void VerticalPut<T>(IEnumerable<T> a) { foreach (var z in a) Put(z); }
  public static void YN(bool i) { if (i) Put("Yes"); else Put("No"); }
}