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;
class Program
{
	static void Main(string[] args)
	{
		int N = int.Parse(Console.ReadLine());
		string[] str = Console.ReadLine().Split();
		int[]B = new int[N];
		for(var i=0;i<N;i++){
			B[i] = int.Parse(str[i]);
		}
		int[]A = new int[N];
		bool flag = true;
		for(var i=N-1;i>=0;i--){
			int ct = 0;
			bool flag2 = false;
			for(var j=0;j<N;j++){
				if(A[j]==0){
					ct++;
				}
				if(B[i]==ct){
					if(A[j]==0){
						A[j]=B[i];
						flag2 = true;
						break;
					} else {
						flag=false;
						break;
					}
				}
			}
			if(!flag2){
				flag = false;
				break;
			}
			if(!flag){
				break;
			}
		}
		if(!flag){
			Console.WriteLine("-1");
		} else {
			for(var i=0;i<N;i++){
				Console.WriteLine(A[i]);
			}
		}
	}
}