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 Java7 (OpenJDK 1.7.0) (judge verdict: Time Limit Exceeded)

import java.util.ArrayList;
import java.util.Scanner;
public class Main {

	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		//Scanner sc = new Scanner("3\n1 1 2");
		// 整数の入力
		int n = sc.nextInt();
		//int s = 0;
		int end =  0;
		int na[] = new int[n];
		int a, b, c;
		ArrayList<Integer> ans_nar = new ArrayList<Integer>();
		for (int i = 0; i < n; i++)
		{
			ans_nar.add(sc.nextInt());
		}
		//System.out.println(ans_nar);
		ArrayList<Integer> nar = new ArrayList<Integer>();
		Nar narn = new Nar(nar, ans_nar, n, 0);
		ArrayList<Integer> result;
		result = narn.cac();
		//System.out.println(result);
		if(result.get(0)==-1) {
			System.out.println(-1);
		}
		else
		{
			for (int i = 0; i < n; i++)
			{
				System.out.println(result.get(n-i));
			}
		}
	}

}



class Nar {
	public ArrayList<Integer> nar;
	public ArrayList<Integer> ans_nar;
	public int n;
	public int i;
	Nar(ArrayList<Integer> naro, ArrayList<Integer> ans_naro, int no, int io){
		nar = naro;
		ans_nar = ans_naro;
		n = no;
		i = io;
		//System.out.println(nar);
	}
	public ArrayList<Integer> cac(){
		if(n==i) {
			ArrayList<Integer> ans = new ArrayList<Integer>();
			if(nar.equals(ans_nar)) {
				ans.add(1);
				return ans;
			}
			else {
				ans.add(-1);
				return ans;
			}
		}
		else {
          	ArrayList<Integer> ans = new ArrayList<Integer>();
			for (int p=0; p <= i; p++) {
				ArrayList<Integer> narc = (ArrayList<Integer>) nar.clone();
				narc.add(p, p+1);
				Nar narn = new Nar(narc, ans_nar, n, i+1);
				ans = narn.cac();
				if(ans.get(0) != -1) {
					ans.add(p+1);
					return ans;
				}
			}
		}
		ArrayList<Integer> ans = new ArrayList<Integer>();
		ans.add(-1);
		return ans;
	}

}