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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Scanner;
public class Main{
	public static void main(String[] args){
		Scanner sc=new Scanner(System.in);
		int n = sc.nextInt();
		int[] b =new int[n];
		for(int i = 0; i<n; i++){
			b[i]= sc.nextInt();
			if(i+1<b[i]){
				System.out.println(-1);
				return;
			}
		}
		int[] ans=new int[n];
		ans[0]=1;
		int count=1;
		for(int i=n-1; i>0; i--){
			if(b[i]>=3 && count<3){
				int b1=b[i];
				int u=0;
				for(int j=1; j<=b[i]-count+u; j++){
					if(b[i-j]<b1){
						b[i-j+1]=b[i-j];
					}else{
						u++;
					}
				}
				b[i-b1+count]=b1;
			}
			ans[n-i]=b[i];
			count++;
		}
		for(int i = 0; i<n; i++){
			System.out.println(ans[i]);
		}
	}
}