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.*;
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(b[i] > i + 1) {
				System.out.println(-1);
				return;
			}
		}
		
		int ans[] = new int[N];
		boolean flag[] = new boolean[N];
		int ans_cnt = 0;
		int total = 0;
		int now = N - 1;
		for(int i = N - 1; i >= 0; i--) {
			if(b[i] == 1) {
				ans[ans_cnt] = 1;
				flag[i] = true;
				ans_cnt++;
				int n = 1;
				int cnt = i;
				int max = 1;
				int cnt_n = 2;
				out : while(cnt + total != N - 1) {
					n++;
					in : for(int j = i + 1; j < N; j++) {
						if(b[j] == 1) break;
						if(b[j] == n && !flag[j]) {
							ans[ans_cnt] = b[j];
							ans_cnt++;
							flag[j] = true;
							cnt++;
							break in;
						}
						 if(b[j] > j - i + 1) {
							System.out.println(-1);
							return;
						}
					}
					for(int j = now; j >= i + 1; j--) {
						if(b[j] <= n && !flag[j]) {
							cnt++;
							ans[ans_cnt] = b[j];
							flag[j] = true;
							ans_cnt++;
							continue out;
						}
					}
					//System.out.println(total + cnt);
				}
				//System.out.println(cnt);
				total = total + cnt - i + 1;
				now = i - 1;
				//System.out.println("t");
			}
			//System.out.println(i + "t");
		}
		for(int i = 0; i < N; i++) {
			System.out.println(ans[i]);
		}
	}
}