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];
        int[] c = new int[n];
        for(int i = 0;i < n;++i){
            b[i] = sc.nextInt();
            c[i] = i + 1 - b[i];
            if(c[i] < 0 || (i >= 1 && c[i] < c[i - 1])){
                System.out.println(-1);
                return;
            }
        }

        LinkedList<Integer> marks = new LinkedList<>();
        LinkedList<Integer> res = new LinkedList<>();
        for(int i = n - 1;i >= 0;--i){
            if(i >= 1 && c[i] == c[i - 1])continue;
            if(res.size() + 1 < b[i]){
                marks.add(i);
            }
            else{
                res.add(b[i]);
                if(i < n - 1 && c[i + 1] == c[i])marks.add(i + 1);
                int last = -1;
                boolean flag = true;
                while (flag) {
                    flag = false;
                    //last = marks.size();
                    LinkedList<Integer> newMarks = new LinkedList<>();
                    for(int i2 = 0;i2 < marks.size();++i2){
                        int j = marks.get(i2);
                        if (flag || res.size() + 1 < b[j]) {
                            newMarks.add(j);
                        } else {
                            int now = j;
                            res.add(b[now]);
                            ++now;
                            while (now < n && c[now - 1] == c[now]){
                                if(i2 > 0 && b[marks.get(0)] == b[now]){
                                    newMarks.add(now);
                                    break;
                                }
                                res.add(b[now]);
                                ++now;
                            }
                            flag = true;
                        }
                    }
                    marks = newMarks;
                }
            }
        }
        for(int k:res){
            System.out.println(k);
        }
     /*   System.out.println();
      LinkedList<Integer> test = new LinkedList<>();
      for(int k:res){
          test.add(k - 1,k);
      }
      for(int k:test){
          System.out.println(k);
      }*/

    }

}