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: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Vector;
import java.util.Scanner;
import java.util.Stack;
import java.util.ArrayList;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author silviase
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        ALimitedInsertion solver = new ALimitedInsertion();
        solver.solve(1, in, out);
        out.close();
    }

    static class ALimitedInsertion {
        public void solve(int testNumber, Scanner in, PrintWriter out) {
            // 逆順でやればいい
            // ここでやばなのは後ろから順番にやること
            int n = in.nextInt();
            ArrayList<Integer> al = new ArrayList<>();
            Stack<Integer> st = new Stack<>();
            for (int i = 0; i < n; i++) {
                al.add(in.nextInt());
            }

            while (!al.isEmpty()) {
                boolean f = true;
                for (int i = al.size() - 1; i >= 0; i--) {
                    if (al.get(i) == i + 1) {
                        f = false;
                        st.add(al.get(i));
                        al.remove(i);
                        break;
                    }
                }
                if (f) {
                    out.println(-1);
                    return;
                }
            }

            while (!st.isEmpty()) {
                out.println(st.pop());
            }

        }

    }
}