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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
class c
{
    static void Main()
    {
        int n = int.Parse(Console.ReadLine());
        var b = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
        for (int i = 0; i < n; i++)
        {
            if (b[i] > i + 1)
            {
                Console.WriteLine(-1);
                break;
            }
            if (i == n - 1)
            {
                var ans = b[0].ToString();
                for (int j = 1; j < n; j++)
                {
                    int skip = j - b[j] + 1;
                    ans = ans.Substring(0, ans.Length - skip) + b[j].ToString() + ans.Substring(ans.Length - skip, skip);
                }
                foreach (var c in ans) Console.WriteLine(c);
            }
        }
    }
}