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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <vector>
using namespace std;
int n, a;
vector<int> b, ans;
int main(void){
    // Your code here!
    cin >> n;
    for (int i = 1; i <= n; i++)
    {
        cin >> a;
        b.push_back(a);
    }
    while(b.size() != 0)
    {
        bool jud = false;
        for (int i = b.size() - 1; i >= 0; i--)
        {
            if (b[i] == i + 1)
            {
                ans.push_back(b[i]);
                b.erase(b.begin() + i);
                jud = true;
                break;
            }
        }
        if (!jud)
        {
            cout << -1 << endl;
            return 0;
        }
    }
    for (int i = ans.size() - 1; i >= 0; i--)
    {
        cout << ans[i] << endl;
    }
}