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 main(){
    int n;cin >> n;
    vector<int> v(n);
    vector<int> ans;
    for(int i=0;i<n;i++){
        cin >> v[i];
    }
    while(v.size() >0){    
        int max = 0;
        int index = 0;
        for(int i=0;i<v.size();i++){
            if(v[i] >=max && i+1 == v[i]){
                max = v[i];
                index = i;
            }
        }
        if(max == 0){
            cout <<"-1" << endl;
            return 0;
        }
        else{
            ans.push_back(max);
            v.erase(v.begin()+index);
        }
    }
    for(int i=0;i<ans.size();i++){
        cout << ans[ans.size()-1-i] << endl;
    }
    return 0;
}