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 <bits/stdc++.h>
using namespace std;

int main() {
    int N;
    cin >> N;
    vector<int> A(N);
    for (int i = 0; i < N; i++) { 
        cin >> A[i];
        A[i]--;
    }
    
    vector<int> ans;
    bool judge = true;
    for (int cnt = 0; cnt < N; cnt++) {
        bool del = false;
        for (int i = (int)A.size()-1; i >= 0; i--) {
            if (A[i] == i) {
                del = true;
                ans.push_back(A[i]);
                A.erase(A.begin() + i);
                break;
            }
        }
        if (del == false) { judge = false; break; }
    }
    
    reverse(ans.begin(), ans.end());
    if (judge) {
        for (auto an : ans) cout << an+1 << endl;
    } else {
        cout << -1 << endl;
    }
    return 0;
}