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<algorithm>
#include<functional>
#include<cmath>
#include<string>
#include<vector>
using namespace std;
const int mod = 1000000007;
#define ll long long

int main()
{
	int N; cin >> N;
	vector<int> a, b;
	int B;
	for (int i = 0; i < N; i++) {
		cin >> B;
		B--;
		b.push_back(B);
	}
	bool flag = false;
	while (!b.empty()) {
		flag = false;
		for (int i = b.size() - 1; i >= 0; i--) {
			if (b[i] == i) {
				a.push_back(b[i] + 1);
				b.erase(b.begin() + i);
				flag = true;
				break;
			}
		}
		if (!flag) {
			cout << "-1" << endl;
			return 0;
		}
	}
	reverse(a.begin(), a.end());
	for (int i = 0; i < N; i++) {
		cout << a[i] << endl;
	}
}