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.

Examples

Input

3
1 2 1


Output

1
1
2


Input

2
2 2


Output

-1


Input

9
1 1 1 2 2 1 2 3 2


Output

1
2
2
3
1
2
2
1
1
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
ll a[110];
bool f[110];
int main(){
	ll n;
	vector<ll>ans;
	cin>>n;
	for(int i=0;i<n;i++)cin>>a[i];
	for(int i=1;i<=n;i++){
		ll cnt=0;
		bool ok=0;
		for(int j=n-1;j>=0;j--){
			if(f[j]){
				cnt++;
				continue;
			}
			if(a[j]==i-cnt){
				ok=1;
				ans.push_back(a[j]);
				f[j]=1;
				break;
			}
		}
		if(!ok){
			cout<<-1<<endl;
			return 0;
		}
	}
	for(auto x:ans){
		cout<<x<<endl;
	}
	return 0;
}
