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<cstdio>
#include<cstring>
#include<algorithm>
#define SF scanf
#define PF printf
#define MAXN 100010
using namespace std;
int n;
int a[MAXN];
int ans[MAXN],cnt;
bool solve(int tot){
	if(tot==0)
		return 1;
	for(int i=tot;i>=1;i--)
		if(a[i]==i){
			ans[++cnt]=i;
			for(int j=i;j<tot;j++)
				a[j]=a[j+1];
			return solve(tot-1);
		}
	return 0;
}
int main(){
	SF("%d",&n);
	for(int i=1;i<=n;i++)
		SF("%d",&a[i]);
	if(solve(n)){
		for(int i=n;i>=1;i--)
			PF("%d\n",ans[i]);	
	}
	else
		PF("-1");
}	