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 (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>

int main(){
	int n,i,j,k,b[100];
	scanf("%d",&n);
	for(i=0;i<n;i++)scanf("%d",&b[i]);
	int f=0;
	for(i=0;i<n;i++){
		f+=b[i];
		if(b[i]>i+1){
			puts("-1");
			return 0;
		}
	}
	if(f>n*(n+1)/2){
		puts("-1");
		return 0;
	}
	int ans[100],ansc=0;
	for(i=n-1;i>=0;i--){
		for(k=i;k>=0;k--){
		if(b[k]==k+1){
			ans[ansc++]=b[k];
			for(j=0;j+k+1<=i;j++){
				b[k+j]=b[k+j+1];
			}
			break;
		}
		}
	}
	for(i=n-1;i>=0;i--)printf("%d\n",ans[i]);
	return 0;
}