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.

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.

Constraints

• All values in input are integers.
• $1 \leq N \leq 100$
• $1 \leq b_i \leq N$

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

见题面 Input 部分

见题面 Output 部分