Score : 400 points
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 is given from Standard Input in the following format:
N b_1 \dots b_N
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.
3 1 2 1
1 1 2
In this sequence of operations, the sequence a changes as follows:
2 2 2
-1
2 cannot be inserted at the beginning of the sequence, so this is impossible.
9 1 1 1 2 2 1 2 3 2
1 2 2 3 1 2 2 1 1