Score : 800 points
Niwango has N cards, numbered 1,2,\ldots,N. He will now arrange these cards in a row.
Niwango wants to know if there is a way to arrange the cards while satisfying all the N conditions below. To help him, determine whether such a way exists. If the answer is yes, also find the lexicographically smallest such arrangement.
Input is given from Standard Input in the following format:
N a_1 a_2 \ldots a_N
If no arrangements satisfy the conditions, print -1
. If such arrangements exist, print the lexicographically smallest such arrangement, in the following format:
b_1 b_2 \ldots b_N
Here, b_i represents the i-th card from the left.
4 2 3 4 1
1 3 2 4
2 2 1
-1
-1
.13 2 3 4 5 6 7 8 9 10 11 12 13 12
1 3 2 4 6 5 7 9 8 10 12 11 13