Arrangement

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.

• To the immediate right of Card 1 (if any) is NOT Card a_1.
• To the immediate right of Card 2 (if any) is NOT Card a_2.
• \vdots
• To the immediate right of Card N (if any) is NOT Card a_N.

Constraints

• 2 \leq N \leq 10^{5}
• 1 \leq a_i \leq N
• a_i \neq i

Input

Input is given from Standard Input in the following format:

N a_1 a_2 \ldots a_N

Output

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.

Examples

Input

4 2 3 4 1

Output

1 3 2 4

Input

2 2 1

Output

-1

Input

13 2 3 4 5 6 7 8 9 10 11 12 13 12

Output

1 3 2 4 6 5 7 9 8 10 12 11 13

inputFormat

Input

Input is given from Standard Input in the following format:

N a_1 a_2 \ldots a_N

outputFormat

Output

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.

Examples

Input

4 2 3 4 1

Output

1 3 2 4

Input

2 2 1

Output

-1

Input

13 2 3 4 5 6 7 8 9 10 11 12 13 12

Output

1 3 2 4 6 5 7 9 8 10 12 11 13

样例

4
2 3 4 1

1 3 2 4