Problem Background

Xiao W has purchased a robot.

Problem Description

Now, Xiao W wants the robot to help him complete \( n \) tasks.

Each task has two attributes: the cost \( w_i \) required to complete it, and the success rate \( p_i \).

Xiao W needs to arrange the tasks in a certain order, after which the robot will perform the tasks in the following manner:

• Start with the first task;
• After spending the cost to complete the \( i \)-th task, if successful, continue with the \( i+1 \)-th task; otherwise, restart from the first task;
• After successfully completing the \( n \)-th task, the process ends.

For example, when \( n=2 \), a possible process is:
- Perform task 1, fail;
- Perform task 1, succeed;
- Perform task 2, fail;
- Perform task 1, succeed;
- Perform task 2, succeed;
- The process ends, with a total cost of \( 3w_1 + 2w_2 \).

Now, Xiao W hopes that you, an OI enthusiast, can help him find an arrangement order that minimizes his expected cost.

Input Format

The first line contains an integer \( n \), representing the number of tasks.

The next line contains \( n \) integers \( w_1, w_2, \cdots, w_n \), as described above.

The following line contains \( n \) integers \( P_1, P_2, \cdots, P_n \), where \( P_i = p_i \times 10^4 \), and \( p_i \) is as described above.

Output Format

If it is impossible to complete the tasks under any circumstances, output a single line containing the string Impossible.

Otherwise, output a single line containing \( n \) integers \( c_1, c_2, \cdots, c_n \), which is a permutation of \( 1, 2, \cdots, n \), indicating the arrangement order of the tasks, where the \( i \)-th task in the arrangement is the \( c_i \)-th task in the input.

Sample Input and Output

Sample Input #1

2
999 1
5000 10000

Sample Output #1

1 2

Sample Input #2

1
1
0

Sample Output #2

Impossible

Notes

Explanation of Sample 1: Intuitively, since task 2 is guaranteed to succeed, placing it last cannot be worse.

Explanation of Sample 2: Clearly, this task cannot be completed since its success rate is 0.

Note: The cost \( w_i \) is always incurred regardless of whether the task is successful or not.

This problem includes a Special Judge (SPJ). If your output is as optimal as the answer's output (or both are Impossible), you will receive full marks for this test case; otherwise, you will receive no points for this test case.

Due to certain reasons, the SPJ is not provided to the contestants.

Data Range

For 10% of the data, \( 1 \le n \le 10 \).
For another 20% of the data, all \( w_i \) are equal.
For another 20% of the data, all \( p_i \) are equal.
For all data, \( 1 \le n \le 2 \times 10^5 \), \( 1 \le w_i \le 10^9 \), \( 0 \le P_i \le 10^4 \).

见题面 Input 部分

见题面 Output 部分