The people of Hackerland start every year with a competitive notion and there are several competitions held in the city. This year there is a special Tug of War tournament being played by N people. These N people are standing on a straight line where the \(i^{th}\) person is standing at a distance \(D_i\) from Hackerland Central building to the right having strength \(A_i\). The tournament trophy needs to be placed somewhere along the straight line and then the game will begin. All the people on the left side of the trophy form a team and the people on the right side of the trophy form another team. The teams have to pull the trophy towards them where \(i^{th}\) person can apply a maximum force of \(A_i / log_{2} (2+dist)\) towards him where \(dist\) is the distance between the \(i^{th}\) person and the trophy. The total force each team can apply will be the sum of forces applied by all the individuals of the team.

You know that if a particular team wins, they are going to mock the other team for the whole year so you are given the task to place the trophy in such a position that no team wins the tournament and such mockery is prevented. Output the count of all such possible positions and all the possible positions. Make sure that you output the positions in increasing order.

Input Format:

The first line contains a single integer N denoting the number of participants for the Tug of War tournament.

The next line contains N space separated floating point numbers where the \(i^{th}\) floating point number corresponds to \(D_i\) which denotes the distance of \(i^{th}\) person from the Hackerland Central building. It is ensured that all \(D_{i}'s\) are unique, i.e., no two participants are standing at the same position.

The next line contains N space separated integers where the \(i^{th}\) integer corresponds to \(A_i\) which denotes the strength of \(i^{th}\) person.

Output Format:

Output the count of all possible positions in the first line. Let that count be X.

In the second line, output X space separated numbers which denotes all such possible positions. Make sure that you output the positions in increasing order.

Your answer is considered correct, if it's absolute error does not exceed \(10^{-9}\). Namely, let your answer be a and the jury's answer be b. Your answer is considered correct, if \( |a - b| \le 10^{-9} \).

Constraints:

\( 2 \le N \le 500 \)
\( 0 \le D_i \le 100 \)
\( 1 \le A_i \le 100 \)