Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

E. Petya and Post

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputLittle Vasya's uncle is a postman. The post offices are located on one circular road. Besides, each post office has its own gas station located next to it. Petya's uncle works as follows: in the morning he should leave the house and go to some post office. In the office he receives a portion of letters and a car. Then he must drive in the given car exactly one round along the circular road and return to the starting post office (the uncle can drive along the circle in any direction, counterclockwise or clockwise). Besides, since the car belongs to the city post, it should also be fuelled with gasoline only at the Post Office stations.

The total number of stations equals to *n*. One can fuel the car at the *i*-th station with no more than *a*_{i} liters of gasoline. Besides, one can fuel the car no more than once at each station. Also, the distance between the 1-st and the 2-nd station is *b*_{1} kilometers, the distance between the 2-nd and the 3-rd one is *b*_{2} kilometers, ..., between the (*n* - 1)-th and the *n*-th ones the distance is *b*_{n - 1} kilometers and between the *n*-th and the 1-st one the distance is *b*_{n} kilometers. Petya's uncle's high-tech car uses only one liter of gasoline per kilometer. It is known that the stations are located so that the sum of all *a*_{i} is equal to the sum of all *b*_{i}. The *i*-th gas station and *i*-th post office are very close, so the distance between them is 0 kilometers.

Thus, it becomes clear that if we start from some post offices, then it is not always possible to drive one round along a circular road. The uncle faces the following problem: to what stations can he go in the morning to be able to ride exactly one circle along the circular road and visit all the post offices that are on it?

Petya, who used to attend programming classes, has volunteered to help his uncle, but his knowledge turned out to be not enough, so he asks you to help him write the program that will solve the posed problem.

Input

The first line contains integer *n* (1 ≤ *n* ≤ 10^{5}). The second line contains *n* integers *a*_{i} — amount of gasoline on the *i*-th station. The third line contains *n* integers *b*_{1}, *b*_{2}, ..., *b*_{n}. They are the distances between the 1-st and the 2-nd gas stations, between the 2-nd and the 3-rd ones, ..., between the *n*-th and the 1-st ones, respectively. The sum of all *b*_{i} equals to the sum of all *a*_{i} and is no more than 10^{9}. Each of the numbers *a*_{i}, *b*_{i} is no less than 1 and no more than 10^{9}.

Output

Print on the first line the number *k* — the number of possible post offices, from which the car can drive one circle along a circular road. Print on the second line *k* numbers in the ascending order — the numbers of offices, from which the car can start.

Examples

Input

4

1 7 2 3

8 1 1 3

Output

2

2 4

Input

8

1 2 1 2 1 2 1 2

2 1 2 1 2 1 2 1

Output

8

1 2 3 4 5 6 7 8

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Oct/20/2017 06:23:13 (c4).

Desktop version, switch to mobile version.

User lists

Name |
---|