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

C. Division into Teams

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputPetya loves football very much, especially when his parents aren't home. Each morning he comes to the yard, gathers his friends and they play all day. From time to time they have a break to have some food or do some chores (for example, water the flowers).

The key in football is to divide into teams fairly before the game begins. There are *n* boys playing football in the yard (including Petya), each boy's football playing skill is expressed with a non-negative characteristic *a*_{i} (the larger it is, the better the boy plays).

Let's denote the number of players in the first team as *x*, the number of players in the second team as *y*, the individual numbers of boys who play for the first team as *p*_{i} and the individual numbers of boys who play for the second team as *q*_{i}. Division *n* boys into two teams is considered fair if three conditions are fulfilled:

- Each boy plays for exactly one team (
*x*+*y*=*n*). - The sizes of teams differ in no more than one (|
*x*-*y*| ≤ 1). - The total football playing skills for two teams differ in no more than by the value of skill the best player in the yard has. More formally:

Your task is to help guys divide into two teams fairly. It is guaranteed that a fair division into two teams always exists.

Input

The first line contains the only integer *n* (2 ≤ *n* ≤ 10^{5}) which represents the number of guys in the yard. The next line contains *n* positive space-separated integers, *a*_{i} (1 ≤ *a*_{i} ≤ 10^{4}), the *i*-th number represents the *i*-th boy's playing skills.

Output

On the first line print an integer *x* — the number of boys playing for the first team. On the second line print *x* integers — the individual numbers of boys playing for the first team. On the third line print an integer *y* — the number of boys playing for the second team, on the fourth line print *y* integers — the individual numbers of boys playing for the second team. Don't forget that you should fulfil all three conditions: *x* + *y* = *n*, |*x* - *y*| ≤ 1, and the condition that limits the total skills.

If there are multiple ways to solve the problem, print any of them.

The boys are numbered starting from one in the order in which their skills are given in the input data. You are allowed to print individual numbers of boys who belong to the same team in any order.

Examples

Input

3

1 2 1

Output

2

1 2

1

3

Input

5

2 3 3 1 1

Output

3

4 1 3

2

5 2

Note

Let's consider the first sample test. There we send the first and the second boy to the first team and the third boy to the second team. Let's check all three conditions of a fair division. The first limitation is fulfilled (all boys play), the second limitation on the sizes of groups (|2 - 1| = 1 ≤ 1) is fulfilled, the third limitation on the difference in skills ((2 + 1) - (1) = 2 ≤ 2) is fulfilled.

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: May/27/2018 07:56:07 (d3).

Desktop version, switch to mobile version.

User lists

Name |
---|