Forming Badminton Doubles Teams

Members of the badminton club at Korea University want to play badminton. So that everyone can play at the same time and have fun, they want to form doubles teams as follows, taking each member's skill into account.

In badminton doubles, two players pair up to face another pair, so a game involves a total of four people, two on each side. Every person's badminton skill can be represented as a positive integer. For each team, define its skill gap as (maximum skill) - (minimum skill). People of similar skill should play together to have fun, so the smaller the skill gap, the more fun the game is. Apart from the skill gap, not playing badminton at all is the least fun, so as many teams as possible must be formed.

Since there are many people right now, several teams must be formed, and the sum of the skill gaps of all teams must be minimized. However, the number of participants may not be a multiple of 4, so some people may not get to play.

Write a program that, when forming teams so that the sum of the skill gaps is minimized, finds the minimum value of that sum and determines who does not get to play badminton.

The first line gives the number of participants $N$. ($4 \leq N \leq 10^5$)

The second line gives $N$ integers $m_0,m_1,\ldots ,m_{N-1}$ representing the badminton skills, separated by spaces. ($1\leq m_i \leq 10^9$)

Skills are given in order of person number, so the skill of person $i$ is $m_i$, and numbering starts at 0.

On the first line, print the minimum value of the sum of the skill gaps.

From the second line, print the numbers of the people who do not get to play badminton, one per line. If there are several valid cases, print any one of them.