A7794 | Looking for Order

Girl Lena likes it when everything is in order, and looks for order everywhere. Once she was getting ready for the University and noticed that the room was in a mess — all the objects from her handbag were thrown about the room. Of course, she wanted to put them back into her handbag. The problem is that the girl cannot carry more than two objects at a time, and cannot move the handbag. Also, if he has taken an object, she cannot put it anywhere except her handbag — her inherent sense of order does not let her do so.

You are given the coordinates of the handbag and the coordinates of the objects in some Сartesian coordinate system. It is known that the girl covers the distance between any two objects in the time equal to the squared length of the segment between the points of the objects. It is also known that initially the coordinates of the girl and the handbag are the same. You are asked to find such an order of actions, that the girl can put all the objects back into her handbag in a minimum time period.

井然有序

Lena喜欢一切井然有序的东西。有一天当她收拾好东西前往自己心仪的大学的时候，她发现宿舍非常的乱 - 她手提包中的东西全都散在了地上。当然，Lena想要把所有东西重新放回自己的手提包中。

一个显而易见的问题是Lena没有办法同时在同一时间内拿超过两个物品（一只手一个），而且她也没有办法移动自己的手提包。同时，如果她拿走了某一个物品，她只能将这个物品放回自己的手提包中。

你将会接受手提包和所有零散物品的坐标（参考笛卡尔平面直角坐标系）。Lena一开始的坐标与手提包的坐标相同。如果Lena从一个点到另一个点所花费的时间为这两个点的直线距离的平方。

你的任务是找到一条最佳的路线，使得Lena将左右物品摆放回手提包的时间最短。

感谢[Macw](https://www.acgo.cn/person/929871)提供翻译

The first line of the input file contains the handbag's coordinates $x_{s},y_{s}$ . The second line contains number $n$ ( $1<=n<=24$ ) — the amount of objects the girl has. The following $n$ lines contain the objects' coordinates. All the coordinates do not exceed 100 in absolute value. All the given positions are different. All the numbers are integer.

输入包含多行。
第一行输入两个整数$x,y$，表示手提包和Lena一开始的坐标。
第二行输入一个整数$n$，$1 \le n \le 24$，表示有$n$个零散的物品需要Lena捡起来并放回手提包中。
接下来的$n$行每一行输入一个物品的坐标。

所有输入的坐标的绝对值都不会超过100。同时没有两个物品的坐标是相同的。输入的坐标有且仅有整数。

In the first line output the only number — the minimum time the girl needs to put the objects into her handbag.

In the second line output the possible optimum way for Lena. Each object in the input is described by its index number (from 1 to $n$ ), the handbag's point is described by number 0. The path should start and end in the handbag's point. If there are several optimal paths, print any of them.

输出包含两行。
第一行有且仅有一个整数，表示Lena将所有物品摆放回手提包的最短用时。
接下来的一行有多个整数，表示最优解的路线。其中，用0表示手提包的位置，用索引来描述每一个物品（索引从1开始）。