CF277E.Binary Tree on Plane

A root tree is a directed acyclic graph that contains one node (root), from which there is exactly one path to any other node.

A root tree is binary if each node has at most two outgoing arcs.

When a binary tree is painted on the plane, all arcs should be directed from top to bottom. That is, each arc going from u to v must meet the condition y__u > y__v.

You've been given the coordinates of all tree nodes. Your task is to connect these nodes by arcs so as to get the binary root tree and make the total length of the arcs minimum. All arcs of the built tree must be directed from top to bottom.

根树是一种有向无环图，其中存在一个节点（称为根节点），从该节点出发到任意其他节点都恰好存在一条路径。

若一棵根树的每个节点至多有两个向外的有向边，则称其为二叉根树。

当将一棵二叉树绘制在平面上时，所有有向边必须自上而下指向。即，对任意一条从节点 $u$ 指向节点 $v$ 的有向边，必须满足 $y_u > y_v$。

你已获得树中所有节点的坐标。你的任务是用有向边连接这些节点，构造一棵二叉根树，并使所有有向边的总长度最小。所构造树中的所有有向边均须满足自上而下的方向要求。

The first line contains a single integer n (2 ≤ n ≤ 400) — the number of nodes in the tree. Then follow n lines, two integers per line: x__i, y__i (|x__i|, |y__i| ≤ 103) — coordinates of the nodes. It is guaranteed that all points are distinct.

第一行包含一个整数 $n$（$2 \leq n \leq 400$）——树中节点的数量。接下来是 $n$ 行，每行两个整数：$x_i,\,y_i$（$|x_i|,\,|y_i| \leq 10^3$）——各节点的坐标。保证所有点互不相同。

If it is impossible to build a binary root tree on the given points, print "-1". Otherwise, print a single real number — the total length of the arcs in the minimum binary tree. The answer will be considered correct if the absolute or relative error doesn't exceed 10 - 6.

如果无法在给定的点上构建二叉根树，则输出 -1。否则，输出一个实数——最小二叉树中所有弧的总长度。若答案的绝对误差或相对误差不超过 $10^{-6}$，则视为正确。